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The diagram at the left shows solution paths that result from using a concept-based approach to problem solving. There may be several possible concepts which respond to the question asked. These lead to different paths through solution space and draw on different concepts in knowledge space. A solution path consists of continuous, logically connected steps.
Details of a particular solution path for a problem are illustrated below.
The fundamental element of a problem solution is the REQUEST-RESPONSE-RESULT structure shown above. This is the familiar hierarchical arrangement commonly used in organizing information. Note that the solution presented above shows exactly what was actually done.
The expression to be evaluated is shown.
The values to be substituted are obtained.
These are substituted.
The result is calculated.
The typical textbook solution presentation omits step 1 above. The thing to be done
is not included in the presentation. Thus the reason for obtaining the values chosen in step 2 is not known to the reader. The solution to a textbook problem is only partly shown on the printed page. Much of the conceptual development which the writer did is not shared with the reader.
Answer book solutions tend to focus on steps 3 and 4. Concepts are rarely shown as a basis for problem solutions in textbooks and answer books.
Solutions to more complex problems involve the recursive use of the REQUEST-RESPONSE-RESULT structure.
An example is shown below and on other pages of this web.
The starting equation is the answer to the question Where to Start? This equation then tells one What to do Next.
This process is applied recursively by reading equations left-to-right, responding to requests made by the equations. This hierarchical use of REQUEST-RESPONSE-RESULT leads to the solution of the problem.
Using different solution paths and making different decisions at branches along the
path leads to a variety of solution structures for a given problem. In this way one can explore a problem. It provides a way of finding the most elegant solution. This is the solution we show to others! By exploring a problem, one comes to understand the problem and the concepts and tools used to solve the problem.
Each step of a problem requires a verbal statement of the reason for the step. The more challenging a problem is, the greater is the need for the verbal statement. Verbal statements form probes to locate information in one's knowledge space. Verbal statements inform others and one's "self" of the reasoning involved in solving a problem.
Mathematically, the solution consists of an organized, self-driven approach to solving simultaneous equations. Typical word problems consist of several conditions which must be satisfied simultaneously. For this reason problems in all subjects across the curriculum are solved in the same way. The words change, the symbols change, the ideas change but the problem solving process remains the same.
The diagrams above illustrate an essential feature of a problem solution. This is the indentation of subproblems. The provides a logical structure to the solution. The indentation process is used in a large number of areas for effective communication. Outlines,
indexes, tables of contents, bulleted charts, and computer programming are a few example. Indentation serves to break a problem into smaller parts in coherent manner.
There has been a massive amount of research, mainly by the interview method, showing that students use the spaghetti approach to organizing a problem solution. This is a natural consequence of the emphasis on the spaghetti approach in early training in arithmetic and algebra. |
The Advanced Algebra Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers quadratic functions in algebra, including what a quadratic function is and why they are important in algebra. Grades 9-College. 25 minutes on DVD. |
the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject.
A comprehensive and authoritative text that treats some of the main topics of modern analysis
A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables
Key results in each area discussed in relation to other areas of mathematics
Highlights the organic unity of large areas of analysis traditionally split into subfields |
Glendale Heights CalculusThe math sections measure a student?s ability to reason quantitatively, solve mathematical problems, and interpret data presented in graphical form. These sections focus on four areas of mathematics that are typically covered in the first three years of American high school education: Arithmetic... |
Algebra
This clear, accessible treatment of beginning algebra features an enhanced problem-solving strategy. This enhanced problem-solving strategy is ...Show synopsisThis clear, accessible treatment of beginning algebra features an enhanced problem-solving strategy. This enhanced problem-solving strategy is highlighted by A Mathematics Blueprint for Problem Solving that helps determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Also includes Step-by-Step Procedure, realistic Applications, and Cooperative Learning Activities in "Putting Your Skills to Work" Applications.Hide synopsis
Description:Good. Minimal shelf wear, 8th edition Item may show signs of...Good. Minimal shelf wear, 8th editionNew. BRAND NEW INSTRUCTORS EDITION! ! ! SAME AS THE STUDENT...New. BRAND NEW INSTRUCTORS EDITION! ! ! SAME AS THE STUDENT EDITION, BUT MAY CONTAIN ADDITIONAL TEACHING NOTES & ADDITIONAL/ALL ANSWERS IN THE MARGINS! ! ! THIS IS THE TEXT ONLY; NO CD's, DVD's, ACCESS CODES, OR ANY OTHER SUPPLEMENTS! ! !17695271769527.
Reviews of Beginning Algebra
I saved almost a hundred dollars by renting this book, and it was awesome. Everything from the shipping, to sending it back was super easy, and I recommend students to take advantage of this site |
Find a Manhattan, IL CalculusThe topics covered were logic, proofs, mathematical induction, sets, relations, graph theory etc. I apply this knowledge almost daily when I program in excel. Whenever you make a decision based based on two things happening you apply "and" logic. |
Algebra Geometry Formulae is an ideal free app for all students above 12th grade, college graduates, engineering graduates and students preparing for various exams. We have compiled all the algebra, geometry and statistics related formulas to cover all the Math's formulas. The maths topics covered in this free app are: ALGEBRA *Basic Properties and Facts *Factoring and Solving Formulas *Factoring and solving Methods (completing the squares methods etc...) *Functions and Graphs *Common Algebraic Errorsapp opens at half screen my only problem is, when i open the app, it stays at the half left corner of my galaxy note screen. really difficult to read. can u pls fix this? i really want to see the content on the entire screen. thanks.
SimilarGeometry Pad is a dynamic geometry application for Android tablets with universal appeal. Teachers can use it in a geometry class for better students engagement and deeper understanding of geometric concepts. Students would benefit from using Geometry Pad while working on geometry assignments at home as well. Easily create complex geometric sketches, measure everything you have in your document, experiment with shapes and transformations.
Use following tools to sketch your geometry constructions (*): - Move and scale. Scroll the workbook by your finger. Pinch and zoom the content of your workbook. Move and modify geometric shapes. - Compass to create arcs. - Point. Plot a point on the workbook. Customize point name and color. - Line. Create a line. Customize line style, color and start/end points. Calculate line length (distance between points). - Midpoint for lines. Show/hide midpoint for lines and polygon sides. Snap to midpoints. - Parallel, perpendicular and tangent lines. The lines can be created as easily as regular lines. Just create and move the line until it automatically snaps to parallel, perpendicular or tangent. - Angle. Create an angle with up to 1 degree precision. Customize angle line style and color. - Triangle. Create a triangle of one of the predefined types: regular, right triangle, isosceles, equilateral. Customize sides style and color. Calculate triangle perimeter and area. Calculate inner angles of the triangle and length of its sides. - Triangle lines. Create altitude, bisector and median lines in a triangle. Calculate length of triangle lines. Customize lines style and color. - Quadrilateral. Create a quadrilateral of one of the predefined types: regular, square, rectangle, parallelogram, rhombus. Customize sides style and color. Calculate quadrilateral perimeter and area. Calculate inner angles of the quadrilateral and length of its sides. - Circle. Create a circle. Calculate circle perimeter and area. Easily create circles inscribed into a triangle by placing circle's center close enough to the incenter of a triangle. - Circle radius and chord. Create radius and chord lines for a circle. Customize lines style and color. Calculate the length of the lines. - Polygons and regular polygons. - Arcs and circular sectors. - Ellipses. - Text annotations. Create floating and pinned single and multiple lines text annotations. Customize text/background color and transparency. - Measurements tool. Measure shape properties in single touch. Measure intersection points (line & line, line & circle). Use multitouch to measure distance between points and angle between lines. - Transformation tools: rotation, reflection, enlargement and translation. - Manual input of coordinates, lengths and angles. Use manual input to precisely locate points, setup custom length for a line or a polygon side, and change angle value. - Built-in calculator: basic arithmetic functions, square root, sin, cos, tan.
Manage multiple documents with your geometric sketches at the same time using Save and Load features. In addition, you can share documents through e-mail or Dropbox.
Some of the tasks you can solve with Geometry Pad: - Create geometric shapes and measure all its possible metrics like length, angle, area, perimeter, intersections, distance between points, angles between lines. - Move/resize geometric shapes and watch how its metrics are changing in real time. - Demonstrate circle theorems by creating and changing inscribed and center angles. - Demonstrate theorems about incircles and excircles locations. - Create and annotate complex geometric figures. Share them through export to image and e-mail features.
* Geometry Pad is a commercial product and some of its features are unavailable in the free version. A paid in-app unlock is required to get access to the premium features (Premium Features Pack).
Learn the Basics of Sacred Geometry The Flower of life The Tree of Life The Vesica Picsis The Platonic Solids The Golden Mean
The strongest science we have that proves creation as the method of our existence and a continuing method we should use while we are in existence ourselves.
One of the few concepts in the world that uses left and right brain thinking.
It's time to unlock the creative genius within yourself.
Study this subject and you will begin to see a whole new world around you that you never new existed.
Learn what George Washington and the Freemasons knew and still know today.
There are so many ancient secrets that are being discovered today through the common knowledge of Sacred Geometry.
The Flower of life has been discovered in every major country around the world through their ancient text and in every one of them it is known as the flower of life.
True understanding of the concept of creation. . Learn Sacred Geometry through this collection of data.
Soon everyone will understand Sacred Geometry
•
Need more than free videos to learn math? YourTeacher's GeometryThank you for the program. It has shown immediate results. My sophomore daughter is failing geometry because she doesn't understand it. In three hours of using YourTeacher, she completed an entire packet of assignments, 4 days worth, and as the student in the class with the worst grade and most amount of incomplete assignments, she was the first to turn in all the work! And she no longer feels like a failure. That is absolutely amazing!" Bryan
perimeter and area of a square Area of an equilateral triangle area of a regular polygon with n sides
Square area Area of a rectangle Finding the side of a square surface Trapezoid area Parallelogram area Dalton area Scope Square Scope of the rectangle Square volume Triangle Area Scope of the triangle
Regular Shapes
the radius of the circle Perimeter of a circle, Perimeter of a square radius larger & smaller
Need more than free videos to learn math? YourTeacher's AlMy daughter is doing Algebra 1 in 8th Grade. She had been getting really low grades because they are moving through the material so quickly. She had a test 3 days after we bought your program and she got 94% (the highest score in the class) because we had her work through the modules over and. She really enjoys the program and her motivation is good again." Melanie
CHAPTER 4: INEQUALITIES, ABSOLUTE VALUE, FUNCTIONS, GRAPHING Solving and Graphing Inequalities Combined Inequalities The Coordinate System Domain and Range Definition of a Function Function and Arrow Notation Graphing within a Given Domain Graphing Lines The Intercept Method Graphing Inequalities in Two Variables
CHAPTER 5: LINEAR EQUATIONS Patterns and Table Building Word Problems and Table Building Slope as a Rate of Change Using the Graph of a Line to Find Slope Using Slope to Graph a Line Using Coordinates to Find Slope (Graphs and Tables) Using Coordinates to Find Slope Using Slope to Find Missing Coordinates Using Slope-Intercept Form to Graph a Line Converting to Slope-Intercept Form and Graphing Linear Parent Graph and Transformations Using Graphs and Slope-Intercept Form Using Tables and Slope-Intercept Form Direct Variation Applications of Direct Variation and Linear Functions
Get all the Geometry formulas and concepts on your phone. This app is particularly designed to help students to check out the geometry formulas and concepts, just in few taps. The app is particularly designed to consume the least memory and processing capability.
Attention All Passengers! Board the plane and begin your quest! With Geometry Quest you travel the world solving geometry problems that increase in difficulty with each city. Be careful not to lose all of your passports or you will have to revisit the city to gain more knowledge. Your worldly adventure will cover geometry concepts such as categorization of shapes, area, perimeter, lines, types of angles, angle measurement, volume, circumference, coordinates, symmetry and the Pythagorean Theorem. Over 190 problems from simple geometry vocabulary to middle-school level concepts. Please help support more advanced math games for kids by purchasing this app. Bugaboo Math Games wishes you a safe and educational journey!
• Animated character gives hints on solving problems • Passport stamps awarded for perfect quests • Successfully solving a city unlocks the next city on the map • Covers Common Core Standards: 3MD, 3G, 4MD, 4G, 5MD, 5G, 6G, 7G, 8G • No ads • No in-app purchases or links to the web
Having difficulty with geometry? This is the app for you! Simply enter in the known variables and it will calculate any single unknown variable. It calculates more than any other app on the market. With the most powerful calculation engine, it can calculate ANY missing value in the formulas. This is the only geometry calculator you will need. This geometry calculator will solve your problems accurately.
Currently it calculates many geometry related formulas and a few miscellaneous formulas. More formulas have been added!DragonBox Algebra 12+ is a must-have tool for students so they can earn better grades and gain confidence in algebra and mathematics. It is based on the award winning game DragonBox Algebra 5+ but covers more advanced topics in mathematics and algebra:
DragonBox Algebra 12+ gives players a greater understanding of what mathematics is all about: objects and the relationships between objects.
This educational game targets children from the ages of 12 to 17 but children (or adults) of all ages can enjoy it. Playing doesn't require supervision, although parents can enjoy playing along with their children and maybe even freshen up their own math skills.
DragonBox Algebra 12+ introduces all these elements in a playful and colorful world appealing to all ages.
The player learns at his/her own pace by experimenting with rules that are introduced gradually. Progress is illustrated with the birth and growth of a dragon for each new chapter.
Dr. Patrick Marchal, Ph.D. in cognitive science, and Jean-Baptiste Huynh, a high school teacher, created DragonBox Algebra 12+ as an intuitive, interative and efficient way to learn algebra.
DragonBox Algebra 12+ is based on a novel pedagogical method developed in Norway that focuses on discovery and experimentation. Players receive instant feedback which differs from the traditional classroom setting where students can wait weeks for feedback. DragonBox Algebra 12+ creates an environment for kids where they can learn, enjoy and appreciate math.
Our previous educational game, DragonBox Algebra 5+ has received many distinctions including the Gold Medal of the 2012 Serious Play Award (USA), the Best Serious game at Bilbao´s Fun and Serious Game Festival and the Best Serious Game at the 2013 International Mobile Gaming Awards. It is also recommended by Common Sense Media where it won the Learn ON award.
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GK Quiz 2014 is an interesting quiz game with a huge question bank from the topics science, fiction, trivia, history, geography, Current Affairs, Sports, Cinema, Politics, Awards, Corporate, economy, environment etc. It is a timer based game with a database of more than 1000 multiple choice questions.
Disclaimer : Please note that we are not related to KBC or who wants to be a millionaireKids Learning Games is a totally FREE app for 2 - 6 year old kids, keeping them entertained. This app contains kids learning games activities which teaches in school - ALPHABETS, NUMBERS, COLORS, SHAPES, FRUITS, VEGETABLES, ANIMALS, BIRDS. It helps the kids to learn each section with images. The app makes learning easy and interesting.
App Features: - It teaches Alphabets (uppercase and lowercase) from A to Z with images. Images has objects starting with each letter. - It teaches sequential order of Numbers from 1- 10. Images in this section is with counting objects. - It teaches all basic and more colors with pictures. - It teaches different SHAPES. - It teaches many type of FRUITS & VEGETABLES with pictures - It teaches ANIMALS & BIRDS with cute cartoon picturesThis is ideal for all students preparing for GRE exam,SAT entrance,IELTS exam.This app will help you to build vocabulary as well Antonym and Synonym in preparation for the different exams.Also ideal for students preparing for CET exam,ASVAB & GMAT exam.There are 4 options also available with scores.It has a database of 1200 + questions and is good for USA and UK students preparing for entrance exams.
Put your baby's favourite lullaby from 'Lullabies for baby' and your baby will sleep like an angel. This app has good quality songs which will make a crying baby to listen and smile. It contains the most popular lullabies like Twinkle twinkle, Hush little baby etc. You can choose the loop mode which will play your favorite lullaby repeatedly. This app also contains volume control facility.
Maybe you think you're a physicist just like Keanu Reeves in the movie Chain Reaction. Whether you are more of a mechanical engineer who cares about simple machines trivia or a nuclear physicist who can name the six flavors of quarks in our quarks quiz, there will be a physics quiz for you! Perhaps you're a student in physics who needs practice with S.I. Units game, crazy formulas, or learning the parts of the electromagnetic spectrum quiz. Or perhaps you can identify famous physicists by appearance or remember their first names based on units? No matter the trivia, this will help you.
This Physics Quiz game is a great resource for learning about the science of physics. The multiple-choice trivia format is a learning tool for high school students, educators, and anyone interested in learning more about physics.
Convert world currency with this Currency Converter App. Easily convert between currencies. Use currency graphs over time (1 day - 1 year) and get the latest news on each currency.Track Currencies from around the world. This easy-to-use currency calculator.
App Features: - You can see the rate - high & rate-lows for multiple time frames.( from 1 day to 1 year) - Calculate prices with the currency converter - Search function to quickly add a new currency - All currencies with country flags. - Realtime values - Downloaded by 10000+ people
Football Quiz game is a free quiz with more than 5000 questions and multiple choice answers.
Best Football Quiz Game if you are a lover of Manchester United, Manchester City, Arsenal, Liverpool, Everton, Chelsea, Tottenham, Newcastle United etc. No Football trivia game is as up to date as this App.
Disclaimer This app is only for recreational purposes does not intend to harm anyone, and no brand associated with it. No Copyright. All other trademarks and trade names are the property of their respective owners. |
Item #: 032593 ISBN: 9780471225546
Retail: $15.95 Rainbow Price: $7.18
Just who is Dr. Math? Actually, Dr. Math is not any one person. The title applies to any of the hundreds of "Math Doctors" who volunteer their math expertise to help answer questions posted by students on the Math Forum website ( I stumbled across this website years ago when I was taking math education courses, and I still highly recommend it to anyone who has any question, be it a specific problem or an abstract concept, about math. In response to posted questions, Math Doctors are trained to give hints and thorough explanations, not solutions. This particular book is a topically organized compilation of the "best of" the Math Doctor responses to real Pre-Algebra questions posted by actual students. So if you're having trouble grasping the jump between concrete and abstract math, don't worry. You are not alone. Without other students asking questions just like the ones you probably have, this book would not exist. ~ Anh
Resulting from his work with dyslexics, Ron Davis (author of The Gift of Dyslexia) has developed effective techniques to address other learning difficulties often associated with dyslexia - ADD, dyscalculia (trouble with math) and dysgraphia (trouble with handwriting). Coming to an introductory understanding of the learning theory behind these techniques has literally reoriented my thinking on the subject - and reorientation is what his methodologies are all about. It all has to do with whether we utilize verbal conceptualization (thinking with the sounds of symbols and words) or nonverbal conceptualization (thinking with visual images). Dyslexics are primarily picture thinkers; but this method of thinking is subliminal - faster than the person can be aware of - and therefore most dyslexics are not aware of what their minds are doing. When an individual becomes disoriented (such as happens when you look at an optical illusion), perception becomes distorted. Many picture thinkers learn to use disorientation very early in life and it seems to work - until the child starts school, that is, and tries to learn the symbols of language. A picture thinking child will encounter so many sources of confusion in a single sentence that disorientations spontaneously occur, one after another. If the main problem is with reading, the child is labeled dyslexic. If the disorientation causes his sense of time to distort and his attention to jump around, he has ADD. If it affects math, he has dyscalculia. If it causes bad handwriting, he has dysgraphia. By showing a dyslexic how to turn off the disorientations at the moment they occur, and then helping him find and master the symbolic information that triggered the disorientation (and the majority of this book is detailed instruction in how to do this), the reading, math, writing, and spelling problems begin to disappear. Janice
Item #: 031286 ISBN: 9781580894210
Retail: $7.95 Rainbow Price: $5.95
(description by publisher - stay tuned for our own!) Hop, skip, and jump through a school day. In this follow-up to Teddy Bear Counting and Teddy Bear Math, kids will be jumping, wriggling, and spinning as they practice their math skills. In Simon Says-like fashion children are asked to moo like cows, fly like planes and pat their heads while they count, add, sort, and subtract. The hands-on interaction makes math exciting for young learners and teachers will find this book perfect for use with bear counters or other classroom manipulatives. Studies show that movement stimulates the brain and helps kids focus. With its bright, colorful illustrations and simple sing-song rhymes, this book will have little ones eager to go back to the beginning and do more math! This book is good for your brain because it provides: Math skills, rhythm and rhyme
Each one of these 50 unique mazes depends on simple math skills to navigate successfully through. Early mazes involve following patterns, matching objects to number numerals, or simple counting and the book progresses in difficulty until ending mazes require simple addition and subtraction, skip counting, and picking up a certain number of objects along the way. Each colorful maze has a different engaging story such as helping a blackbird pick bunches of cherries, guiding Collie the sheepdog through the pasture to say hello to exactly five sheep on her way, or jumping Bobby bug on toadstools with only odd numbers. - Steph
This book has some overlapping content with E-Z Arithmetic. Theres a short review of the four basic operations in chapter one, but then it jumps right into fractions, decimals, percents, beginning algebra, factoring, equations, geometry, tables and graphs, word problems, and probability and statistics. Explanations of concepts and terminology are clear and to the point. Algebraic processes, such as graphing a linear equation or solving a quadratic equation, are systematically broken down and presented as step-by-step procedures. Steps in worked examples are correspondingly numbered for clarity. Each chapter includes a pretest, a posttest, and numerous practice sets. The answer key also provides solutions for more difficult practice problems. 230 pgs. ~ Anh
Item #: 032483 ISBN: 9781603575003
Retail: $8.95 Rainbow Price: $6.95
(description by publisher - stay tuned for our own!) Ahoy maties! Jump aboard our ship as we learn about the tale of Blackbeard the pirate. Are you scared of pirates? Blackbeard was a pirate with lots of treasures. He hid his treasures so well some of them still havent been found. Embark on a scavenger hunt and you may just find some. In this book youll not only learn about pirates, but youll also learn how to use distance to decide how far apart pirate ships are and how far you are from the treasure. Concepts include metric and customary units of length, unit conversion, and how to compare distances.
This one might be too pretty to be a math game! The smooth colorful tiles, the chunky die, the cone-shaped pouch it all adds up to a game that begs to jump off the shelf and be played. In the game, 2-5 players all use their tiles to add onto a central number crossword made up of tiles. At the beginning of the game, the die is rolled to find the key number. This will be 3, 4 or 5. Players will each draw eight tiles to start, and the first player uses as many of their tiles as possible to build a row that not only adds up to a multiple of the key number, but doesnt repeat any color of tile. So if the key number is 5 you could lay down a green 1, an orange 9, a purple 3 and a red 7. The total of the tiles is 20, which is a multiple of five, and no color is used more than once. The next player then uses as many of their tiles as possible, while adding onto the first players row. You can also add more tiles to an existing row, as long as you dont break the color or number rule. The game ends when all tiles have been used that can be used, and the player with the most points wins. Variations for other versions are also included its almost like a hands-on, open-ended critical thinking program! The center activity, where the lentil workstation would be set up somewhere in the classroom, and students would take turns playing with it. Because of this, the student portion of the activity book is formatted as activity cards, pour, search, compare, design, measure, divide, and calibrate.ll lay out a city in a grid pattern, and add street names, landscape props, |
More About
This Textbook
Overview
In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof on finding an unknown can be of help in attacking any problem that can be "reasoned" out - from building a bridge to winning a game of anagrams.
Editorial Reviews
Mathematical Monthly— E. T. Bell
Mathematical Review— Herman Weyl
Scientific Monthly
I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it.
American Journal of Psychology
Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.
— A. C. Schaeffer
Mathematics Magazine
Every mathematics student should experience and live this book
Mathematical Monthly
- E.TMathematical Review
- Herman Weyl
American Journal of Psychology
- A.C. Schaeffer
Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.
Mathematical Monthly
- E. TAmerican Journal of Psychology
- A. C. Schaeffer
Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.
From the Publisher
" "—E. T. Bell, Mathematical Monthly
"[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."—Herman Weyl, Mathematical Review
"I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."— Scientific Monthly
"Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art."—A. C. Schaeffer, American Journal of Psychology
"Every mathematics student should experience and live this book"— Mathematics |
Initial student placement in developmental
courses is based on individual college placement testing policies and
procedures. Students should begin developmental course work at the appropriate
level indicated by the college's placement test.
MAT 050Basic
Math Skills
This course is designed to
strengthen basic math skills. Topics include properties, rounding, estimating,
comparing, converting, and computing whole numbers, fractions, and decimals.
Upon completion, students should be able to perform basic computations
and solve relevant mathematical problems. A discussion of ratios, rates, proportions, and applications of these topics will be included.
This course is a comprehensive
study of mathematical skills which should provide a strong mathematical
foundation to pursue further study. Topics include principles and applications
of decimals, fractions, percents, ratio and proportion, order of operations,
geometry, measurement, and elements of algebra and statistics. Upon
completion, students should be able to perform basic computations and
solve relevant, multi-step mathematical problems using technology where
appropriate.
This course establishes a
foundation in algebraic concepts and problem solving. Topics include
signed numbers, exponents, order of operations, simplifying expressions,
solving linear equations and inequalities, graphing, formulas, polynomials,
factoring, and elements of geometry. Upon completion, students should
be able to apply the concepts learned in problem solving using appropriate
technology. Solving quadratic equations by factoring is also included.
This course continues the
study of algebraic concepts with emphasis on applications. Topics include
factoring; rational expressions; rational exponents; rational, radical,
and quadratic equations; systems of equations; inequalities; graphing;
functions; variations; complex numbers; and elements of geometry. Upon
completion, students should be able to apply the concepts learned in
problem solving using appropriate technology.
This course covers algebraic
concepts with emphasis on applications. Topics include those covered
in MAT 070 and MAT 080. Upon completion, students should be able to
to apply algebraic concepts in problem solving using appropriate technology.
Course Hours Per Week: Class,
3; Lab, 2
Semester Hours Credit: 4
Prerequisite: MAT
060 or satisfactory score on placement test and permission from
the instructor or math discipline chair.
This course provides an activity-based
approach to utilizing, interpreting, and communicating data in a variety
of measurement systems. Topics include accuracy, precision, conversion,
and estimation within metric, apothecary, and avoirdupois systems; ratio
and proportion; measures of central tendency and dispersion; and charting
of data. Upon completion, students should be able to apply proper techniques
to gathering, recording, manipulating, analyzing, and communicating
data
This course develops the ability
to utilize mathematical skills and technology to solve problems at a
level found in non-mathematics-intensive programs. Topics include applications
to percent, ratio and proportion, formulas, statistics, functional notation,
linear functions and their graphs, probability, sampling techniques,
scatter plots, and modeling. Upon completion, students should be able
to solve practical problems; reason and communicate with mathematics;
and work confidently, collaboratively, and independently. Applications
may be drawn from the fields of business, public services, and various
technologies.
This course provides an integrated
approach to technology and the skills required to manipulate, display,
and interpret mathematical functions and formulas used in problem solving.
Topics include simplification, evaluation, and solving of algebraic
and radical functions; complex numbers; right triangle trigonometry;
systems of equations; and the use of technology. Upon completion, students
should be able to demonstrate an understanding of the use of mathematics
and technology to solve problems as well as analyze and communicate
results. A basic introduction to statistics is also included.
This course extends the concepts
covered in MAT 121 to include additional topics
in algebra, function analysis, and trigonometry. Topics include exponential
and logarithmic functions, translation and scaling of functions, Sine
Law, Cosine Law, vectors, and statistics. Upon completion, students
should be able to demonstrate an understanding of the use of technology
to solve problems and to analyze and communicate results.
This course provides an introduction
in a non-technical setting to selected topics in mathematics. Topics
include, but are not limited to, sets, logic, probability, statistics,
matrices, mathematical systems, geometry, topology, mathematics of finance,
and modeling. Upon completion, students should be able to understand
a variety of mathematical applications, think logically, and be able
to work collaboratively and independently. This course has been approved
to satisfy the Comprehensive Articulation Agreement for the general
education core requirement in natural sciences/mathematics.
This course is a laboratory
for MAT 140. Emphasis is on experiences that enhance
the materials presented in the class. Upon completion, students should
be able to solve problems, apply critical thinking, work in teams, and
communicate effectively. This course has been approved to satisfy the
Comprehensive Articulation Agreement for transferability as a pre-major
and/or elective course requirement.
This course provides a project-based
approach to the study of basic probability, descriptive and inferential
statistics, and decision making. Emphasis is on measures of central
tendency and dispersion, correlation, regression, discrete and continuous
probability distributions, quality control, population parameter estimation,
and hypothesis testing. Upon completion, students should be able to
describe important characteristics of a set of data and draw inferences
about a population from sample data. Students are able to compare two
population means of both large and small groups as well as compare population
proportions. This course has been approved to satisfy the Comprehensive
Articulation Agreement for the general education core requirement in
natural sciences/mathematics. Students may not receive credit for both
MAT 151 and MAT 155.
This
course provides an integrated technological approach to algebraic topics
used in problem solving. Emphasis is on applications involving equations
and inequalities; polynomial, rational, exponential, and logarithmic
functions; and graphing and data analysis/modeling. Upon completion,
students should be able to choose an appropriate model to fit a data
set and use the model for analysis and prediction. This course is designed
to satisfy the needs of the Associate in Arts student and does not satisfy
the prerequisite for MAT 172. This course has been approved to satisfy
the Comprehensive Articulation Agreement for the general education core
requirement in natural sciences/mathematics for the Associate in Arts
Degree.
This
course is a laboratory for MAT 161is the first of two courses designed to emphasize topics which are fundamental
to the study of calculus. Emphasis is on equations and inequalities;
functions (linear, polynomial, and rational); systems of equations and
inequalities; and parametric equations. Upon completion, students should
be able to solve practical problems and use appropriate models for analysis
and predictions. Additional topics include, but are not limited to,
exponential and logarithmic functions and their applications. This course
has been approved to satisfy the Comprehensive Articulation Agreement
for the general education core requirement in natural sciences/mathematics.
This
course is a laboratory for MAT 171 is the second of two
courses designed to emphasize topics which are fundamental to the study
of calculus. Emphasis is on properties and applications of transcendental
functions and their graphs, right and oblique triangle trigonometry,
conic sections, vectors, and polar coordinates. Upon completion, students
should be able to solve practical problems and use appropriate models
for analysis and prediction. This course has been approved to satisfy
the Comprehensive Articulation Agreement for the general education core
requirement in natural sciences/mathematics. MAT 161 does not satisfy
the prerequisite for MAT 172.
This
course is a laboratory for MAT 172. Emphasis is on experiences that
enhance the materials presented in the class. Upon completion, students
should be able to solve problems, apply critical thinking, work in teams,
and communicate effectively. This course has been approved to satisfy
the Comprehensive Articulation Agreement pre-major and/or elective course
requirement.
This course provides an intense study of the topics which are fundamental to the study of calculus. Emphasis is placed on functions and their graphs with special attention to polynomial, rational, exponential, logarithmic and trigonometric functions, and analytic trigonometry. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and prediction. This course has been approved to satisfy the Comprehensive Articulation Agreement general education core requirement in natural sciences/mathematics.
This course is a laboratory for MAT 175. Emphasis is placed on experiences that enhance the materials presented in the class. Upon completion, students should be able to solve problems, apply critical thinking, work in teams, and communicate effectively. This course has been approved to satisfy the Comprehensive Articulation Agreement for transferability as a premajor and/or elective course requirement. Course Hours Per Week:
This
course introduces concepts of differentiation and integration as well
as their applications to solving problems. The course is designed for
students needing one semester of calculus. Topics include functions,
graphing, differentiation, and integration with emphasis on applications
drawn from business, economics, and biological and behavioral sciences.
Upon completion, students should be able to demonstrate an understanding
of the use of basic calculus and technology to solve problems and to
analyze and communicate results. This course has been approved to satisfy
the Comprehensive Articulation Agreement for the general education core
requirement in natural sciences/mathematics.
This
course is a laboratory for MAT 263course covers in depth the differential calculus portion of a three-course
calculus sequence. Topics include limits, continuity, derivatives, and
integrals of algebraic and transcendental functions of one variable,
with applications. Upon completion, students should be able to apply
differentiation and integration techniques to algebraic and transcendental
functions. This course has been approved to satisfy the Comprehensive
Articulation Agreement for the general education core requirement in
natural sciences/mathematics.
This
course provides a rigorous treatment of integration and is the second
calculus course in a three-course sequence. Topics include applications
of definite integrals, techniques of integration, indeterminate forms,
improper integrals, infinite series, conic sections, parametric equations,
polar coordinates, and differential equations. Upon completion, students
should be able to use integration and approximation techniques to solve
application problems. This course has been approved to satisfy the Comprehensive
Articulation Agreement for the general education core requirement in
natural sciences/mathematics.
This
course covers the calculus of several variables and is the third calculus
course in a three-course sequence. Topics include functions of several
variables, partial derivatives, multiple integrals, solid analytical
geometry, vector-valued functions, and line and surface integrals. Upon
completion, students should be able to solve problems involving vectors
and functions of several variables. This course has been approved to
satisfy the Comprehensive Articulation Agreement for the general education
core requirement in natural sciences/mathematics.
This
course provides an introduction to ordinary differential equations with
an emphasis on applications. Topics include first-order, linear higher-order,
and systems of differential equations; numerical methods; series solutions;
eigenvalues and eigenvectors; Laplace transforms; and Fourier series.
Upon completion, students should be able to use differential equations
to model physical phenomena, solve the equations, and use the solutions
to analyze the phenomena. This course is approved to satisfy the Comprehensive
Articulation Agreement for transferability as a pre-major and/or elective
course requirement. |
North Houston PrecalculusRobertThis course introduces the properties and operations of the real number system as well as the use of algebraic expressions, equations, and inequalities. Students learn to construct graphs of linear and quadratic functions and to use graphs to solve problems. Students are given opportuniti... |
Each module was designed to improve students' understanding and desire to continue mathematics, with the goal of increasing enrollment in Calculus. During the discussion phase of elevating the role of history of mathematics, it was decided to move beyond the level of history seen in even the most progressive of textbooks. Each week, a significant essay was written about both the development of mathematics as a tool to improve society, as well as the need for each generation to improve their mathematics skills to ensure the further advancement of society. The modules helped motivate the student on the topic of the week, but also was connected with previous lessons so that each lesson increased understanding of the effort required to be successful in mathematics, and also gave the students a greater appreciation for the need of mathematics in their lives.
The modules tell solid stories at manageable lengths. Students were asked to read two to three pages of mathematics history each week. Every teacher of every section of College Algebra implemented the historical modules beginning in 2005. The first nine history lessons are outlined below.
Introductory Lesson: Introduces the term "algebra" and its Arabic origin. It then briefly gives a timeline of the movement through Europe, including the addition of the Cartesian coordinate system, the introduction of the function nomenclature by Leibniz, and the popularization by Euler of the symbolic notation \(f(x)\) for a function (The Function Concept, 2007). The goal was to introduce both the longevity of the subject and the amount of effort required to invent the subject as it is known today.
Quadratics and Parabolas: Looks at the development of quadratic equations (as an application of finding areas for quadrilaterals) and parabolas. The goal is to further extend the notion of the fluidity of mathematics and the time span required to develop today's mathematics. Also, this module introduces the need for vocabulary and the process in which vocabulary was developed.
D. Goodwin (Black Hills State University) and G. W. Hagerty (Black Hills State University) and S. Smith (Black Hills State University), "The Unique Effects of Including History in College Algebra - The Modules (1)," Loci (June 2010), DOI:10.4169/loci002530 |
Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well... more...
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries,... more... |
Line
lesson from Illuminations asks students to measure the diameter and circumference of various circular objects, plot the measurements on a graph, and relate the slope of the line to π, the ratio of circumference to diameter. A student activity sheet is included. The material is appropriate for grades 9-12 and should require 1 class period to complete.Wed, 19 Jan 2011 03:00:02 -0600Smokey Bear Takes Algebra
interdisciplinary lesson ties earth science concepts in with algebra. The forest-fire danger rating index is applied to a mathematical model. Students will learn real-world meaning of the intercepts and slope in the Angstrom index as well as how to model the relationship between the slope of the land versus rate of fire spread. The material includes student activity sheets. It is intended for grades 9-12 and should require 3 and a half class periods to complete.Tue, 18 Jan 2011 03:00:01 -0600Growth Rate
lesson from Illuminations uses growth charts for girls and boys to examine rates of change. The material uses slope to approximate the rate of change in height. Students will learn how to translate this data into a graph. The lesson is appropriate for grades 9-12 and should require 1 class period to complete.Fri, 14 Jan 2011 03:00:03 -0600Movie Lines
algebra lesson from Illuminations involves using linear equations and graphs in a real world context. Students will graph a line based on data points, find the equation of the line, identify y-intercept and slope, and extrapolate data. The material is appropriate for grades 9-12 and should require 1 class period to complete.Tue, 11 Jan 2011 03:00:02 -0600Pedal Power
algebra lesson from Illuminations involves slope as a rate of change. Distance-time graphs for three bicyclists climbing a mountain are compared and contrasted. The material will help students understand how to interpret a graph in the context of a real-world situation. Questions for students are also included. This lesson is intended for grades 9-12 and should require 1 class period to complete.Fri, 10 Dec 2010 03:00:02 -0600Ramps and Ratios
this activity students view and analyze images of ramps and steps to see if they conform to the requirements of the Americans with Disabilities Act. Students measure horizontal and vertical distances and compute the percent slope for each image. Image measurements are performed using WebImage, a Web-based, customized version of ImageJ.Mon, 26 Jul 2010 03:00:02 -0500Slope Fields
by David Smith for the Connected Curriculum Project, this module develops a graphical representation for a differential equation that reveals the nature of solutions, even when formulas for those solutions are not available. This is one within a much larger set of learning modules hosted by Duke University.Fri, 4 Jun 2010 03:00:02 -0500Application of the Finite Element Method to Slope Stability
document outlines the capabilities of the finite element method in the analysis of slope stability problems. A description of the constitutive laws of material behavior such as the Mohr-Coulomb failure criterion, and material properties input parameters, required to adequately model slope failure is given as well.Tue, 23 Sep 2008 20:51:53 -0500Dave's Short Trig Course
introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations. Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and slope, the trigonometry of right triangles, the trigonometric functions and their inverses, oblique triangles, and a summary of trigonometric identities.Mon, 22 Sep 2008 03:00:02 -0500SIMULATION OF SLOPE FAILURE USING A MESHED BASEDPARTITION OF UNITY METHOD
mesh based partition of unity method, known as the manifold method, is used in simulating the evolution of a slope failure. The problem configuration consists of a simple slope that has pre-existing tensile cracks along its crest. The slope failure is triggered by rainfall which raises water pressure in the crack. As the tensile stress around the crack tip increases, an existing crack grows and a failure surface is eventually developed. The maximum stress criterion is adopted in determining the crack growth and growth direction. After a failure surface is formed, the unstable soil mass, bounded by the failure surface, slides down the slope. This sliding process is also modeled.Mon, 25 Aug 2008 03:00:07College Algebra Online Tutorials
introduction to this site remarks, "If you need help in college algebra, you have come to the right place." Their statement is accurate, as the staff members at the West Texas A&M University's Virtual Math Lab have done a fine job creating a series of online algebra tutorials for students and anyone else who might be returning to the world of algebra. First-time visitors should look at their online guide to the tutorials to learn how their tutorials are organized. After that, they should feel free to browse through any of the 59 tutorials offered here. Each tutorial contains information about learning objectives, full explanations, and numerous examples of how to correctly solve problems.Mon, 10 Dec 2007 03:00:01 -0600Practical Algebra Lessons
to you by Elizabeth Stapel and purplemath.com, this collection of learning modules contains over 100 mathematics modules designed to teach beginning, intermediate, and advanced algebra concepts. Some algebra topics include graphic linear equations; adding, subtracting, multiplying, and dividing polynomials; and solving linear and literal equations. Intermediate algebra topics include domain and range, even and odd functions, factor theorem, and solving systems of non-linear equations. Finally, advanced algebra topics include complex fractions, complex numbers, matrix addition and subtraction, and partial fraction decomposition. This is a great reference and teaching resource for teachers and students of introductory algebra courses. This is an especially good resource for teachers looking for in-class illustrations of fundamental algebra concepts.Fri, 19 Oct 2007 03:00:01 -0500 |
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This is the 2nd edition with a publication date of 6Precalculus Concepts Through Functions, A Right Triangle Approach to Trigonometry Plus NEW MyMathLab with eText -- Access Card Package
Summary
This package consists of the textbook plus an access kit for MyMathLab/MyStatLab. Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Second Editionembodies Sullivan/Sullivanrs"s hallmarksaccuracy, precision, depth, strong student support, and abundant exerciseswhile exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals:preparingfor class,practicingtheir homework, andreviewingthe concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus. MyMathLabprovides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online. |
Student in preparation MPSI / MP, you can now enjoy the time you waste every day (bus, subway line at the supermarket ...) to prepare your competition instead of playing Angry Birds!
The Mathafix application is the first Android application which offers you simulate your future oral tests of mathematics through small exercises corrected oral type of competition / khôlles random.
These exercises and a selection of books math exercises and other less serious things (. Parodies videos about life in preparatory classes CPGEs, etc.) are also available on the website Mathafix: http:// mathafixweb.appspot.com / (useful, for example, if you have a smartphone or a tablet, but not Android ...).
Note that some of these exercises are very difficult, especially without oral evidence that might give you an examiner (although some reviewers are not very talkative ...). Since every minute counts in your exam preparation, so do not hesitate to take a look at the solution of a year as soon as you dry it.
★ Information about the future of the application
The evolution of Mathafix application will depend largely on you: - Your use of the application / ta rating (good or less good, whatever) / your sharing with friends encourage the regular addition of new exercises (if the application you used to anything, it will be discontinued!)
- Your suggestions for exercises help prioritize adding new exercises (if you do not say you want more exercises integrals, nobody will do it for you!)
- Your feedback on exercises will improve (if you find a solution is not very clear but you do not Tell, there is unlikely to rewrite it alone!)
Mathafix The application requires an Internet connection. One reason is that the exercises are downloaded from the website Mathafix, which allows you to not have to install a new version of the application whenever new exercises are available or old exercises are made day.
The Mathafix application is a completely free tool at your disposal to prepare your contest. However, as you can you imagine, search and seizure exercise time consuming. Therefore shalt thou not vexed to see a banner at the top of the application, headband that you can also completely ignore (although it may be that advertising for a math book interests you :-) struggling with your math homework, or just want an easier way to look up things for your math homework, this app is for you. It is the largest and most complete database of math terms and formulas from Pre-Algebra all the way up to Algebra II. It basically replaces the glossary in the back of your book that you used to spend all that time looking up terms and formulas in! You will improve your grades, and spend less of your time working on homework!
There are pictures for many of the terms and all of them have a definition. There is also a very handy search feature, so you don't have to take the time to search in the back of your math book. It also supports Multi-Window technology for even greater multitasking!
There are a total of 993 definitions you can choose from, not only that but there are 453 pictures available for various definitions!
This app is regularly updated also so you can stay ahead of the game in your math class.
Why this app needs internet and location permissions: I use a debugging and analytics API called flurry (flurry.com). This is the only reason this app requires these permissions. The location data and analytics collected are only viewed by the developer and NO ONE else. Your information is sent to flurry's servers using HTTPS encryption so your information is secure. I use the location data to see which languages I should consider supporting, and also what are the most popular definitions so I can consider which ones to expand and improve. Like I have said, your privacy is the #1 priority. Tags: Math, Algebra, Algebra 2, Pre Algebra, Pre-Algebra, Help, grades sinceMore from developer |
'Over 100 math formulas at high school level. The covered areas include algebra, geometry, calculus, trigonometry,...
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'Over 100 math formulas at high school level. The covered areas include algebra, geometry, calculus, trigonometry, probability and statistics. Most of the formulas come with examples for better understanding. Use the powerful search function to find what you are looking for and mark your favorites for easier access. A convenient tool for students and teachers and a handy reference for anyone interested in math!'This app costs $0.99
We are developing a unique approach that uses affordable handheld IR cameras (under $900) to visualize invisible energy flows...
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We are developing a unique approach that uses affordable handheld IR cameras (under $900) to visualize invisible energy flows and transformations in easy-to-do science experiments. Using this "desktop remote sensing" approach, thermal energy can be readily "seen." Other types of energy that convert into thermal energy can be inferred from thermal signals. Hence, many invisible physical, chemical, and biological processes that absorb or release heat can be visualized, discovered, and investigated.
NOTE: Must create an account in order to download book.A book of free economics notes based on more than thirty years'...
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NOTE: Must create an account in order to download book.A book of free economics notes based on more than thirty years' experience of teaching and supervising students on three continents.The contentsr:Chapter 1 An Introduction to Economics in 5,000 Words and a BitChapter 2 Trying to Make Sense of Economic Policy—Part 1: What Do Governments Try to Do?Chapter 3 Trying to Make Sense of Economic Policy—Part 2: Why is it so Difficult to Get it Right?Chapter 4 Business Cycles, Recessions and Economic BoomsChapter 5 Understanding Economics: a Summary of the Advantages and Disadvantages of the Price MechanismChapter 6 Notes on the Difference Between "Economic Growth" and "Economic Development" |
This is at least partly true. The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems! |
, Hints and Solutions Manual for Part a Problems: A Contemporary Approach
This leading mathematics text for elementary and middle school educators helps you quickly develop a true understanding of mathematical concepts. It ...Show synopsisThis leading mathematics text for elementary and middle school educators helps you quickly develop a true understanding of mathematical concepts. It integrates rich problem-solving strategies with relevant topics and extensive opportunities for hands-on experience. By progressing from the concrete to the pictorial to the abstract, Musser captures the way math is generally taught in elementary schools. This title will give you all the essentials mathematics teachers need for teaching at the elementary and middle school levels: Highlights algebraic concepts throughout the text and includes additional supporting information. Provides enhanced coverage of order of operations, Z-scores, union of two events, Least Common Multiple, and Greatest Common Factor. Focuses on solid mathematical content in an accessible and appealing way. Offers the largest collection of problems (over 3,000!), worked examples, and problem-solving strategies in any text of its kind.Includes a comprehensive, five-chapter treatment of geometry based on the van Hiele model |
algebra
The definition of algebra is a type of math that focuses on demonstrating the properties and relationships of abstract things in symbolic form.
Graphing, absolute value equations and scientific notation are each an example of a topic in algebra.
Examples of algebra on a chalkboard.
algebra
noun
a mathematical system using symbols, esp. letters, to generalize certain arithmetic operations and relationships (Ex.: x + y = x represents a unique relationship between x and y, and has an infinite number of examples, as 3 + 6 = 9)
algebra
noun
A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
A set together with a pair of binary operations defined on the set. Usually, the set and the operations simultaneously form both a ring and a module.
(countable, set theory, analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (thereby also under intersections and differences).
(countable, mathematics) One of several other types of mathematical structure.
(figuratively) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas. |
This text is designed to help teachers work with beginning ESL students in grades 5 to 12. It provides lessons and activities that will develop the students' vocabulary, English usage, and mathematical understanding. A balance of high-interest activit more...
Mathematics scares and depresses most of us, but politicians, journalists and everyone in power use numbers all the time to bamboozle us. Most maths is really simple - as easy as 2+2 in fact. Better still it can be understood without any jargon, any formulas - and in fact not even many numbers. Most of it is commonsense, and by using a few really...Written by an experienced author with a strong background in applications of this field, this monograph provides a comprehensive and detailed account of the theory behind hydromechanics. He includes numerous appendices with mathematical tools, backed by extensive illustrations. The result is a must-have for all those needing to apply the methods in... more...
The main focus of this book is to introduce computational methods for fluid flow and heat transfer to scientists, engineers, educators, and graduate students who are engaged in developing and/or using computer codes. The topics range from basic methods such as a finite difference, finite volume, finite element, large eddy simulation, and direct numerical... more... |
offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the...
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This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the most powerful and influential branch of all Mathematics. Its influence is strongly felt in almost all scientific and artistic disciplines (in Music, in particular) and in Mathematics itself. Group Theory extracts the essential characteristics of diverse situations in which some type of symmetry or transformation appears. Given a non-empty set, a binary operation is defined on it such that certain axioms hold, that is, it possesses a structure (the group structure). The concept of structure, and the concepts related to structure such as isomorphism, play a decisive role in modern Mathematics.The general theory of structures is a powerful tool. Whenever someone proves that his objects of study satisfy the axioms of a certain structure, he immediately obtains all the valid results of the theory for his objects. There is no need to prove each one of the results in particular. Indeed, it can be said that the structures allow the classification of the different branches of Mathematics (or even the different objects in Music (! )).The present text is based on the book in Spanish "Teoría de Grupos: un primer curso" by Emilio Lluis-Puebla, published by the Sociedad Matemática Mexicana This new text contains the material that corresponds to a course on the subject that is offered in the Mathematics Department of the Facultad de Ciencias of the Universidad Nacional Autónoma de México plus optional introductory material for a basic course on Mathematical Music Theory.This text follows the approach of other texts by Emilio Lluis-Puebla on Linear Algebra and Homological Algebra. A modern presentation is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, among other disciplines, is introduced.This work consists of four chapters. Each section contains a series of problems that can be solved with creativity by using the content that is presented there; these problems form a fundamental part of the text. They also are designed with the objective of reinforcing students' mathematical writing. Throughout the first three chapters, representative examples (that are not numbered) of applications of Group Theory to Mathematical Music Theory are included for students who already have some knowledge of Music Theory.In chapter 4, elaborated by Mariana Montiel, the application of Group Theory to Music Theory is presented in detail. Some basic aspects of Mathematical Music Theory are explained and, in the process, some essential elements of both areas are given to readers with different backgrounds. For this reason, the examples follow from some of the outstanding theoretical aspects of the previous chapters; the musical terms are introduced as they are needed so that a reader without musical background can understand the essence of how Group Theory is used to explain certain pre-established musical relations. On the other hand, for the reader with knowledge of Music Theory only, this chapter provides concrete elements, as well as motivation, to begin to understand Group Theory.'
This is a free textbook offered by BookBoon.'Essential Group Theory is an undergraduate mathematics text book introducing the...
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This is a free textbook offered by BookBoon.'Essential Group Theory is an undergraduate mathematics text book introducing the theory of groups. It has been aimed primarily at mathematics students but those studying related disciplines such as computer science or physics should also find it useful. The first part summarizes the important points which will be found in most first undergraduate courses in group theory in brief concise chapters.The second part of the book forms an introduction to presentations of groups.'
This is a free textbook offered b BookBoon.'In this book, which is basically self-contained, we concentrate on partial...
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This is a free textbook offered b s a free textbook offered by BookBoon.'This book is a guide through a playlist of Calculus instructional videos. The...
see more classroom" model.'
This is a free textbook offered by BookBoon.'The workbook is designed as a supplement for a Calculus II course taught at most...
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This is a free textbook offered by BookBoon.'The workbook is designed as a supplement for a Calculus II course taught at most American universities.Instructors are required to cover a lot of material in a short period of time and this schedule only allows for one or two examples for each topic which is not sufficient for most students.The workbook provides many more examples with solutions videos to help students master the material and prepare for exams and quizzes.The author used these examples and videos in the Fall 2012 Calculus II course at the University of Illinois at Chicago with significant improvement in exam and quiz scores from previous semesters.'The table of content is:Area ProblemsVolume by Cross-SectionDisk/Washer MethodMethod of Cylindrical ShellsIntegration by PartsTrigonometric IntegralsTrigonometric SubstitutionMethod of Partial FractionArc LengthInfinite Series Test for DiverganceInfinite Series Geometric SeriesInfinite Series Telescoping SeriesInfinite Series Integral TestLimit Comparison Test
This is a free textbook offered by BookBoon.'This book is the exercise companion to A youtube Calculus Workbook (part II)....
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This is a free textbook offered by BookBoon.'This book is the exercise companion to A youtube Calculus Workbook (part II). Its structures in modules mirrors that of the workbook. The book includes, for 31 topics, a worksheet of exercises without solutions, which are typically meant to be either worked out in class with the help of the teacher or assigned, a homework set consisting of exercises similar to those of the worksheet, and the complete solutions of the homework sets. It also contains four mock tests with solutions, and a sample final exam with solutions.Additionally, a brief discussion of the use of the Workbook and the exercise book in a flipped classroom model is included.'
This is a free textbook from BookBoon.'״Free ebooks + free videos = better education" is the equation that describes this...
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This is a free textbook from BookBoon.'״Free ebooks + free videos = better education" is the equation that describes this book's commitment to free and open education across the globe. Download the book and discover free video lessons on the Author's YouTube channel.״Engineering Mathematics: YouTube Workbook" takes learning to a new level by combining free written lessons with free online video tutorials. Each section within the workbook is linked to a video lesson on YouTube where the author discusses and solves problems step-by-step.The combination of written text with interactive video offers a high degree of learning flexibility by enabling the student to take control of the pace of their learning delivery. For example, key mathematical concepts can be reinforced or more deeply considered by rewinding or pausing the video. Due to these learning materials being freely available online, students can access them at a time and geographical location that suits their needs.'The table of contents includes:Partial derivatives & applicationsPartial derivatives & partial differential equationsPartial derivatives & chain ruleTaylor polynomial approximations: two variablesError estimationDifferentiate under integral signs: Leibniz ruleSome max/min problems for multivariable functionsHow to determine & classify critical pointsMore on determining & classifying critical pointsThe method of Lagrange multipliersAnother example on Lagrange multipliersMore on Lagrange multipliers: 2 constraintsA glimpse at vector calculusVector functions of one variableThe gradient field of a functionThe divergence of a vector fieldThe curl of a vector fieldIntroduction to line integralsMore on line integralsFundamental theorem of line integralsFlux in the plane + line integralsDouble integrals and applicationsHow to integrate over rectanglesDouble integrals over general regionsHow to reverse the order of integrationHow to determine area of 2D shapesDouble integrals in polar co-ordinatesMore on integration & polar co-ordinatesOrdinary differential equationsSeparable differential equationsLinear, first–order differential equationsHomogeneous, first–order ODEs2nd–order linear ordinary differential equationsNonhomogeneous differential equationsVariation of constants / parametersLaplace transforms and applicationsIntroduction to the Laplace transformLaplace transforms + the first shifting theoremLaplace transforms + the 2nd shifting theoremLaplace transforms + differential equationsFourier seriesIntroduction to Fourier seriesOdd + even functions + Fourier seriesMore on Fourier seriesApplications of Fourier series to ODEsPDEs & separation of variablesDeriving the heat equationHeat equation & separation of variablesHeat equation & Fourier series.' |
Pembroke Pines CalculusAs a professor of applied math at Concordia University, I taught math for the decision sciences. Among the courses taught were subjects focused heavily on deterministic methods. So it is that Linear Algebra figured heavily in my undertakings |
Pages
Given algebraic, tabular, graphical, or verbal representations of linear functions in problem situations the student will determine the meaning of slope and intercepts as they relate to the situations.
Given verbal and tabular representations of situations involving direct variation, the student will relate direct variation to linear functions and solve problems involving proportional change. This interactive demonstrates how the slope of a line changes when the line between the points changes.
This collection explores how Project Share is transforming learning at school districts across Texas. Whether districts have chosen to fully immerse their schools in Project Share or have just gotten started by identifying a single tool or set of resources to enhance their classroom experience, all have seen value in leveraging this free, online environment. |
Money and Capital Markets offers thorough coverage of financial institutuions and markets for upper level endergraduate and MBA students. Prerequisites for the text are an introductory finance course and basic knowledge of algebra. |
A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras... more...
Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at... more...
This book gives the concepts and background necessary to understand and build algorithms for computing elementary functions, presenting and structuring the algorithms (hardware- oriented as well as software-oriented), and discusses issues related to the accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to... more...
"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews
"Surveys and applies fundamental ideas and techniques in the theory of curves, surfaces, and threefolds to a wide variety of subjects. Furnishes all of the basic definitions necessary for understanding and provides interrelated articles that support and refer to one another."
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his... more...
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties... more...
Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the |
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Pilkington: I can put my math skills to good use these days even though they're 30 years old by tutoring high school and college kids.
Miu: Is it a bit overkill?
Kutt: Bendo. Ugh. That's insane.
Broschinsky: Didn't know how an average book would look like so i bought this one.
Marcello: It covers, qmatomic structure etc which i don't even need.
Altonen: Are you a physics student?
Jucean: I remember engineering physics 180181 Nord mode enabled.
Simcheck: Math major, but we have a test in the basic chapters of physics. Like newtons laws, momentum etc.
Coyier: I was hoping for something along the lines of dcosx4y, x=5t4, y=1t but that doesn't work.
Sivia: Wait, you want to compute partial derivatives, right?
Abrahamsen: So i thou, ok let's get this book, it probably covers everything.
Butland: Yeah, bendo, sounds like it.
Coyier: Dzdt and then partials as well.
Sivia: Well, compute them one at a time, then.
Sivia: If you want mathematica, get mathematica.
Ptak: Mechanics is covered in the early chapters, so i guess even if you don't plan to study the whole thing, it could be good. Amazon reviews seem very positive, but as i said i can't really comment, i don't know this book.
Coyier: Mathematica has syntax to enter in that sort of thing?
Garman: Ok but should i study the areas i wont need? Such as atomic structure particles behave like waves etc or can i skip these chapters? I need tho nuclear physics which comes after these chapters.
Sivia: I'm sure there's some complicated way to compute all derivatives, yes.
Coyier: I really just need dzdt not partial so i can check my work.
Sivia: So substitute in x and y.
Coyier: 52 minutes? I'm outta here.
Vivino: Hi, could someone explain why Sweeton's theorem is true? "Sweeton's theorem states that truth of sentences in the vocabulary language of arithmetic cannot be expressed by.
Kotur: You can use a gödel numbering to express the statement p = "p is not true".
Kotur: Do you have a more specific question? That looks like a fairly standard treatment.
Magin: Why do many people make functions that are fnx instead of just fx,n etc.
Swezey: Because you're looking at it as a function of x.
Kotur: It has the connotation that n is 'fixed'.
Jansky: The n just describes which function of x.
Deshazer: I just think it could work either way.
Kotur: Also if n is discrete, x is real, you want to be able to say things like "fn is differentiable" which is awkward otherwise.
Dominquez: What does it mean for "n to be discrete".
Pressman: Er bad placement of quotes lol.
Kotur: In this case i just mean n is a natural number.
Bouleris: I don't understand the proof that's in the notes, when it defines subm, n.
Kotur: Subm,n takes the goedel number of some sentence which has a free variable, and puts the nth sentence in place of that variable.
Kotur: So sub"x is prime", 7 gives you "7 is prime".
Kotur: It is defined awkwardly because you need to unquote and quote to do the substitution.
Kotur: Oh, when i said "nth sentence" i meant "nth natural number", sn is defined that way on the first page.
Mahmoud: When a probability question asks what is the probability that this event happens or this event or both events, what are they really asking? It feels like its an and question disguised as an or?
Vodder: The problem was "out of a standard deck of 52 playing cards, john picks one card. What is the probability that john picks a queen, a red card or both? " so pq = 452, and pr = 2652 and both would be pqpr?
Devillez: I can't even figure out how to use an opamp to amplify an audio signal!
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Devillez: And then p*** it to the filters.
Cheslak: No friend of mine told me about all sorts of crap because somebody paid them to. Furthermore, no friend of mine has ever been obcessed with telling me about 6,660,000 irrelevant things. Google does all this crazy stuff, and more. No friend of mine. Tool, yes. Friend, no.
Basa: It's something a professor at school drew for me.
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Cicerchia: The left side is the input, the right side the output.
Rexroat: The top and bottom are the an supplies.
Zane: You really only need a center tapped pair of 9 volts connected in series.
Corcino: Center for the ground, the on the right of the 9 volts in series for 9v, and the one on the left for 9 volt.
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Sansoucy: Of course, they don't need to be perfect.
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Alexandropoul: But it probably helps to have them balanced.
Larousse: The and are actually inverting and noninverting inputs.
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Posch: Honestly, i don't know how those work.
Buckwalter: I've never tried an opamp that doesn't require a dual supply.
Devillez: I'll grab a handful of 741′s and one or two of those to play around with then.
Devillez: So that's a basic signal amplifier schematic in the picture? What values should i use in my case?
Devillez: I don't even know the amplitudes of the audio line, let alone what to amplify them to.
Meers: For 2x amplification, will reach 2 volts from 1 volt.
Devillez: How do i achieve 2x amplification?
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Devillez: I'm mostly worried about not distorting the signal i'm trying to ****yze.
Devillez: Also, what do i do with the negative line of the cable?
Twiss: But for audio it may help to make r1 or r2 a variable resistor.
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Nippe: The input audio cable goes to and ground.
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Schimke: R2 connects between r1 and to the ground.
Geasley: Just the center of the two 9 volts in series.
Devillez: Also, the signal is stereo. Do i amplify it and then sum it somehow?
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Tinucci: For right and left, you need to duplicate the design for the other channel. |
combinatorial analysis.
Introductory text surveys the theory of permutations and combinations associated with elementary algebra; the principle of inclusion and exclusion; ...Show synopsisIntroductory text surveys the theory of permutations and combinations associated with elementary algebra; the principle of inclusion and exclusion; and the theory of distributions and partitions in cyclic representation. Includes problems. 1958 edition.Hide synopsis |
The Matrix Algebra Tutor: Learning by Example DVD Series teaches students about matrices and explains why they're useful in mathematics. This episode teaches students about row equivalent matrices in the context of matrix algebra. Students are taught rules which can be used to simplify the form of a matrix, similarly to when we use rules to simplify fractions. Grades 9-College. 43 minutes on DVD. |
College Algebra - 6th edition
Summary: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth Edition. This straightforward and easy-to-use algebra book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section to prepare you for what you're about to learn, and a list of formulas and key concepts after each section that help reinf...show moreorce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology. ...show less
James Stewart James Lothar Redlin Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology. Saleem Watson Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysisIMPORTANT! Please read before buying. AIE - Instructor's Edition with same identical content as regular student edition but may include instructor's notes and ALL answers.
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Please read description before purchase >>> instructor annotated version printed on cover with all identical Students content with teaching tips, and all solutions text only no access code. satisfacti...show moreon guarantee Quicker shipper with tracking # Expedited shipping available with Priority mail for fastest delivery used book -MAY NOT CONTAIN SUPPLEMENTS, book appears to be recovered - has some used book stickers - free tracking number with every order. book may have some writing or highlighting, or u...show moresed book stickers on front or47 +$3.99 s/h
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Intermediate Algebra (Concepts and Graphs, Chapters 1 - 8 (pages 550)
9781936368006
ISBN:
1936368005
Edition: 1ST Publisher: XYZ Textbooks
Summary: Charles P. McKeague is the author of Intermediate Algebra (Concepts and Graphs, Chapters 1 - 8 (pages 550), published under ISBN 9781936368006 and 1936368005. One hundred sixty two Intermediate Algebra (Concepts and Graphs, Chapters 1 - 8 (pages 550) textbooks are available for sale on ValoreBooks.com, forty one used from the cheapest price of $14.89, or buy new starting at $230.911936368013-2-0-1 Orders ship the same or next business day. Expedite [more]
book taught me the many examples of the different ways that a problem can appear. In many of the other textbooks I have used in math classes there will be one or two examples on a particular problem, and then when it comes time to take the test there is a curve ball and a new form of the same equation. This book does an excellent job of making sure that doesn't happen by offering help on many different forms rather than just a few. All in all the book helped me to better understand math by seeing problems as smaller pieces of math rather than a standardized equation that is solved in a particular way.
As with any math book, a few more examples of real life applications would be nice to have. Being able to apply you work to the real world is invaluable.
ISBN-13:9781936368006
ISBN:1936368005
Edition:1STth
Publisher:XYZ Textbooks
Valore Books is a student's number one resource for cheap Intermediate Algebra (Concepts and Graphs, Chapters 1 - 8 (pages 550) rentals, or used and new condition books available to purchase and have shipped quickly. |
This non-credit course is a refresher for students entering a SIAST technology program. It is recommended for students who completed high school math more than five years ago or any student who is anxious about the mathematics component of their program. The course will review the basics of algebra, geometry, trigonometry, exponential and logarithmic equations. Students will have an opportunity to develop skills in problem solving, and calculator use. Exams are optional |
Book summary
Continues the outstanding tradition of earlier volumes with attention to detail, well-written explanations and a lively, accessible approach to learning. The size of this edition has been substantially reduced by rewriting major portions of the material for more efficient exposition and effective use of space. New material has been added on parametric representations of surfaces, Jacobians and Kepler's laws. Also includes new reference matter on complex numbers as well as biographies and historical notes which capture the personalities of the great mathematicians. [via]
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Softcover, ISBN 0471105899 Publisher: John Wiley and Sons (WIE), 1995 Very Good. US Edition. Item in very good condition and at a great price! Textbooks may not include supplemental items i.e. CDs, access codes etc.... |
Tag Archives: Richard Elwes
I can't score this book more than 3 stars because it's not really popular maths, but it does what it sets out to do rather well, so it should be seen in this context. As Richard Elwes points out in his introduction 'I was never any good at maths,' is something you hear all the time. What he sets out to do – and succeeds in admirably – is taking the reader step by step through the basics of maths to be able to manage those slippery figures with ease.
The approach is not as heavy as a textbook, though occasionally I did get the feel of a slight older, fussy teacher at work. (It's notable that the precise expression we're told Elwes has heard from 'a thousand different people' is 'I was never any good at mathematics.' Hardly anyone would say 'mathematics' rather than 'maths'. Now it's possible he was trying to avoid the UK/US maths/math split – but it still fits that slightly fussy precision we meet on a regular basis through the text.)
I really can't fault the step-by-step progress, starting with basic arithmetic, taking us on to fractions and powers, roots and logs, percentages, algebra, geometry and even a brief intro to probability and statistics. Each of the sections is quite short, easily digested, well laid out and illustrated and finished off with a little quiz that's not too taxing but helps reinforce the message. I suppose the only question is whether it's best to arrange such an introduction by the structure of maths itself (as this book is) or by application, taking the reader through typical mathematical chores from checking a shopping bill to calculating odds at a bookies. That way you could cover the same ground but perhaps make it seem more real world. However, Elwes doesn't resort to an excess of mathematical jargon, keeping the focus simple – and at least by structuring the book on the maths itself it can have the most logical progression of experience.
As I mentioned at the start, this isn't popular maths. A popular maths book is not a tutorial in how to use it, with tests, but an exploration of some aspect of maths, the people involved, the history and its significance. This is much more a practical book. I would it see it being particularly useful to an adult learner who had trouble with maths at school and now wants to come back to it and take it on. It is a lot less condescending than most modern maths textbooks and would appeal more to a mature reader. So for this particular audience it is definitely an option well worth considering – and it's excellent value, priced like cheap paperback but actually a good size and well-made book. Just not really for someone wanting a voyage of discovery about the history or nature of mathematics.
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Like its sister title Science 1001, this book takes on an enormous task: telling us 'everything we need to know about mathematics in 1001 bite-sized explanations'.
It's a handsome, if rather heavy book, somewhere between a typical hardback and a small coffee table book in size (though with floppy covers). Inside, it's divided into 10 main sections – from the obvious ones like geometry and algebra, through to the exotics from statistics to game theory. Each section is split into topics – so in geometry you might get 'Euclidian geometry' and within each topic there may be around 12 entries.
In a sense, then, this is a mini-encyclopaedia of maths, though arranged by subject, rather than alphabetically. I had mixed feelings about the science entry in the series and those feelings are more extravagantly mixed than ever here. There is no doubt whatsoever that this is a useful book. A good marker of this is that, unlike many of the books that come into the review pile, I intend to keep this one. I think I will come back to it time and again to brush up on what some specific aspect of maths is. (As it is, really, a reference book, it would have been more helpful if the topics were alphabetic, but hey, what do you expect from a mathematician?)
However, as a popular science book to read from cover it has a number of deep flaws. Firstly it's much too broken up into tiny segments. There is a bit of a flow, brought in by the way the topics are organized, but it's very weak, and certainly doesn't make for casual reading matter.
Secondly, far too much of the book is definitions. Time after time, a topic consists of defining what a mathematical term means. I feel a bit like Richard Feynman, who was told in a biology class, when explaining what the various bits of a cat were called, that everyone would be expected to memorise these. He said something to the effect of 'no wonder this course takes so long' – he didn't see why people need to keep all those definitions in memory, and I rather feel the same about maths.
Then there's the difficulty that the structure has in terms of dealing with some of the essentials of maths. Time after time, the author refers to the number e, without telling us what it is until over 200 pages after it is first mentioned. The assumption for a reader who hasn't come across it might be that e is just a placeholder, the way j is used elsewhere – although many definitions here aren't necessary, explaining what something like e is, and why it's important, is pretty crucial.
As someone with a physics background, I particularly struggle to understand why there's a whole section in here called 'mathematical physics.' No, it's just physics. Newton's laws don't belong in a book on maths – there's much too much to get your head around already without straying into a different subject.
And to top it all, I think the approach taken is often wrong. Popular science/maths, as opposed to textbooks, adds in explanation and context, not just the theory. By being so strong on definitions, there doesn't seem to be room for this here. We find very little out about all the fascinating people involved. But even if you decide the format doesn't allow for context and history, there is still far too little explanation. Two example out of literally hundreds: we are told 'Up until the early 20th century, 1 was classed as prime, but no longer.' Why? There are good reasons for this, but it is totally counter-intuitive. The number 1 seems like a prime. After all, it is only divisible by 1 and itself. We need explanation, not statement from authority. Another example is the topic on Bayes' theorem. This is fascinating in its application, but the explanation is almost unreadable, being mostly equations, and there is nothing about its application in that section (a later one does make use of it, but doesn't mention it is doing so). Highly frustrating.
Overall then, this is a very useful book if you dip into maths and need a quick reminder of what various things mean. It really is a great resource as a reference book. But it just doesn't work as popular maths.
Paperback (US is hardback):
Review by Brian Clegg
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Richard Elwes is a writer, teacher and researcher in Mathematics and a visiting fellow at the University of Leeds. Dr Elwes is passionate about the public understanding of maths, which he promotes at talks and on the radio. His more recent book is Maths 1001.
Why maths?
I don't know anything else!
I have always enjoyed the subject, and the more I have studied, the more I have realised how incredibly deep it goes, and just how much there is to know. At the same time, I am aware of the gulf between how most people see maths (a horrendous mix of tedious equations and incomprehensible jargon), and how I see it, which is as a whole other world, packed full of amazingly cool, interlocking ideas. So, as well as enjoying studying maths myself, I suppose I have a drive to try to close this gap.
Why this book?
There are two answers, both true.
The first is that I don't think a book like this has ever been attempted before. Of course, there are plenty of excellent books discussing various mathematical topics for a general audience. But I don't believe any have tried to be as comprehensive as this. It's ambitious, there's no doubt about it, and I was excited by the challenge.
At the same time, there seems to be a gap between 'popular' books on one hand, which take a completely equation-free, discursive approach to a mathematical subject, and 'technical' volumes or textbooks on the other, which go fully into all the gory details. My book treads a middle path. I didn't want to sex things up too much, I wanted the mathematics to speak for itself, and for the book to work as a reference volume. At the same time, some of the material is undoubtedly difficult and unfamiliar, and people need a way in, to understand what fundamental questions are being addressed. I wanted it to be enjoyable to read, and for people genuinely to learn from it. In some ways, I suppose I wanted to write the book that I would like to have read aged 17.
The second answer is… someone offered me money to write it.
What's next?
I'm pleased to say that I have a couple of projects in the pipeline. In Spring 2011 I have a book called "How to build a brain (and 34 other really interesting uses of mathematics)" coming out, which has been a fun one to write. It covers some of the same areas as Mathematics 1001, but in a much more light-hearted and less technical style. Perhaps you could guess that from the title.
There are other things in the works too… but it is probably still too early to go into details. I can say that I am looking forward to working on them though!
What's exciting you at the moment?
Maths 1001 is my first book, and it's just come out. I'm quite excited about that, to be honest!
Otherwise, I find that the internet makes a wonderful blackboard, these days. There are so many people out there talking about maths, from primary school teachers discussing games kids can play to start to enjoy numbers, right up to Fields medallists presenting their latest research. I follow several mathematical and scientific blogs (I've got my own too, may I plug it? Thank you!). It is just fun to be a part of that huge conversation.
In terms of mathematics itself, I have been thinking about recent work by the logician Harvey Friedman, which I find very exciting. It's a sort of sequel to Kurt Gödel's famous work. I think it will turn out to be important. I am getting quite interested in ideas from logic to do with provability, computability, and randomness, and how they relate. My background is not in exactly this type of logic, but I do find it fascinating. |
Woodacre PrecalculusIn Algebra 1 we also study graphical methods in order to visualize functions as straight lines or parabolas. Further we learn about factorization and the solutions of quadratic equations. Seeing many advanced students who struggle with algebra 1 concepts makes me feel good about my algebra 1 students because I help them to learn it properly from the beginning |
MAA Bookstore - Mathematical Association of America
A searchable list of books, with descriptions, in the following categories: Algebra; Analysis; Applied Mathematics; Calculus; Career Information; Computing and Computers; Elementary Models; Games, Puzzles, and Popular Exposition; Geometry and Topology;
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Math shareware from Germany (English, French, and German versions are available) for secondary level or high school students and teachers. Math-Assist helps in solving most of the tasks of algebra, geometry, analysis, stochastics, and linear algebra.
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Lessons, resources, books, and classroom packs for making Mathematica software an integral part of math education in university and college classrooms. Also features Mathematica versions geared and priced for students, as well as flexible academic purchase
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Mathematical Analysis II - Elias Zakon
This is the final text in the Zakon Series on Mathematical Analysis, containing nearly 500 exercises. The work is free to students using it for self-study. Find contents, index, and purchasing information on the site.
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A page on electronic publishing in mathematics, with sections on mathematical journals and bibliographies, separated into references to E-journals, General Journals and Bibliographies, and Subject Specific Journals and Bibliographies. Also Preprint Archives,
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Science Search is a directory for scientific topics, including this subsection of Math. Individual entries include description, category, and a user rating of the site.
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maths online - University of Vienna, Austria
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A "platform to promote, propagate, and mediate applied mathematics and computer sciences," with emphasis on cryptography, number theory, financial mathematics, logic and knowledge representation, and quantum computation. In particular, m@th IT offers
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An interactive analysis and visualization program for Windows. Provides extensive analysis and graphic capabilities, an integrated debugger, a profiler, a full-screen editor and a matrix-oriented interpreted language, with analysis functions in the following
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OpenFVM CFD solver
OpenFVM is a general CFD solver released under the GPL license. It was
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Elementary Geometry for College Students
9781439047903
ISBN:
1439047901
Edition: 5 Pub Date: 2010 Publisher: Brooks Cole
Summary: If you want to rent Elementary Geometry for College Students online, we can help you. This text book, written by Daniel C Alexander and Geralyn M Koeberlein, was published by Brooks Cole in 2010. Now you can get cheap Elementary Geometry for College Students here in its 5th edition for an affordable price. We specialize in providing great deals that are heavily discounted for previously owned copies. You can buy Elem...entary Geometry for College Students online here for a price far lower than you might think, and sell back later on too. We provide the whole deal for every college student.
Alexander, Daniel C. is the author of Elementary Geometry for College Students, published 2010 under ISBN 9781439047903 and 1439047901. Three hundred seventy four Elementary Geometry for College Students textbooks are available for sale on ValoreBooks.com, one hundred twenty six used from the cheapest price of $26.39, or buy new starting at $153.83.[read more]
Ships From:Lincoln, NEShipping:StandardComments:A FEW LOOSE PAGES, LOOSE BINDING. This item may not include any CDs, Infotracs, Access cards or o... [more]A FEW LOOSE PAGES, LOOSE BINDING this book was getting across the basics of geometry. I found this book very effective because it gave you review and test questions/answers which was very helpful when preparing for a test. Most of the time teachers will use problems from here for quizzes or test so practicing these problems is crucial. The examples in each chapter are very helpful as well because they give a break down of each problem.
If I could change one thing about this book it would be to provide all the answers for every other problem. Sometimes in certain chapters, answers to the odd problems would be missing. But other than that this book was very helpful in helping me pass with an A this semester! |
Ken-Thomas Nilsen
Reviews
I only read the last parts, starting from the chapter about induction, so take that into consideration.
The 'scratch work' sections are great, and this book did what other books didn't, it gave me a tactic for doing proofs. Other books show a lot of proofs and explain why the proofs are correct. That is great, but without a 'tool set' for working with proofs it is hard to know were to start when you are supposed to do them yourself. This is the only book I have read, also since, that do this deliberately and it gave me the foundations I needed to follow discrete math courses. |
Instead of using numbers algebra introduces letters as symbols to represent generalized numbers that may vary(Variables). Algebra also defines the rules of mathematical expressions and equations. To me problem solving is like to solve a puzzle. You list the information you know and use variables for unknown information |
Peyton Statistics has provided me with an extensive knowledge of mathematics. Differential equations are commonly used throughout all areas of physics. For instance, one cannot solve the Schrodinger equation in quantum mechanics without knowledge of differential equations. |
Mathematics
For Sixth from primary
First term
Authors
Dr. / Mahmoud Ahmed M. Naser Dr./ Rabee Mohamed Othman Ahmed
Professor of teaching Lecturer of teaching
mathematics faculty of education mathematics faculty of education
Beni – Suef University Beni – Suef University
2011 - 2010
Introduction
My dear pupils, sixth grade primary … it give us pleasure to introduce this book for you as
part of developed mathmastics series. We dedicated many things for you when we composing
this book many things were taken in consediration in order to make studying mathematics an
interesting, popular and useful duty for you:
(1) Displying the topics in the easiest way and clearness using aproperiate language that adope
with your information and experiences. So that it will help you to cope in the knowledge and
ideas which were involved in each a topic a lon.
• The given ideas are listed gradually from the simplest to the hardest
• We ensure forming the new concepts and ideas correctly before setting up associated
operations, via suitable activates.
• Linking the mathematical lessons with life, through realistic Issues and problems in various
applications hoping that you will fell the value of the mathematics and studying it as a useful
in life.
• At many points within this book, we give you opportunity to deduce ideas, and reach
information your self, depending on your experiences, and thinking to grow up searching and
self learning.
• At other points we invite you to work in groups with your colleagues to know their ideas and
introduce to gather one part work .
• At other points too, we call you to check the solution which were introduced to in rich your self
confident, and increase your ability for reach the correctness of things.
• The book was divided into units, the units were divided into lesson which involved with
Images figures, and illustrated diagrams. At the end of each lesson evaluated exercises were put
. besides general exercises and unit test .
The book end contains model answers.
• The unit end contains activity for the portfolio To practice with your teacher help, and you
will find technological activity , to deal with computer.
Finally … my dear pupil, in your classroom with your teacher and classmate, you should acte
posietily. Donot hesitate to ask questions. Trust that your participating will be appreciated,
remember forever, mathematics involve many questions have more than one solution.
We ask allah that, we did well for our lovely Egypt.
Authors
املؤلفان
Contents
The first unit : Ratio
Meaning of the Ratio 2
Properties of ratio 6
Miscellaneous exercises on ratio and its properties 10
The ratio among three numbers 15
Applications on ratio (The rate) 19
General exercises on the first unit 21
Technological activity 22
The portfolio 23
Unit test 24
The Second unit : Proportion
The meaning of proportion 26
Properties of proportion 29
Drawing Scale 34
The proportional division 38
Percentage 43
Applications on the percentage 48
Technological activity 52
The portfolio 53
Unit test 54
54
The third unit :Geometry and measurement
The relations between the geometrical shapes 56
The visual patterns 61
Volumes 64
The volume of the cuboid 70
The volume of the cube 76
The Capacity 69
General exercises on the third unit 82
A technological activity 85
The portfolio 84
Unit test 86
The Fourth unit :Statistics
The Kinds of Statistics data 88
Collecting descriptive statistic data 91
Collecting The statistics quantative data. 94
Representing the Statistics Data by the frequency curve 98
General exercises on unit 4 101
A technological activity 102
The portfolio 103
Unit test 104
Ratio
• The first lesson : Meaning of Ratio
• The second lesson : properties of ratio
• The third lesson : Miscellaneous exercises on the ratio and its properties
• The fourth lesson: The ratio among three numbers
• The fifth lesson : Applications on the ratio (The rate)
- General exercises on the unit
- Technological activity
- The portfolio
- Unit Test
The first unit
1 Meaning of the Ratio
Notice and Discuss
What do you learn from this
comparing between two quantities form the same kind for example:
lesson?
- Through your active First : Comparing between prices
participating you can
come to: In the opposite figure, the price of the blouse is LE 40 and the price
* The meaning of the ratio. of a pair if Trousers is LE 80 we can compare between the prices as
* expressing the ratio. follow :
* elements of ratio.
a) the price of the blouse is less than the
price of the pairs of trousers or the price
The mathematical concepts of :
of the pair of trousers is greater than the
* The ratio between two
quantities. price of the blouse.
* The antecedent of the ratio. 1
b) The price of the blouse = the price of the pair of trousers
* The consequent of the ratio. 2
price of the blouse
40 4 1
because = = = .
price of the pair of trousers 80 8 2
price of the pair of trousers
c) Price of the pair of trousers is double the price of the blouse because
price of the blouse
80 8
= = =2
40 4
price of the blouse
1
• The fraction
price of the pair of trousers = 2
Is called a ratio of the price of blouse to the price of the pair of trousers.
price of the pair of trousers 2
Also = (is called a ratio of the price of the pair of trousers to the
price of the blouse 1
price of the blouse.
Second : Comparing between lengths :
From the opposite figure we can compare between the height of the
9m
tree (3 meter) and the height of the house (9 meters) using one of the
following methods.
1- The height of the house exceeds the height of the tree or the height
3m
of the tree is less than the height of the house.
2
The ratio
2- The height of the house is greater than the height of the tree.
or the height of the tree is less than the height of the house.
3- The height of the house is three times the height of the tree.
The height of the house 9 3
Because = = =3
The height of the tree 3 1
9
The fraction is called a ratio
3
or the height of the tree is the third of the height of the house.
The height of the tree 3 1
because = =
The height of the house 9 3
1
The fraction is called a ratio.
3
Now we hope that you had recognized that meaning of the ratio to be
As comparing between two quantities or two numbers of the same kind and of the same unit then the
produced fraction (or the resultant fraction) is called a ratio.
i.e. The ratio between
The first number
a number and another one =
The second number
Expressing the ratio
- In the case of the price of blouses and the price of apair of trousers we could express the ratio in the form
1
of a fraction which is .
2
We can write it in another form as 1 : 2 it is read as ( 1 to 2 ) where 1 is called the antecedent of the ratio or
its first term and the number 2 is called the consequent of the ratio or its second term.
- Similarly in the case of the height of the tree and the height of the house we could express the ratio
1
in the form of a fraction to be and it can be written in another form as 1 : 3 and it is read as ( 1
3
to 3 ).
Where 1 is called the antecedent of the ratio or its first term and 3 is called the consequent of the ratio
or its second term.
Drill (1) Complete :
If Khalid has LE 15 and Ahmed has LE 25 then
The ratio between what Khalid has and what Ahmed has is = ....................................
= .................................... or ……….. : ………
.................................
.................................
The ratio between what Ahmed has and what Khalid has = ....................................
= .................................... or ……… : …………
.................................
.................................
3
The first unit
6 cm
Drill (2) Complete :
When we compare between the area of The area = ....... The area = ............
2cm
the square and the rectangle in the shown
2cm
figure then
The area of the square = ............................... = ..........................................
The area of the rectangle .................................. .......................................
or ……… : ………
Remember that :
The area of the square = side length itself
Drill (3) Complete : The area of the rectangle = length width
When we compare between the number of small square in column (A) and the number
of small squares in column (B) then the ratio between them is :
The number of squares in column (A)
(a)
The number of squares in column (B)
= .................................. = ................................. or ……… : ………
................................. ....................................
The number of squares in column (B)
(b)
The number of squares in column (A)
.................................. ..................................
= = or ……… : ……… )B( ) A (
................................. .................................
Drill (4) :
A B
Express the ratio in each of the following cases by two different methods
(a) The ratio between the length of AB to the length of CD C D
(b) The ratio between the age of Nabeel and the age of Khalid where
The age of Nabeel = 40 years
The age of Khalid = 25 years
(c) The ratio between the two areas of the two rectangles ABCD and XYZL
X L
A D
2 cm 1 cm
B C
2 cm
Y 3 cm Z
4
The ratio
Exercise (1 - 1)
1
Write the ratio between the two numbers 21 and 9 in the simplest form.
2
Complete the following table.
The antecedent of the ratio The consequent of the ratio The form of the ratio
3 5
.....
5:3
.....
7 10 ........ ........
7
........ ........ 5
........
........ ........ ........ 11 : 3
3 Write the ratio between the two numbers in each of the following in its simplest form :
19 57
(a) (b)
144 76
4 In one of the classes of the first primary grade the number of boys is 15 pupils and the number
of girls is 20 pupils.
Calculate :
(a) The ratio between the number of boys to the number of girls.
(b) The ratio between the number of girls to the number of all pupils in the class.
(c) The ratio between the number of boys to the number of all pupils in the class.
5 Write each of the following ratios in its simplest form :
3
(a) 2.3 : 5.76 (b) 0.84 : 2
9
6 Express the ratio between the two numbers 8 and 12 by two methods.
5
The first unit
2 Properties of ratio
Participate and discuss
What do you learn from this
Property (1) :
lesson?
The ratio has the same properties of the common fraction in :
Through your active participating
you will come to : reduction , simplification and comparison.
- ratio has the same properties of
the common fraction in: Example (1) :
reduction , simplification and
Omar saved 32 pounds and Khalid saved 48 pounds.
comparison
Find the ratio between what Omar saved to what Khalid saved.
- The two terms of the ratio are
two integer numbers . Solution :
- The unit of each of the two
What Omar saved 32 Notice That we divided
terms of the ratio is the same =
unit. What Khalid saved 48 each of the two terms of
- The ratio between two the ratio by 4 then by 4 to
quantities of the same kind has 8 2
= = or 2 : 3 simplification the ratio.
no unit. 12 3
The mathematical concepts:
Example (2) :
- The terms of the ratio. 3 5
Find the ratio between the two fractions and
- simplifying and comparing. 4 6
- Measuring units.
Solution :
3 5 3 5 9
4
:
6
= 4
÷
6
=
10
or 9 : 10 (reduction)
Similarly :
64 16 64 16 64 1 4 5
6.4 : 16 = : = ÷ = = =
10 1 10 1 10 16 10 5
or 2 : 5 (simplifying)
(reduction and simplification)
6
The ratio
Example (3) :
3 4
Compare between the two ratios and (using < or >)
5 7
Solution :
Because of there's no simplifying we should get the L.C.M (lowest common multiple)
21 20
of the deominators for the two ratios become ,
21 20 35 35
> This means
35 35
The first ratio is greater than the second ratio
3 4
i.e. >
5 7
Drill (1)
Write the ratio between the two numbers 25 and 75 .
3 5
Compare between the ratios and
4 8
Property (2)
The two terms of the ratio should be integer numbers:
From the previous two examples in the first property, the final results were as follow respectively.
2 : 3 and 9 : 10 and 2 : 5
All these numbers are integer numbers.
Property (3) :
At comparing two quantities to form the ratio between them, they must have the same unit i.e. (The
units are of the same kind).
For example :
At comparing the two lengths 160 cm and 2 metres we should firstly convert them to be of the
same unit.
This will be carried out by two methods.
The first: We convert 2 metres into 200cm then we use the property of simplifying for the ratio
becomes :
160 4
= or (4 : 5)
200 5 160 16
The second . We convert 160 cm into metres to become = metres.
100 10
Then we use the property of reducion and simplification for the ratio becomes :
16 16 2 16 1 4
:2= : = x = or (4 : 5)
10 10 1 10 2 5
7
The first unit
Example (1) :
1
Compare between kilogrames and 700 grammes.
2
Solution :
Converting to the same unit can be found out two methods.
The first :
1
Convert kilogrames into 500 grames then the ratio becomes
2
500 5
= or (5 : 7)
700 7
The second
Convert 700 grames into kilogrames
700 7
= kilograms
1000 10
1 7 1 7 1 10 10
The ratio becomes : = ÷ = or (5 : 7)
2 10 2 10 2 7 14
Drill (2)
Compare between 27 months and 3 years to get the ratio between them
Property (4) :
The ratio between two quantities of the same kind (it is anumber that) has no unit.
You opserved from the previous property and after converting the two quantities to the same unit that
the ratio in the first case is hold between length units either centimeters or metres and in the second
case the ratio is hold between weight unit either in grames or in kilogrames therefore the result ratio
has no unit in each of the two cases because they are of the same unit.
Drill (3)
The distance between Hosam house and his sporting club is 250 metre, and the distance between his
house and his school is 0.4 kilometres.
Find the ratio between the two distances.
Drill (4) 2 metres
In the opposite figure 120 cm
A rectangle in which the length = 2 metres and its width =
120cm. Calculate :
The ratio between the width of the rectangle and its length.
And the ratio between the length of the rectangle and its perimeter.
8
The ratio
Exercise (2 - 1)
1 In the following figures, a square of side length 4cm and a rectangle whose dimensions are 6
cm and 3cm Find:
4 cm 3 cm
6 cm
(a) The ratio between the perimeter of the square and the perimeter of the rectangle.
(b) The ratio between the area of the square and the area of the rectangle.
(c) The ratio between the length of the rectangle and its perimeter.
2 Find in the simplest form the ratio between each of the following:
(a) 250 p.t and 7 ½ pounds.
(b) 2 ½ hours and 75 minutes.
(c) 12 kirats and 1.25 feddan.
(d) 75 kirats and 16 sahms
3 Write the ratio between the two numbers in each of the following cases :
1 3 3
(a) and (b) 18 : 6.3 (c)1 : 2.2
2 4 5
4 Complete the following :
- The ratio between the side length of a square and its perimeter = ……… : ................
- The ratio between the circumference of the circle and its diameter length = ………. : ............
- The ratio between the length of the side of the equilateral triangle and its perimeter = … : …
5 The area of a rectangle is 32cm² and its width = 4cm . Find :
- The length of the rectangle.
- The ratio between the width of the rectangle and its length.
- The ratio between the length of the rectangle and its perimeter.
9
The first unit
3 Miscellaneous exercises on ratio and its
properties
What do you learn from this Preface:
lesson?
Sometimes we need to calculate an unknown quantity if we know
Through your active participating
you can recognize : How to :
another quantity and the ratio between them .
- Calculate a quantity if you have And we sometimes need to divide a given quantity into two parts if
given another quantity and the the ratio between them is known.
ratio between them.
- Divide a given quantity into
Remark :
two quantities by a given ratio.
The given quantity is a specified quantity for example: as the weight
of a person or the price of a good or the area of a piece of land or the
Mathematical specify concepts: number of the pupils in a school ….etc.
- The given quantity.
- The unknown quantity.
The unknown quantity is an unspecified quatity or unknown thing
- The ratio between them.
and we want to it for example: the need to.
specify The weight of a person, the price of a good or the number of
boys and girls in a school …. Etc.
Notice and think through the following examples .
Example (1):
If the ratio between the weight of Hani and the weight of Ahmed is 5 : 6 and if the weight of Ahmed
is 60 kilogrames. Calculate the weight of Hani.
Solution
We can solve the example using the idea of the value of one part as follows:
The weight of Hani 5
=
The weight of Ahmed 6
That means : 6 equal parts are equal to 60 kilogrames (Ahmed's weight)
This mean that the value of one part
60
= =10 kilogrames
6
Then the weight of Hani = 10 5 = 50 kilogrames
10
The ratio
The weight of Hani 5
=
The weight of Ahmed 6
That means
5
The weight of Hani = The weight of Ahmed thus
6
5
The weight of Hani = 60= 5 10 = 50 k.g
6
You can check the solution as follows :
The weight of Hani : The weight of Ahmed
50 : 60
(dividing by 10)
5 : 6
(This is the given ratio in the problem).
Example (2) :
A primary school has 540 pupils. If the ratio between the number of boys to the number of girls is
4 : 5 , calculate the number of each boys and girls.
Solution :
The number of boys 4
=
The number of girls 5
Using the idea of the sum of parts we get :
The sum of parts = 4 + 5 = 9 parts :
That means (540 pupils) equals (9 equal parts) .
i.e. The value of one part = 540 ÷ 9 = 60 pupils.
i.e. The number of boys = 4 60 = 240.
The number of girls = 5 60 = 300.
11
The first unit
You can check the solution as follows :
The number of boys : The number of girls
240 : 300 (Dividing by 10)
24 : 30 (Dividing by 6)
4 : 5 (It is the given ratio in the problem)
Example (3) :
A rectangular shaped piece of land the ratio between its length
and its width is 9 : 7 .
If the difference between the length and the width is 18 metres.
Calculate each of the length , the width and the perimeter of the
land.
Solution :
Notice that the ratio between the length and the width is 9 : 7 that means.
The length is divided into 9 equal parts and the width is divided into 7 equal parts the difference
between the number of parts of the length and the number of parts of the width = 9 – 7 = 2 .
i.e. 2 parts equal 18 metres.
i.e. The value of one part = 18 ÷ 2 = 9 metres
i.e. The length of the rectangular land
= 9 9 = 81 metres
The width of the rectangular land = 7 9 = 63m.
The perimeter of the land =
(The length + the width) 2
= (81 + 63) 2 = 144 2 = 288m.
Verifying the solution:
You can check the solution as follows the length of the land : The width of the land
81 : 63 Dividing by 9
9:6 (it is the given ratio)
The difference between the length and the width = 81 – 63 = 18 metre.
12
The ratio
Drill (1)
The ratio between the heights of two buildings in a town is 4 : 7.
If the difference between their heights is 9 metres. Find the height of
each of them.
Drill (2)
Two wire pieces, the ratio between their length is 5 : 9 .
If the sum of their lengths is 126 metres calculate the length of each piece.
Exercise (3 - 1)
1 Complete :
In the opposite figure
(A) (B) (C)
• The ratio between the number of squares in figure A to the number of squares in figure B is
4
or ……… : ……….
9
• The ratio between the number of squares in figure B to the number of squares in figure C is
..................................
or ……… : ……….
...................................
The ratio between the number of squares in figure ………… to the number of squares in figure
.....
………… is or 4 : 25
.....
(2) Write in the simplest form each of the following ratios
3 5 8 2
(a) : (b) :2
8 4 9 3
13
The first unit
3 A salary of cleaning worker LE 400 monthly. He spends LE 340
and saved the remainder. Find:
a- The ratio between what the worker spend to his salary.
b- The ratio between what he saves to his salary.
c- The ratio between what he spends to what he saves.
4 The opposite table shows the quantities of
1st quantitiy 2nd quantitiy 1st : 2nd
the same kind but in different units.
1
Calculate the ratio between each two 100 gm ...................................
4 kg
quantities in each case and complete the
table.
8 hours 2 days ...................................
1
2 km
570 m ...................................
1
18 kirat 1 2 feddan ...................................
5 In the opposite figure:
A rectangle with width 3.5 cm and its length = 7cm.
Find : 3.5 cm
(a) The ratio between the length and the width.
(b) The ratio between the width to the perimeter.
7cm
(c) The ratio between the length and the perimeter.
6 A Fruit seller sells one kilogram of apple for L.E 10
If the ratio between the price of apple to the price of banana is 5 : 2 ,
find the price of 5 kilograms of banana.
14
The ratio
4 The ratio among three numbers
Notice and think:
What do you learn from this
If Adel, Ahmed and Hani saved three amounts of money which are
lesson?
Through your active participation LE 180, LE 144 and LE 108 respectively.
you recognize how to : Then we can find the ratio among what Adel, Ahmed and Hani saved
- Find the ratio among three as follows.
numbers.
- Solve miscellaneous
What Adel saved : What Ahmed saved : What Hani saved
applications using the ratio
among three numbers. 180 : 144 : 108 (dividing by 12)
15 : 12 : 9 (dividing by 3)
5 : 4 : 3
Mathematical concepts
- The ratio among three
Example (1) :
number.
A family formed from three persons. If the tallness of the father is 1.8
metre. the tallness of the mother is 1.6 metre and the tallness of the
son is 1.2 metre. Calculate the ratio among the three tallnesses.
Solution :
Tallness of father : tallness of mother : tallness of son
1.8 : 1.6 : 1.2 (multiplying by 10)
18 : 16 : 12 (dividing by 2)
9 : 8 : 6
Example (2) :
ABC is triangle in which AB : BC : CA = 3 : 5 : 7
If the difference between the length of AB and BC is 4cm. Find the lengths of the sides of the triangle
and its perimeter .
Solution :
The ratio among the lengths of the three sides is 3 : 5 : 7 that means that AB is divided into three equal
parts in length.
15
The first unit
and BC is divided into 5 equally parts in length and CA is divided into 7 equally parts in length and
all parts are of the same kind.
The difference between the length of AB and the length of BC = 5 – 3 = 2 parts that means that :
2 parts equal 4cm
i.e. the value of each part = 4 ÷ 2 = 2cm
then:
The length of AB = 2 3 = 6cm,
The length of BC = 2 5 = 10cm
And The length of CA = 2 7 = 14cm
Since the perimeter of the triangle = the sum of length of its sides.
Then the perimeter of the triangle = 6 + 10 + 14 = 30cm
Verifying of solution
AB : BC : CA
6 : 10 : 14 (dividing by 2)
3 : 5 :7 (it is the given ratio)
Example (3) :
a, b and c are three numbers such that the ratio a : b = 4 : 3 and the ratio b : c = 2 : 3 . Find the ratio
among the three numbers a, b and c.
Solution :
To find the ratio among the numbers a, b and c take the ratio.
a 4
= That means a = 4 equally parts
b 3
b = 3 equally parts of the same previous parts
4
a= b
3
c 3 3
then = i.e. c = b
b 2 2
16
The ratio
Then the ratio among the three numbers a, b and c is :
a : b : c
4 3
b : b : b (dividing by b)
3 2
4 3
: 1 : (Multiplying by 6)
3 2
8 : 6 : 9 (this is the ratio among the three numbers)
Another solution (using L.C.M.)
Through the opposite figure
A : B : C
Notice that L.C.M of the two numbers 3 and 2 is 6 that means the
consequent of the first ratio is 3 multiplied by 2 then it becomes 6 4 : 3 :
Therefore we multiply the antecedent of the first ratio which is 4 by
2 to be 8 2 : 3
Also multiply the antecedent of the second ratio which is 2 by 3 to
be 6 . 8 : 6 : 9
Therefore multiply the consequent of the second ratio which is 3 by
3 to be 9
Then the ratio among the three numbers becomes
8:6:9
Example (4) :
If the ratio among the share of Hani and the share of Sherif and the share of Khalid is 3 : 5 : 7 and if
the share of Hani is LE 24 caluclate the share of each of Sherif and Khalid.
Solution :
The share of Hani = 24 pounds and it equals 3 equal parts
24
i.e. The value of one part = = LE 8
3
Then the share of Sherif = 5 8 = LE 40
And the share of Khalid = 7 8 = LE 56
Drill
Find the ratio among the tallnesses of Sahar, Noha and Ola if
The tallness of Sahar : The tellness of Noha
The tallness of Sahar : The tallness of Noha = 2: 3
The tallness of Noha : The tallness of Ola = 6 : 5
17
The first unit
Exercise (1 - 4)
1 If the ratio among the measures of the angles of a triangle is 5 : 6 : 7 and the measure of the first
angle is 50° . Find the measure of each of the other two angles.
2 A fruit seller has three kinds of fruit (banana, grapes and Guava)
If the ratio between the weight of banana to the weight of grapes is 2 : 3 and the ratio between
the weight of grapes to that of guava is 2 : 4 . Find the ratio among the weights of banana, grapes
and guava.
3 If the ratio among the heights of three buildings is 3 : 4 : 5 and if the hight of the first building is
12 metres calculate the heights of the second and the third building.
4 If the ratio among the ages of Hoda, Mona and Ola is 2 : 4 : 5 and if the difference between the
age of Hoda and that of Mona is 8 years. Calculate the age of each of Hoda, Mona and Ola.
5 The ratio between the length and the width of a rectangle is 9 : 5 . If the perimeter of the rectangle
is 56 meters, find out the length and the width of the rectangle, then calculate its area.
6 A triangular piece of land the ratio among the lengths of its side is 4 : 6 : 7 .
If the perimeter of this piece of land equals 51 meters, find the lengths of the sides of the piece
land.
18
The ratio
5 Applications on ratio (The rate)
Notice and Think
What do you learn from this Nabeel held a party for his birthday. He invited 6 friends. He distributed
lesson? 12 pieces of gateaux on
Through your active 6 plates as 2 pieces for
participating you can recognize :
each plate as shown in the
- The meaning of the rate.
opposite figure.
- The unit expressing the rate.
- Solving miscellaneous
applications on the rate.
The ratio between 12 pieces
12
of gateaux to 6 plates is written 2 = pieces for each plate the ratio
6
Mathematical concept
(2 pieces for each plate) is called the rate of distributing the pieces of
- The rate. gateaux on plates and we express it as a ratio which is 2 : 1 .
In spite of the differ between the units of the two numbers of (gateaux
and plate) we can express it in another form which is
2 pieces for each plate, it is denoted by (2 /1 ) where the oblique dash
( / ) means for each or (per).
Such this sign is called a rate
In the previous example it means
The rate of distributing the pieces of gateaux on the plates (2 pieces / plate)
Activity:
If a car covered 180 kilometres within 3 hours then the speed of this
180 km
car is = 06km per hour
30 hours
i.e. The car moves with speed 60 km / hours (which is called the
rate)
The ratio 60km / hour is the rate of covered distance per hour and it
is written as (60km / hour)
19
The first unit
From the previous we deduce that : The ratio between two quantities of different kinds and
The rate is the unit of rate is the unit of the first quantity per each
unit of the second quantity .
Drill (1) Complete the spaces in the following table by writing the suitable rate in front of each
statement as in the example:
The rate
The statement
Symbolically Verbally
A car covers 240km in 3 hours 240/ 3 = 80 km/hour 80km per hour
A family spends LE350 in 7 days ……………. ……LE per day
A secretary lady writes 320 lines within 4 hours ……………. ……. Line per hour
A tap pours 360 litres of water in an hour …………… Litre per minute ….
A butcher sells 108km of meat within 9 hours …………. ……………
Drill (2) A restaurant's owner prepare 80 food meals, all are of the
same kind, using 20kg of meat what is the rate of meat needed
for preparing one meal. What is the rate of meat needed for
preparing 4 meals.
Exercise (1 - 5)
1 Hassan spends LE 45 within three days what is the rate of what Hassan spends per day?
2 A car consumes 20 litre of Benzin to cover a distance 250km. Calculate the rate of consumption
of the car to Benzin.
3 A plough for agricultural land, ploughs 6 feddans within 3 hours.
Find the rate of work of this plough. If another plough, ploughs 10 fedan within 4 hours.
Which of them is better than the other.
20
The ratio
4 A computer colour printer prints 12 paper each 4 minutes. Find the rate of work of this
printer.
General exercises on the first unit
1 Write the ratio between the two numbers in each of the following cases in the simplest form :
(a) 16 and 64 (b) 15 and 105 (c) 128 and 16
2 Write in the simplest form each of the following ratios :
9
(a) 2.7 : 18.9 (b) 5 : 14.5
4
3 Express in two different ways the ratio between each two numbers:
(a) 14 , 128 (b) 2.4 , 18 (c) 185 , 370
4 Write in the simplest form each of the following cases :
(a) half km : 250 metres (b) 125 piasters : 5 pounds (c) 150 grammes : aquarter of kilogram
(d) 2,25 feddans:16 kirats
5 Calculate : using the opposite two figures :
(A)
The ratio between the number of circles in figure. (A) to the number of
circles in figure (B)
the ratio between the number of circles in figure (B) to the number of all
circles in the two figures (A) and (B) . (B)
3
An accountant in a bank earn LE 2000 as a monthly salary. He spends his salary and saves
6 4
the remainder. Find :
(a) The ratio between what the accountant spends to his monthly salary.
(b) The ratio between what he saves to his salary.
(c) The ratio between what he spends to what he saves.
7 Afactory produces 5000 juice cans in 8 hours find the production rate pre hour.
8 Awater tap is leaking 20 litres of water in 5 hours. find the leaking rate of water pre hour. please
advise them:
21
The first unit
Technological activity
calculating the ratio using excel program
What do you learn from this activity
- Inserting a set of data in Excel cells
- Calculating the ratio between two numbers using the properties of Excel program
Example :
A rectangle, its length = 6cm, its width = 4cm calculate its perimeter and its area, then find :
- The ratio between the length of the rectangle and its width.
Practical steps :
1- Click (start) then select program, then select Micro soft Excel.
2- Write the following data in the curtained cells on the screen of Excel program.
3- To calculate the area of a rectangle, determine the cell F4 and write the following:
(D4 x C4 = ) Then click (Enter) to get (24) which is the area of the rectangle as shown in the following
!
figure.
4- To calculate the
ratio between the
length of the rectangle
to its width, determine
area of a perimeter of a rectangl rectangl the two cells D6,
rectangle rectangle width length
C7 and write the
ratio of the leghth to the width
following (D4 C4 / =)
Then click (Enter) to
get (1.5)
22
The ratio
(1) Cut off a rectangular piece of a card paper with length 28cm and width 16cm
shown in the figure.
28 cm
16 cm figure(A) figure(B)
16 cm
(a) Calculate the ratio between the length of the piece of paper and its width.
(b) Shears a square from the piece of paper with side length 16cm (figure A), then find :
* The ratio between the perimeter of the square (figure A) and the perimeter of the whole paper.
* The ratio between the area of figure (B) and the area of the square (figure A).
(C) Calculate the ratio between the side length of the square and the perimeter of figure (B).
(2) You went to grocery shop and you had LE 30. You asked the grocer about the price of one kg of
rice, then he replied : The price is LE 3 . Then you asked him about the price of one kg of suguar, he
3
replied, the price of one kg of suguar = the price of one kg of rice then you bought 2 kg of rice,
4
4kg of sugar. Calculate each of the following:
* The price of one kg of rice.
* The ratio between the price of one kg of rice to the price of one kg of sugar.
* The ratio between what you paid to as a price of rice to what you paid as a price of sugar.
* The ratio between the remainder with you to what you spent.
23
The first unit
Unit Test
(1) In an exam of mathematics in one class the ratio among the weaked pupils to those who succeeded
to the excellent pupils was 1 : 4 : 1 , If the number of all pupils in the class was 30 pupils.
Calculate the number of succeeded pupils and the number of weaked pupils.
(2) The ratio among the lengths of the sides of a triangle is 2 : 3 : 4 . If
the perimeter of the triangle is 54 cm, find the length of each side of
the triangle.
(3) A ship for transporting goods among the countries. Consumms 25
litres of fuel to cover a distance 15km. Calculate the rate of consumption of fuel.
(4) Complete try getting the ratio in each of the following cases :
1
* 250 gm : kg = ………. : ………
2
* 16 kirat : 1 feedan = ……….. : ………..
1
*2 m : 125 cm = ………. : ……….
4
1
* 8 hours : 3 days = …….. : ……….
3
(5) If the ratio between the tallness of Khalid to the tallness of Ahmed is 2 : 3 and the ratio between
the tallness of Ahmed to the tallness of Hani is 4 : 5. Calculate the ratio between the tallness of Khalid
to that of Hani.
24
Second unit
Proportion
first lesson : The meaning of proportion
second lesson : The properties of proportion
third lesson : Drawing scale
fourth lesson: Proportional division
fifth lesson : Percentage
Sixth lesson : Applications on persentage
- General exercises on second unit
- Technology activity
- Portfolio
- Unit' test
Second unit
1 The meaning of proportion
What do you learn from this
Think and discuss:
lesson? If the price of one juice can is LE 2 in one of
- Through your active commerical shops.
participating you will What is the price of two cans?, 3 cans , 4 cans
come to:
……?
* The meaning of proportion.
The following table shows the number of cans
* Writing some forms of
proportion. and the number of pounds representing their
prices in each case.
The mathematical concepts of
proportion. Number of juice cans 1 2 3 4 5 ......
2* ÷2
The price in LE 2 4 6 8 10 ......
It is shown from the table that
First : The number of pounds in each ease is produced by multiplying each number of juice cans
corresponding to it by 2.
In the first case :
The number of cans = 1 then the number of pounds = 1 2 = 2
In the second case 2 2 = 4
In the third case 3 2 = 6 and so on
we can write the ratio between the number of pounds to the number of juice cans in each case as follows
2 4 6 8 10
= = = = =........= 2 constant value
1 2 3 4 5
We deduce that the ratios are all equal
(This form is called a proportion)
Second
The number of juice cans in each case is produced by dividing the corresponding number of pounds
by 2
1
or multiplying it by
2
We can write the rations between the number of juice cans to the number of pounds in each case as
1 2 3 4 5
follows = = = = = = …… (constant value)
2 4 6 8 10
26 A sixth-grader
Proportion
We deduce that all ratios are equal
this form is called a proportion
From the previous we can define the proportion as follows
The proportion is the equality of two ratios or more.
Drill (1)
If the price of one kg of apple is LE 6
Complete the following table . Then write some of forms of proportion:
The weight of apple in kg 1 2 4 ...... 8
×.... ÷ ....
The price in pounds 8 40 48
some forms of proportion are ……… = …… = ……. = ………..
Example (1) :
Complete the following table for the numbers in the first column if it is proportional with the corresponding
numbers in the second column.
3 ×
Then write some of forms of proportion 2
Solution : 2 2
To calculate the missed number in the second column in the third ............ 6
6 ............
and fifith rows we multiply the corresponding number to each of
3 ............ 12
them by to be
2 10 ............
3 6 3 ÷
6 = 3 = 3 3 = 9,
2 2 2
3 10
10 = 3 = 5 3 = 15
2 2
To calculate the missing number for the first column in the second and the fourth rows, we divide the
3
corresponding number to each of them by
2
i.e. multiply 2 to be
3
2 6
6 = 2 = 2 2 =4
3 3
2 12
12 = 2 = 2 4 =8
3 3
After completing the table the proportion will be
2 4 6 8 10
= = = =
3 6 9 12 15
2 4
Some form of proportion : =
3 6
2 6 10 2 4 8
= = , = =
3 9 15 3 6 12
Mathematics 27
Second unit
Drill (2)
Complete the following table for the corresponding numbers if the two rows of the table are
proportional, then write some forms of proportion.
3 6 ...... 15 ...... ....×
4 ...... 12 ...... 28
Exercise (2 - 1)
...... ×
1 Compplete the opposite diagram for the corresponding
16 4 numbers in the two columns of the table are proportional, then
4 ............
complete the form of proportion below the columns.
............ 6
............ 10 4 ..... .... ..... .....
64 ............ = = = =
16 ..... ..... ..... .....
÷ .....
5 ×
2 Complete the opposite diagram for the corresponding 2
numbers in the two columns are proportional then complete 6 15
............ 20
the form of proportion below the columns and write some
15 ............
forms of proportion.
............ 30
14 ............
6 ..... .... ..... .....
= = = =
15 ..... ..... .... .... 5 ÷
2
......×
3
6٫5 1٫3 Complete the opposite diagram for the corresponding
15 ............ numbers in the two columns are proportional, then write some
7٫5 ............ of forms of proportion.
............ 2٫75
12 ............
÷ .....
28 A sixth-grader
Proportion
2 Properties of proportion
What do you learn from this Notice and think through the following figures :
lesson?
2 8 21 7
Through your active
= =
participating you will 3 12 33 11
come to:
In the first case
- determine the properties of 2
proportion.
We multiply the two terms of the ratio by 4 to get the proportion
2 8 3
- determine the terms of =
3 12
proportion
- determine the two extremes In the second case
and the two means of any 21
We divide the two terms of the ratio by 3 to get the proportion
proportion 21 7 33
=
- find a missed term of 33 11
proportion using the other
From the previous we deduce the following property.
given terms
We can form a proportion if we have a ratio as follows :
Mathematical concepts - By multiplying the two terms of the ratio by a non – zero
- The terms of proportion number then the resultant ratio is equal to the first one
- The extremes
(i.e. we get a proportion)
- The means
- Also by dividing the two terms of the given ratio by a non – zero
number then the resultant ratio is equal to the first one
(i.e. we get a proportion)
Notice that :
2 8
In the first case the proportion : =
3 12
The numbers 2, 3, 8 and 12 are called proportional numbers.
The terms of proportion is called as shown in the opposite figure.
2 3 8 12
First term Second term Third term Fourth term
the extremes
The two terms (2 , 12 ) are called the extremes and the two numbers
(3 , 8) are called the means as shown in the opposite diagram. 2 : 3 = 8 : 12
the means
Mathematics 29
Second unit
Drill (1) Notice and complete the following table as in the example
Proportion Terms of Extremes Means
proportion
1 7
4
= 28
1، 4 ، 7 ، 28 1 ، 28 4 ، 7
2 6
6
= 18
2، ..... ، ..... ، ..... 2 ، ........ 6 ، ........
..... 20
..... = 28
5، 7 ، ..... ، ..... 5 ، ........ ....... ، ........
× ......
Drill (2) 1 3
2 ............
A library owner sells the colours case for LE 2
............ 9
complete the opposite diagram of sails. 4 ............
Then write some of forms of proportion ............ 15
.... .... .... .... .... 6 ............
The proportion is = = = =
..... ..... ..... ..... .....
..... ÷
Proportion
Activity: 3 9 7 28 2 24
5
= 15 4
= 16 3
= 36
Think and The product The product The product The product The product The product
deduce
of extremes of means of extremes of means of extremes of means
3 × 15 = 45 5×9= 45 7×16= 112 4×28= 112 2 × 36 = 72 3 ×24 = 72
Compare between the produce of extremes and the product of means in each proportion and show
what you deduce.
You will deduce the following property
If two ratios are equal then
The product of the extremes = the product of the means
Drill (2) Determine which of the following ratios in each case represents a proportion (take the
first case as a hint for you).
2 6
(1) , represents a proportion because
5 15
2 x 15 = 30 and 5 x 6 = 30
i.e. The product of the extremes = the product of the means
30 A sixth-grader
Proportion
6 18
(2) , ……. Because …….. ……. = …… …… = …….
7 21
i.e. The product of the extremes ………. The product of the means.
20 4
(3) , ……… because …….. …… = …….., …….. ……. = ………..
31 8
i.e. The product of the extremes ………. The product of the means.
Example (1) :
Find the missed term denoted by x in the following proportion
2 10
=
6 x
Solution
We can determine the missed term (x) by two methods as follows
First using the correspondence between numbers in rows and columns
(a) by using the correspondence between numbers in rows
First row 2, 10
Second row 6 , x
We notice that 2 became 6
i.e. it is multiplied by 3 2 10
Therefore multiply 10 by 3 to get *3
6 x
x = 10 3 = 30 then the proportion
2 10
because =
6 30
(b) Using the correspondence between the numbers in columns
First column The second column
2 10
6 x
We notice that 2 became 10
i.e. it is we multiply 6 by 5 to get x = 6 5 = 30 then
2 10
the proportion becomes =
6 30
Second : by using the property of proportion which is the product of extremes = the product of means
2 10
since = Then we get 2 x = 6 10
6 x 5
dividing by 2 for the two sides
2 x = 6 10 We get x =
60
= 30 2 10
2 2 2
2 10 6 x
Then the proportion becomes =
6 30
Mathematics 31
Second unit
Example (2) :
If the numbers 4 , x , 12 , 18 are proportional find the value of x
Solution :
Since the numbers are proportional
Therefore we can put it in the form of a proportion which is
4 12
=
x 18
Using the property of proportion which is the product of the extremes = the product of the means we get
12 × x = 18 × 4 dividing by 12
12 x = 18 4 we get =
18
=6
12 12 3
4 12
Then we can write the proportion in the form : =
6 18
Example (3) :
In a shop for selling juice. 2 kg of orange have been squeezed to get 6
glasses of orange juice to clients If 5 kg of orange have been squeezed,
how many glasses of juice will be gotten to offer to clients and how
many kg of oranges are needed to get 27 glasses of orange juice to the
clients?
Solutions :
Such these type of problems can be solved through representing their data in a table as follows .
The weight in kg 2 5 Y
Number of glasses 6 x 27
First :
We can get the value of x regarding 2 , 6 , 5 and x (4 proportional terms)
2 5
Then the proportion is in the form = (from the property of proportion)
6 x
2 x=5 6 (diving by 2)
2x = 5 6 30
then we get x = =15 glasses and the proportion is in the form
2
2 2
2 5
=
6 15
32 A sixth-grader
Proportion
Second :
We can get the value of y regarding 2 , 6 , y , 27 are four proportional terms therefore the proportion
2 y
is = (from the property of proportion)
6 27
Then 6 × y = 2 × 27 dividing by 6
6y = 2 27 we get y = 2 27 = 9kg of orange
6 6 6
2 9
the proportion is in the form =
6 27
Exercise (2 - 2)
1 Find x in each of the following proportions
5 15 x 20
(a) = (b) =
8 x 6 30
2 Find the missed number (x) for the following numbers to be proportional 6, 8 , 3 , x
3 Ali bought 5 kg of orange, he paid LE 15 . How much money does he pay to buy 8 kg?
4 A car consumms 20 litre of Benzin for covering 210 km, How
many litre of Benzin does the car consumm to cover 630 km.
5 The ratio between Hany's weight to the weight of his father = 3 :
5 what is Hany's weight if the weight of his father is 90kg.
6 A primary school, its building height is 14 metre and the shade of
this building at a certian moment is 5m length. What is the height of a
tree in the same moment if its shade length is 3 metres ?
Mathematics 33
Second unit
3 Drawing Scale
What do you learn from this The meaning of drawing scale
lesson?
Through your active Think and discuss
participating you will Khalid made a party for his
come to: birthday. During the party, some
- the meaning of drawing
scale
photo – pictures were taken to
- how to calculate the him and his companies. After
drawing scale in different wards, Khalid measured his
cases
- the relation between length in the picture to be 15cm,
minimizium and enlargement while the real length is 150cm
with drawing scale
that means that 15cm in the picture represents 150cm in reality.
- how to calculate the real
length of a thing i.e. the ratio between the length of Khalid in the picture to his real
- how to calculate the length is
drawing length of a thing.
15 : 150 = 1 : 10
Mathematical concept i.e. each one cm in the picture represents 10cm in reality.
- the real length
- the drawing length That means that
- the drawing scale
- minimization The length of Khalid in the picture 5 1
- enlargement
= =
The real length of Khalid 15 10
This ratio is called (the drawing scale)
The drawing length
i.e. the drawing scale =
The real length
Example (1) :
An engineering design for a villa is made. If the height of the
fence of the villa in the design is 5cm and its real height is 3
metres find the drawing scale.
Solution :
We should convert the two heights to the same unit.
34 A sixth-grader
Proportion
The height of the fence in the picture = 5 cm
the real height of the fence = 3cm = 3 × 100 = 300cm
5 1
The drawing scale = the drawing length ÷ the real length = =
300 60
That means that each 1cm in the drawing represents 60cm in reality.
Example (2) :
Adel took a magnified picture with a camera.
If the length of an insect in the picture is 10cm and its real length is 2mm.
Find the drawing scale.
Solution :
We should convert the two lengths to the same length unit
The real length of the insect = 2mm
The length in the drawing = 10cm × 10 = 100mm
The drawing length 100 50
The drawing scale = =
The real length 2 1
This means that each 50mm in the drawing represent 1mm in reality.
Remark :
1
Now we have a drawing scale less than one which is as in the case of the picture of Khalid and
10
as in the design of the villa. And we have a drawing scale greater than one which is (50 : 1) as in the
case of the magnified picture of the insect.
We deduce that : * If (The drawing scale < 1) this expresses minimization as in the designs
of engineering establishments – Maps of countries – pictures of persons
or places. …. etc.
* If (the drawing scale > 1) this expresses enlargement as in the case of the
picture of the insect – magnifying the picture of a person …… etc.
Mathematics 35
Second unit
Example (3)
If the drawing scale which is registered on a map of some in habitant's cities is 1 : 500000 and if the
distance between two cities on this map is 3cm . Find the real distance between them.
Solution :
The length in the drawing
Since the drawing scale =
The length in reality
1 3
That means : =
500000 The length in reality
And from the property of proportion
The product of the extremes = The product of the means
We get
The length in reality x 1 = 3x500 000
The length in reality = 1500 000
And converting the answer into Km
We get
1500000
The length in reality = = 15 km
100000
Drill
In a mapping picture for some cities is drawn by a drawing scale 1 : 400 000. If the real distance
between two cities is 46 km Find the distance between them on the map
We notice from the previous that
The problems which are connected with the drawing
scale are determined in three kinds they are:-
First kind:- Calculating the drawing scale
(as in examples 1, 2)
Second kind:- Calculating the real length
(as in examples 3, 4)
Third kind :- Calculating The drawing length
(as in The drill)
36 A sixth-grader
Proportion
Exercise (2 - 3)
1 A picture of me of habitation edifices is taken with a drawing scale 1 : 1000. If the height of the
edifice in the picture is 3 cm. What is its real height?
2 Ahmed draw a picture to his brother Osama with a drawing scale 1 : 40. If the real length of
Osama is 160 cm, What is his length in the picture?
3 A magnified picture of an insect was taken with enlargement ratio100:1 If the length of the insect
on the picture is 2.5 cm
What is the real length of the insect?
4 If the distance between two cities on a map is 3 cm, and the real distance between them is 9 km.
Find the drawing scale of the map and what does it mean? Then
If the distance between two cities on the same map is 5 cm. calculate the real distance between the
two cities.
5 Complete the following table.
Drawing enlargement
Description of the case Drawing length Real length
scale minimization
The distance between two
1:50000 2cm ................... ...................
squares on a map of a town
The length of a playground of
1:3600 ................... 12 m ...................
apicture of sport playgrounds
The height of a house on a
................... 3cm 18m ...................
picture of a quarter
The length of an insect on a
................... ................... 2mm ...................
picture of it
Mathematics 37
Second unit
4 The proportional division
What do you learn from this The meaning of proportional division
lesson? Read and think Then discuss Through the following examples
Through your active Example 1
participation you will
A father distributed LE 600 between his sons Maged and Ramez at
come to:
the begining of The school year to buy the school uniform in ratio
- The meaning of proportional
5:7
division
- How to carry out the What is the share of one of them?
operation of proportional Solution
division Magid's share : Ramez's Share
- Solving miscellaneous 5 : 7
applications on proportional i.e the Sum of parts of distributing the sum = 5 + 7 = 12 parts
division 600
i.e The value of each part = = LE 50
12
Mathematical concept
Magid's Share = 5 x 50 = LE 250
-proportional division Ramez Share = 7 x 50 = LE 350
Notice That : In this example The sum of money
is distributed by a given ratio 5 : 7 between two
persons.
Such as this division called proportional
division
Example 2
A man died and left a piece of lend for building, its area is 17 kirats.
We recommended for building on orphan house on area equals 5 kirats. The remainder is distributed
between his son and his daughter in the ratio 2:1. Calculate the share of each of them from the land.
Solution
The remainder = 17 – 5 = 12 kirat
The son's share : The daughter's share
2 : 1
i.e the Sum of parts in which the remained lend will be distributed = 3 parts
that means12 kirat equate 3 parts
38 A sixth-grader
Proportion
12
i.e the value of each part = =4 kirats Notice that in this example, the area of the land
3
The son's share = 4 2 = 8 kirats has been distributed by a give ratio 2:1
The daughter's share = 41 = 4 kirats Such as this division is called proportional
division.
From the previous we deduce that
The proportional division
Is dividing a thing (money, lands, weights, ….)
With a given ratio
Example 3
The number of pupils in the grades four, five, and six) in a primary school is 399 pupils If the number
3
of the pupils of the fourth grade .Equals the number of pupils of the fifth grade and the number
4
6
of pupils of the fifth grade equals the number of pupils of the sixth grade calculate the number
5
of pupils of each grade.
Solution 5 th
The problem will be solved by getting the ratio among 4 grade
th
: : six th grade
grade
the three grades.
4 : 3 :
Using the idea of L.C.M of (3 and 6) which is 18 we
will get that the sum of parts = 24 + 18 + 15 = 57 parts : 6 : 5
That means that 399 pupils equate 57 parts 24 : 18 : 15
i.e The value of each part = 399 ÷ 57 = 7 pupils
The number of pupils of fourth grade = 24 x 7 = 168 pupils
The number of pupils of fifth grade = 18 x 7 = 126 pupils
The number of pupils of fourth grade = 15 x 7 = 105 pupils
Notice that solution is carried out by the idea of L. C. M to get the ratio among three numbers and the
solution is completed as previous.
verifying the truth of the solution
You can check the truth of your solution as follows
The number of pupils of 4 th grade 168 84 12 4
= = = =
The number of pupils of 5 grade th
126 63 9 3
The number of pupils of 5 th grade 126 6
= =
The number of pupils of 6 gradeth
105 5
Mathematics 39
Second unit
Example 4
Three persons participated in a commercial (project) with capital LE 60000.
The first paid LE 15000, The second paid LE 25000 and the third paid LE 20000 At the end of the
year, the profit was LE 5520 Calculate the share of each of them.
Solution
What the 1st paid what the 2nd paid : what the 3rd paid
15000 : 25000 : 20000
15 : 25 : 20
3 : 5 : 4
The sum of parts = 3 + 5 + 4 = 12 parts
That means that
LE 5520 equate 12 parts
5520 Notice That in such as these problems
The value of each part = = LE 460
12 the profits are distributed by the ratio
The share of the First = 3 460 = LE 1380
among the paid money
The share of the second = 5 460 = LE 2300
The share of the Third = 4460 = LE 1840
In the project
Verifying the truth of the solution
You can check the truth of the solution as follows
The share of the first : The share of The second : the share of the third
1380 : 2300 : 1840 (dividing by 10)
138 : 230 : 184 (dividing by 23)
6 : 10 : 8 (dividing by 2)
3 : 5 : 4
This are the some ratio among. The paid money by each person
Example 5
A load of apple fruit weighs 280 kg. is distributed among three
merchants .
2
The share of the first = the share of the second and the share
3
3
of the second = the share of the third.
4
Calculate the share of each of them from this load.
40 A sixth-grader
Proportion
Solution
The share of the 1st The share of the 2nd the share of the 3 rd
2 : 3
4 : 5
8 : 12 : 15
Notice that (L.C.M) of (3,2) is 6 therefore
The sum of parts = 8 + 12 + 15 = 35 parts
That means
280 kg equate 35 parts
280
I.e The value of each part = =8kg
35
The share of the first = 8 x 8 = 64 kg.
The share of the second = 12 x 8 = 96 kg
The share of the third = 15 x 8 = 120 kg
Verifying the truth of the of solution you can check the truth of the solution as follows .
The share of the first : the share of the second
64 : 96 (dividing by 2)
32 : 48 (dividing by 16)
2 : 3
This is the given ratio.
The share of the second : the share of the third
96 : 120 (dividing by 2)
48 : 60 (dividing by 12)
4 : 5
This is the given ratio.
Drill
Hoda, Mona and Thanaa participated in a commerce. Hoda paid LE 1500, Mona paid LE 2000 and
Thanaa paid LE 2500. At the end of the year the loss of the company was LE 1200 Find the share of
each of them from loss.
Mathematics 41
Second unit
Exercise (2 - 4)
1 A piece of building land is distributed between two brothers in the ratio 7:5 . If the share of the
first one exceeds the share of the second by 80 square metre. Find the area of the land and the share
of each of the first and the second.
2 The number of pupils of a primary school in the 1st, the 2 nd and the 3 rd grades is 240 pupils. If
the ratio among the three grades is 5 : 4 : 3.
Calculate the number of pupils in each grade.
3 A father distribute LE 225 among his three sons. The share of the first was third of the sum and
the ratio between the share of the second and the share of the third was 2:3. Find the share of each
them.
4 for solving the illiteracy problem at a village 3 classes have been opened for solving this problem,
the number of learners was 92.
2 5
Person. If the number of learner in the 1st class = the number of learners in the 2nd class =
3 7
5
and the number of learners in the 2nd class . = the number of learners in the 3rd class.
7
5 3
In one of our schools, there are 560 students, if the number of girls = the number of boys
5
find each of the number of looys and girls?
42 A sixth-grader
Proportion
5 Percentage
What do you learn from this Notice and think
lesson? The apposite figure represents a big square
Through your active
divided into 100 small squares, all of them
participation you you will
come to:
are equal in side length.
The meaning of percentage The ratio between the shaded part by green
- How to calculate the 28
calour to the big square = or 28 : 100
percentage of a thing . 100
Notice that the first term in this ratio is 28
- Converting the percentage
and the second term of the ratio is 100 such as this ratio is called
to a fraction.
- converting a fraction to a a percentage and it is written in the form 28 % and it is read 28
percentage. percent.
- solving life problems on
parentage. From the previous we deduce that
The percentage is a ratio its second term is 100 and it is
Mathematical concept
-The percentage
denoted by %
Notice from the figure that
The ratio of the unshaded part = 72 % and it is read as 72 percent
The ratio of the shaded part and the unshaded part = 100 % – 72 % = 28 %.
Drill
Write the percentage which expresses the shaded part and that which represents the unshaded part
below each figure
- The percentage of The percentage of The percentage of
the Shaded part = ............. the shaded part = …….. the shaded part = …….
The percentage of The percentage of The percentage of
the unshaded part= …….. the unshaded part =… the unshaded part = ……
Mathematics 43
Second unit
Remarks from life
- When you enter a bank or post office and you read the statement.
The interest of the saving card is 10 % in the year.
That means that each LE 100 has an interest or profit = LE 10 so the total amount = EL
10
110. That because the interest (10% for each LE 100) is calculated as follows x 100 =
100
LE 10 which is add to the sum LE 100.
- When you read the statement (The percentage of the discount is 30%) in a commercial
shop. That means that.
Each LE 100 has a discount = LE 30 and you pay to the shop LE 70 only That because the
percentage of discount (30 % for each LE 100) is calculated as follows .
30
x 100 = LE 30 which is discounted from each LE 100 as paying
100
- When you read on a piece of clothes the following statement (the ingradients 45 % wool,
25 % cotton30 % synthetic) that means that the sum of all these ingradients = 45 % + 25
% + 30 % = 100%
Remark
100 % of amount = The all amount.
100
It means from the amount
100
= the total unit of the amount
i.e the total amount.
Drill (1)
Explain the meaning of the following statements
- The discount on purchases 22%
- The interest on saving money = 9.5%
- The ingredients 100 % Cotton
- The ingredients 55% wool and the remainder is synthetic
Drill (2)
Calculate the paid money for the following purchases in a company.
Which offer discounts or its sails
1- A shirt, its price is LE 65 and the discount is 15 %.
2- An Iron, its price is LE 120 and the discount is 20%
3- A computer, its price is LE 2700 and the discount is 9%.
44 A sixth-grader
Proportion
Converting a percentage into a common fraction or a decimal.
Example 1
In a class the number of bogs was 35% from the total
number of pupils .
- What is the percentage of girls?
- Convert each of the previous percentage into a common
fraction them to a decimal.
Solution
- The percentage of girls = 100% - 35% = 65%
- Converting the percentage into to a common fraction
35 7
The percentage of bays is 35% = = (common fraction)
100 20
65 13
The percentage of girls is 65% = = (common fraction)
100 20
- Converting the percentage into a decimal
35
The percentage of boys is 35% = = 0. 35 (a decimal)
100
65
The percentage of girls is 65 % = = 0. 65 (a decimal)
100
Drill (3)
An agricultural piece of land. The cultivated part of it by vegetable is 40%
Convert this percentage to common fraction and to decimal.
Converting a common fraction or a decimal into percentage)
Example2
In a village the ratio between the not educated people to those
who are educated is 4 : 25
Write this ratio in the form of a percentage
Mathematics 45
Second unit
Solution
4
4:25 is equivalent to
25
4
To convert to a percentage we should make the second term in this ratio = 100 This will be
25
multiplying the two terms by 4 .
4 4 4 16
i.e = x = i.e 16%
25 25 4 100
Remark
Drill (5) To convert the common
Convert each of the following Common fractions into percentage fraction into percentage we
as the first case try to make the denominator
= 100
3 This will be done by
a) b) 0.12 c) 0.652
4 dividing the fraction by 100
and multiplying it by 100
Solution
3 3 25 - to convert the decimal into
= x = 75 %
4 4 25 percentage we convert it to
a common fraction and do
.....
b) 0.12 = . = …..% what we did before
....
625 ......
c) 0.625 = x .
1000 ....
...... ......
= x = …….%
.... ....
Example 3
In an English exam, Adel scored 13 marks from 20 marks find the percentage of the scared mark of
Adel in English.
Solution
13
The mark of Adel in the exam =
20
13 100 65
The percentage of Adel's mark = x = = 65%
20 100 100
46 A sixth-grader
Proportion
Exercise (2 - 5)
1 In a school trip, 12 pupils from 35 pupils in a class have participated find the percentage of the
participant pupils.
2 Complete the following table as in the example
The fraction The percentage The symbol Verbal expression
75
0. 75 100 75% 75 precent
............ ............ 6 precent
0.06
............ .................... 40% ............
11 ............ ................
25
3 Magid bought a T- shirt, labelled on a small card on it (made of cotton and synthetic).
The percentage of the synthetic 40 % only calculate the percentage of cotton then find the equivalent
fraction to each percentage.
4 If the percentage of the number of girls in a class whish is mixed is 67% find the percentage of
the number of boys in this class.
5 In a conditioned carriage in a train the number of occupied seats is 46 seats if the number of seats
of the carriage is 60 seats . calculate.
a) The percentage of the occupied seats.
b) The percentage of the empty seats related to the number of occupied seats.
6 A man died and left a piece of land whose area is 48 kirat.
He recommended, the half of this area is for building a school, the remained is distributes as
follows.
1
The remainder is for his wife, the remainder after That is distributed among his two sons and his
8
three daughters such that the share of the boy is twice the share of the girl.
Calculate the share of each of them.
Mathematics 47
Second unit
6 Applications on the percentage
What do you learn from this First: Calculating the interest or discount.
lesson?
Through your active
Example 1
participating you will Sara deposit LE 9000 in a bank.
come to: The percentage of interest is
How to calculate the
11% per year.
interest, discount, given the
percentage of each of them. What is the amount of this sum
How to calculate the after one year.
percentage of the profit or
Solution
loss given the value of each
of them. The deposit sum = LE 9000
How to calculate the selling 11
the interest = x 9000 =
price givem the buying price 100
and the percentage of profit LE 990
or loss how to calculate the The amount of the sum after one year = the sum + the interest
buying price given the selling
= 9000 + 990 = 9990 pounds
price and the percentage of
profit or loss. Example 2
In one of commercial shops the percentage of the discount on sails is
Mathematic concerts
- The interest, discount.
20%. If Ahmed bought a trousers,
- The profit, the loss The price written on it was LE 80 find what Ahmed paid after the
- The selling price- discount.
-The buying price
- The percentage of increase Solution
or decrease. The essential price of the trousers = LE 80
20
The discount = x 80 = LE 16
100
What Ahmed paid = The essential price – The discount
= 80 – 16 = LE 64
Drill (1)
In one of commercial shops, the milk box is bought for LE 5. If you bought two boxes there will be a
discount = 15 % for each two boxes. Calculate the buying price of 6 boxes of milk .
Is the saved money enough to buy any boxes of milk ?
48 A sixth-grader
Proportion
Second
Calculating the percentage of profit or loss
Important remarks
- The profit means = Selling price – (buying price + costs)
- The loss means = (buying price + other costs ) – selling price
Example 3
A showkeeper of cars bought a car for LE 45000 Them he spent LE
3000 for repairing it Then he sold it for 50000 pounds Calculate the
percentage of profit
Solution
The original price of the car = LE 45000
The Costs of repaining it = LE 3000
The profit after selling = The selling price
- ( The baying price + Cost price)
= 50000 – (45000 + 3000)
= 50000 – 48000 = LE 2000
2000 2 4
The Percentage of the profit = = = = 4%
50000 50 100
Example 4
A fruit seller bought a load of fruit for LE 18000 After buying it he found a bad prat of it because of
miss – shopping.
He bought the remainder for LE 16000 find the percentage of his loss.
Solution
The original price of fruit = LE 18000
The selling price = LE 16000
i.e the loss = 18000 – 16000 = 2000 pounds
2000 1 1 100
the percentage of loss = = =
18000 9 9 100
=11.11%
Mathematics 49
Second unit
Third :- Calculating the selling price and the buying price
Example 5
Find the buying price of good sold for LE 21520 and the parentage of profit is 15% and find the
profit.
Solution
Buying price profit selling price
100 15 155 (number of parts)
? ? 21520 (values in pounds)
100
Since the buying price = x the selling price
115
100
x 21520 ≃ LE 18 713
115
The profit = selling price – buying price
= 21520 – 18713 = LE 2807
Drill (2)
complete the following table.
The kind Buying Selling profit Percentage of
price price profit
TV 1800 2000 .................. ..................
Refregerator 2400 .................. .................. 12%
Washing .................. 3100 175 ..................
maching
Drill (3)
Heba bought an electric sweeping machine for LE 220, if the discount is 15% Calculate the original
price of the sweeping machine before discount.
Drill (4) Complete the following table.
The original price Percentage of Discount The price after
discount discount
560 10% ................ ..................
................ 15% 65 ..................
................ .................. 32 192
50 A sixth-grader
Proportion
Exercise (2 - 6)
1 If the percentage of the succeeded pupils in an exam. In Arabic in sixth grade in a school is 85%.
Calculate the percentage of failures then write each of the percentage of succeeded pupils and failures
in the form of a common fraction in its simplest form
2 In an European city, the percentage of ill people by flue is 0.12% writ this percentage in the form
of a common fraction in its simplest form.
3 Write in the form of a common fraction in the simplest form each of the following percentages
28%, 8.5%, 20.4%
4 Hassan ate 3 pieces of gateaux from a box contains 24 pieces of gateavx in a party of his
birthday. And he distributed 6 pieces on his family. Calculate the percentage of the number of pieces
that Hassan ate and the percentage of the number of pieces eaten by his family.
5 Hani did not go to his school for 8 days within the school year. If the number of days of the
school year is 214 days .
Calculate the percentage of the number of days in which Hani was absent.
6 In a day 12 pupils were absentees from a primary school whose number of pupils is 350 pupils.
Calculate the percentage of the present pupils and that for the absentees in that day.
7 Khaled bought a flat for L.E 150 000, After selling it he found that the percentage of his loss
was 5%
Calculate the selling price of the flat.
Mathematics 51
Second unit
Gerberal exercises on the second unit
1 Complete the following table for the corresponding numbers in the two rows of the table are
proportional. Then write some form of this proportion.
2 5 ...... 8 ......
...... ......
12 ...... 36 ...... 60
2 Find the number x in each of the following cases
2 8
a) =
7 x
b) If the numbers 9, 21, 3 and x are proportional
c)
x
=15 % d) x 18
=8
9 9
3 If the distance between two cities on a map is 10 cm, the real distance between them is 120 km,
Find the drawing scale of the map. And if the distance between two other cities on the same map is 6
cm calculate the real distance between them.
4 A picture was take to an artificial scene with a drawing scale 1:100.
If the real length of a tree is 8 meter find its length in the picture.
5 two persons started a commercial business the first paid LE 5000 and the second paid LE 8000,
At the end of the year the profit was lE 3000. Calculate the share of each of them from the profit .
6 A company for selling the electric sets It shows T.V for LE 2100. If the percentage of the profit
is 12 % find the buying price of t.v
52 A sixth-grader
Proportion
A technological activity
The subject of the activity
Converting the decimal to a percentage using Excel programme.
What do you learn from this activity?
- Open Excel programme through the computer.
- Enserting data through Excel programme.
- Converting the decimal into a percentage using the properties of Excel programme
An example:-
Convert each of the following decimals into a percentage
(a) 0.26 (b) 0.058.
Practical procedure.
1- Click (start) then select program them select Microsoft Excel.
2- write the following data in the determined cells on the screen of the program as in the flowing figure .
3- To Calculate the percentage of the decimal (0.26) determine the cell D 4 and write the following
(100/ B4 100= )
Then click (Enter) then the result will be appear to 26 %
To Calculator the percentage of the decimal 0.085, determine the cell D5 and write the following (100
/ B5 x 100 = ) then click (Enter ) to appear the result (5.6%) as shown in the following figure.
!
percentage decimal fraction
Mathematics 53
Second unit
olico
Port f
1- A triangular garden in a school the ratio between its sides lengths is 3:4:5. If the perimeter of the
garden is 120 meter. Calculate the lengths of the sides of the garden.
2- Hani travelled with his father from Cairo to Esmaellia. He has a map
for Egyptian governorates. His father asked him to measure the distance
between the two governorates on the map he found it 1.3cm them he
asked the driver about the real distance between the two governorates,
he replied 130 km.
Calculate the drawing scale of the map which is with Hani.
The test of the unit
1- Find the missed number (x) if the numbers 3, 4, 9, x are proportional
2- Write in the form of a common fraction in its simplest form each of the following.
33% , 10.5 % , 75 %
3- The number of pupils of grades first, second and third in a primary school is 475 pupils If the ratio
among the number of pupils in the first grade to those of second grade to those of the third garde is
6:5:4
Calculate the number of pupils in each grade.
4- Nahed bought an automatic washing machine for LE 3400 and the discount was 10% Calculate
the original price of the washing marching. Before discount .
5- An edifice of height 12 meters. It's shade at a momoment was 4 meters. What is the height of a tree
neighboured to the edifice if its shade = 2 meter long at the same moment.
6- Hani, khaled and fady shared a commercial business, Hani, paid LE 30000, Khaled paid LE 40000
and fady paid LE 5000
At the end of the year the loss was 5000 pounds find the share of them from the loss.
7- A shop keeper for electric sets sold a refrigerator for LE 3200 If the percentage of his profit is 6%
find the baying price.
54 A sixth-grader
The third unit
Geometry and measurement
The first lesson: The relations between the
geonetrical shapes .
The second lesson :- the Visual patterns
The third lesson :- Volumes
The forth lesson :- The volume of the cuboids
The fifth lesson :- the volume of the cube
The sixth lesson:- Capacity
General exercise on the unit .
technological activity.
portfolio
test of the unit.
Geometry and mea
sure
1 The relations between the geometrical shapes
Activity1
Notice and deduce
What do you learn from this D A
lesson?
Through your active participation
you will come to:-
- deducing the properties of the
parallelogram .
- the relation between the
parallelogram and each of the C B
rectangle, the square and the
fig 1
rhombus.
In the fig 1
- Solving miscellaneous
applications using the properties ABCD is a parallelogram that means
of the geometric shapes and the
relatians between them. AB = DC, AD // BC
First:-
Mathematical Concepts Using the geometric tools in fig 1 Check that
The two consecutive angles in 1- AB = DC, AD = BC
the parallelogram.
2- m (∠A) = m (∠C)
m (∠B) = m (∠D)
3- m(∠A) + m (∠B) = 180
m (∠B) + m (∠C) = 180
D A
Second:-
Using the geometric tools in fig (2) Check that
M
AM = CM , BM = DM
C fig 2 B
From first and second we deduce that
The parallelogram is a quadrilateral in which :-
- Each two opposite sides are parallel and equal in length .
- Each two apposite angles are equal in measure .
- the sum of the measures of any two consecutive angles equals 180° .
- The two diagonals bisect each the other.
56 First Term Mathematics
The third unit
Study the figures on the square lattice then complete and deduce
Drill 1
D A E
L X
N F
C B Z Y L
(1) (2) (3)
ABCD is a rectangle X YZL is EFLN is
In which a square in A rhombus in which
which
AD // …… EF // …….
XL// …..
AB // …… FL // …….
XY // …….
From the cases 1 , 2 , am 3 Each of the rectangle, the square and the rhombus is a parallelogram.
we deduce that
We can summarize that is the following sketch of concepts.
A rectangle If of its angles is right
one
the If of its angles is right and two adjacent
Is
a square one
parallelogram : sides or equal in length
If adjacent sides are equal in
arhombos two
length or its diagonals are perpendicular
Drill 2 D 7 cm A
Discus with your group
The opposite figure 4cm
ABCD is a trapezium in which m (∠B) = 90,
AD = 7 cm , AB = 4cm
BC = 10 cm , DC = 5 cm C 10 cm B
Locate the point X cn BC for the figure ABXD is a rectangle In this case there will be
Mathematics Sixth grade of primary 57
Geometry and mea
sure
AB = ….. = ……. cm , AD = …… = …… cm
Example 1
In the opposite figure in (∠A) = 60 , m (∠D BC) = 53°
D A
AM = 6 cm, AB = 5 cm, BC = 8 cm 53°
Calculate without using measuring tools each of 6 cm
m
1- m (∠ ABD) M
5c
2- m (∠D) 45°
C 8 cm B
3- AC
4- AD , DC using the properties of the parallelogram.
Solution
The first required:-
Finding m (∠ ABD)
Since m (∠A) + m (∠B) = 180ْ (two consecutive angles)
Then m (∠ABD) = 180- (53 + 45) =82ْ
The second required.
M (∠D) = m (∠B) (two opposite angles)
The m (∠D) = 82 + 45 = 127ْ
The third required
AC = AM + CM = 6 + 6 = 12 cm
(The two diagonals bisects each other)
The foorth required D A
AD = BC = 8 cm (The two opposite sides are equal in length)
Drill 2 In the opposite figure
E
C B
AD // BC , AB // DC
N F
DF // CL
Name and write 3 parallelograms
In the figure
Name and write 3 trapeziums in the figure
Name and write 3 triangles in the figure
58 First Term Mathematics
The third unit
Exercise (3-1)
1
complete the following due to what you studied about the properties of geometric shapes
a) The four sides are equal in length in each of …. , …….
b) The two diagonals are equal in length in each of …., …..
c) The two diagonals are perpendicular in each of …… ,……
d) The four angles are right in each of ….. , …..
e) the two opposite angles are equal in each of ……,…… ,…..,…..
f) The two diagonals bisects each ether in each of ….., ….., ……
g) The sum of measures of the two consecutive angles equals 180ْ in each of …., ….., ……
2 In the opposite figure try to use the
geometric tools
To get the greatest possible number of
parallelogram
Colour the resuting paralleleograms in
different colour
B A
°
30
the opposite figure shows a
3 parallelogram in which.
M(∠B) = 110 , m (∠DAC) = 30ْ
° 110 Find m (∠D) , m(∠BAC)
C D
m (∠ACD)
Mathematics Sixth grade of primary 59
Geometry and mea
sure
D A
4
In the opposite figure
ABCD is parallelogram in which
AB= 9 cm , BC = 6 cm . Determine the point X an the side AB
such that AX=BC 9 cm
And determine the point Y on the side DC such that DY = BC
Complete the following
- The figure AXYD represents ……. Because ……. C B
6 cm
- The figure ABCY represents ……. Because ……
- The figure XBCY represents ……. Because …….
- The type of the triangle AXY according to its sides
is ……………… because ………………
5 Complete the following sketch of concepts using the key words below it
The parallelogram
........ ......
....................... If
. ..
...... ..........
a rhambus
...... .. ..... ...... .......
If ............. ...... If ...... If .............
. ......
One of its angles is ....................... Its sides are equal
right and the two in length or the two
diagonals are equal ........ ...... diagonals are …….
in length
Its adjacent sides are equal
in length and its angles are
The key words right
A square
is the two dimensions
A rectangle are equal
are Perpendicular
the two diagonals
If
are equal in length
60 First Term Mathematics
The third unit
2 The visual patterns
What do you learn from this Think and discuss
lesson?
Through your active In the previous years you have studied the visual patterns and the
participation you will
recognize numerical patterns
- The concept of visual
pattern - the visual pattern is a consequence of shapes or
symbols according to a certian rule.
- discrebe the visual pattern
- Discovering visual patterns
and completing its repetition.
- forming visual patterns from The following examples represents visual patters and its
geometric shapes
- Discovering the visual description is below it.
patterns in our natural life.
- forming repetition of the
pattern and colouring it
suitably to form on art figure
(The description of the pattern is repetition of)
Mathemalical
- concepts
- visual pattern
(The description of the pattern is repetition of ) ............
Drill 1
Discover the pattern in the following, then write its description and complete its repetition twice
...................... -
……… ( the description of the pattern ………)
................. -
…….. ( the description of the pattern ………..)
Mathematics Sixth grade of primary 61
Geometry and mea
sure
Drill 2 Discuss with your group , then draw the next shape in each pattern in each of
the following.
1- ……………………
2- ……………………
3- … …………………
4- ……………………
Drill 3 Study the following geometric shapes, form visual patterns from it then describe
each pattern and repeat it twice
the shapes
Example
(the descption of the pattern is repaating )
1-............................................. ( the descption of the pattern.............................................................)
2-............................................ ( the descption of the pattern..............................................................)
Drill 4 In our natural life there are many visual pattern, discover the pattern in each
case in the following then coloure it with suitable coloure.
! ! ! !
62 First Term Mathematics
The third unit
Exercise (3 - 2)
1 Discover the pattern in each case of the following and describe it then
complete its repetition twice
............................................
............................................
............................................
............................................
2 Discover the pattern,describe it, then
complete by repeating it(twice)
3 Discover the pattern and colour it's
repetition in each shape alone with
different colours to get an art figure
!
Mathematics Sixth grade of primary 63
Geometry and mea
sure
3 Volumes
What do you learn from this 1- The solids
lesson ?
Through you active You studied in the previous years the solids and you knew that .
participation you will come to:
- The concept of the solid all the following represents a solida
-The concept of volume The case of geometical instruments – the pen , The match case –
- The volume units
mobile set ,the water bottle, the cube games, the ball bus , the car
the house in which you live …. tc
- Calculating the volume of
a solid by counting the units
this means that solid which occupies a roomin thes pace
which formed it.
Notice that
- converting from a unit of
volume to another unit of The solids are two kinds
volume.
- The geometric solid such as:
Mathematical concepts
The solid
The volume
The decimeter cube
The meter cube
The millimeter cube. The cube the cuboid the cylinder
The sphere the pyramid the cone
And other solids which has no geometric shape as.
!
collapsed house a Car seashell a piece of stone
64 First Term Mathematics
The third unit
this year we will give importance to two solids which are.
The cuboid
- It has six faces each of them is a rectangle.
- It has 12 edges and 8 vertices
the cuboid
- Each two apposite faces are equal in area and they are parallel .
- Each two adjacent faces intersect at a line segment which is called on edge
The cube
- It has six faces each of them is a square (They are all equal in all measures.
( congruent)
- It has 12 edges , they are equal in length. It has 8 vertices
The cube
B- The volume
If The solid is any thing occupying a room in the space then .
The volume is the magnitude of this room which the solid occupies in the space.
How can we measure the volume?
! !
We can consider any solid as a unit for measuring the volume as
Match case – cube game – a bloc of soap – Juice can ….. etc
! !
In This case the volume of the solid is the number of these units contained by the solid.
! !
!
The number of blocks The number of juice cases The number of match - cases
of soap = 24 = 18 = 25 cases
The volume of the solid The volume of the solid = The volume of the solid = 25
= 24 cases 18 cases cases
Mathematics Sixth grade of primary 65
Geometry and mea
sure
Drill 1 Each of nada , Maryam, Omar and Magid builds a solid from cubes. Considering one
cube is a uint for the valume complete the following table.
Solid of Maryam solid of Omar solid of Nada solid of Magid
The number of The number of The number of The number of
Cubes = …….. Cubes = …….. . Cubes = …….. Cubes = ……..
The volume = The volume= The volume= The volume=
From the previous table compare
- the solid formed by Omar occupies a room in space …….. that the solid of Nada.
- The solid formed by Magid occupies room in space …… than the solid of Maryam .
- The solid formed by Omar occupies a room in space ……. Than the solid Maryam
Notice That
The previous units used to measure the volume (soap plocks – Match cases, cube games …..)
not international units to measure the volume because the volume of the solid changes if we change
the used unit in measure and depends on the person who does the measure .
Then it is necessary to search for constant units agreed by the whole world to use them to measure
the volume.
It is agreed to consider the cube whose edge length = (1 cm) as shown in the figure is the unit for
measuring the volume.
i.e The unit which is used for measuring the volume is
The centimeter cube
It is the volume of a cube of edge length equals 1 cm 1 cm
It is denoted by 1 cm3
1 cm
1 cm
66 First Term Mathematics
The third unit
Example 1
Find the volume of the following solids consider the unit of measure of the volume is cm3 (1cm3)
Fig. (1)
fig. (2) fig. (3) fig.(4)
Solution
In fig. (1) the number of cubic units = 5 units The volume of the solid = 5 cm3
In fig (2) The number of cubic units = 8 units The volume of the solid = 8 cm3
In fig (3) The number of cubic units = 16 units The volume of the solid = 16 cm3
In fig (4) The number of cubic units in each Layer = 9 cubic units
The solid consists of 3 layers
The number of cubic units in the solid = 3 x 9 = 27 units
The volume of the solid = 27 cm3
Another units for measuring the volumes
(a) In the case of great volumes
1- The decimeter cube
1 دي�سم
It is the volume of a cube of edge length one decimeter (1 dm) as
shown in the figure. It is denoted by (dm3) It is used sometimes to
measure the volume of solids as the iron boxes, the carton case of 1
دي
�سم
television, washing machine or computer …. Etc 1 دي�سم
21 is formed from 10 layers in each of them 100 cm3
2- The meter cube
It is the volume of a cube of edge length (1m) as shown in the
10 dm
figure It is denoted by (metre3) or (m3) it is used sometimes to
measure the volume of containers of factories or water tanks or
edifices …. etc, it consists of 10 layers in each of them there are
100 dm3
1m
10 dm
(b) In the case of small volumes
The millimeter cube
It is the volume of a small cube of edge length 1 millimetr
It is denoted by (m m3)
It is used to measure the small volumes
Mathematics Sixth grade of primary 67
Geometry and mea
sure
Now we deduce that. x1000
1m3 = 10 dm x 10 dm x 10 dm = 1000 dm3 1000 dm
3
1dm3 = 10 cm x 10 cm x 10 cm = 1000 cm3 1000 cm3
1 cm3 = 10 mm x 10 mm x 10mm = 1000 mm3 1000 mm3
1000÷
large unit small unit
Notice that as converting from a large unit of volume to smaller unit of volume we use
multiplication operation.
As converting from a small unit of volume to larger unit of volume we use division operation.
Example 2: convert each volume's unit in the following to the opposite volume's unit
1- 4 m3 = ……………….. = ………….. dm3 2- 0.5 cm3 = …………… = ……… mm3
3- 300 mm3= ……………. = ……….. cm3 4- 6500 dm3 = …………. = ………………m3
Solution
(1)- 4 m3 = 4 x 1000 = 4000 dm3 (2)- 0.5 cm3 = 0.5 x 1000 = 500 mm3
(3)- 300 mm3 = 300 ÷ 1000 = 0.3 cm3 (4)- 6500 dm3 = 6500 ÷ 1000 = 6.5m4
Drill 1 Calculate the volume of each of the following solids consider the volume unit is cm3
Fig (1) Frg. (2) Frg. (3)
Fig (4)
The number of cubic The number of The number of cubic The number of cubic
units = ……… cubic units = ……. units = …………. units = …………
The volume of The The volume of the The volume of the The volume of the
solid = ….. cm3 solid = ….. cm3 solid = ….. cm3 solid = …… cm3
68 First Term Mathematics
The third unit
Exercise (3 – 3)
1 Find the volume of each solid in the following considering the volum's unit is cm³:
Fig (1) fig (2) fig (3)
The volume of The volume of
The volume of
The solid = .cm³ The solid = .cm³
The solid = .cm³
Fig (4) Fig (5) Fig (6)
The volume of The volume of
The volume of
The solid = .cm³ The solid = .cm³
The solid = .cm³
Find the volume of each of the following solids
2 considering the volum's unit is the games cube whose
volume is 8 cm³.
3 Convert each of the following volumes into the opposite volume's units:
(a) 120dm³ = .. =....................cm3
(b) 8200mm³ = .. =....................cm3
(c) 3m³ = .. =....................mm3
(d) 2.1cm³ = .. =....................mm3
(e) 56000cm³ = .. = .. =....................dm3
Mathematics Sixth grade of primary 69
Geometry and mea
sure
4 The volume of the cuboid
Think and discuss
What do you learn from this
lesson?
The teacher of mathematic asked his
Through your active
participation you will come to :
students to make groups, each consists
of 2 pupils to work together to use games
- How to calculate the volume
of a cuboid by different ways. cubes for making a cuboid of dimensions
- Solving miscellaneous the length 4 cubes, the width 3 cubes, the
applications on the volume of fig (1)
the cuboid. height 2 cubes. After giving the suitable
chance the teacher selected the design of (Ola and Nabeela) as in
figure (1). He asked them to show their idea to their companions.
Ola : We thought together to form the first
The mathmetical concepts
layer which is formed from 3 rows in each
- The cuboid
- The volume
row 4 cubes, then the length of the layer
became 4 cubes and its width became 3
cubes as shown in figure 2. fig (2)
Nabeela : We formed the second layer in the same way and put it on the first, then we get the required
cuboid. Fig (1)
The teacher : Thanks for you all, the question now is : How can we calculate the volume of the
resultant cuboid?
Mohamed : The volume is the room occupied by the cuboid in the space.
The teacher : Wonderful, but How can we calculate this room?
Adel : We count the volume units used which is the games cubes.
The teacher : Good answer – but How can we carry out this operation?
Merna : We count the volume units in the first layer which is 3 row and each rows contains 4 cubes,
then its volume is 4 × 3 = 12 cubes.
The teacher : Very good – Then what afterwards?
Ahmed : We count the volume units in the second layer in the same way i.e. its volume = 4 × 3 = 12
cubes.
The teacher : Very good. What later?
70 First Term Mathematics
The third unit
Omar : We add the volume cubes in the two layers, the volume of the cuboid = 12 + 12 = 24 cubes.
The teacher : Excellent answer. Who can get the same answer by another way?
Karmina : We multiply the volume of one layer by 2.
Then the volume of the cuboid = (4 × 3) × 2 = 24 cubes.
The teacher: Very good. But what do we mean by 4 × 3 × 2?
Mina : it represents the product of the length × the width × the height.
The teacher : That is best. Who can express this result in another form?
Khalid : The product of the three dimensions.
The teacher : Excellent answer. But what's ment by (the length × the width)?
Fady : It represents the area of the base.
The teacher : Very good. Who can express the volume of the cuboid in another way?
Zeinab : The volume of the cuboid = The base area × The height.
The teacher : That is a correct answer and now who can summarize the mathematic statements of the
volume of the cuboid?
Mustafa : There are four correct statements which are.
!
The volume of the cuboid.
= The number of the volume units which form it.
14
��!
=The product of length x width x height.
= The product of the three dimensions.
19
��!
= The base area × The height.
The teacher very good - What is the volume of the cuboid in fig (1) if it is
rotated as in the figure (3).
Nady :- the volume = the base'area x the height. = (4x2) x 3 = 24 cubes
The teacher very good answer what does that mean upon your own views.
Hassan: the volume does not change
That means
We can consider any face of the cuboid as a base for it. fig (3)
Mathematics Sixth grade of primary 71
Geometry and mea
sure
The volume of the cuboid = the area of any face x the corresponding height.
The teacher: Excellent answer
And now what about if the units of volume became the (cm3) instead of gams cubes as in fig. (4).
What is its volume?
Shady: cm3 is the unit of measuring the volume
In this case the volume of the cuboid = 4x3x2 = 24 cm3
The teacher:- Excellent answer and thanks for you all.
fig. (4)
Example (1) find the volume of the cuboid in each of the following cases.
3 cm
7 cm
m
4 cm 2c
9 cm m
fig. (1) 3c
fig. (2)
Solution
In fig . the volume of the cuboid = length x In fig. (2) the volume of the cuboid = the
width x height. area of the base x the height
= 4 x 2 x 3 = 24 cm3 = (9 x 3) x 8 = 216 cm3
Notice from fig. (2)
the volume of the cuboid
The area of the base of the cuboid =
the height
the volume of the cuboid
The height of the cupoid =
the area of the base
72 First Term Mathematics
The third unit
!
Example 2 In The opposite figure
A cuboid of volume is 2128cm3
14
Its length is 19cm, its height is 14cm ��!
Find the area of its base and its width
Solution
19
The volume of the cuboid = The area of the base x The height ��!
i. e 2128 = The area of base x 14
That means
2128
The base area = = 152 cm2
14
Since the base area = length x width
!
That means The width = 152
19
i.e. The width = 8 cm
Example 3
40 cm
A box made of cartoon in the shape of a cuboid, its internal
dimensions are 50, 40 and 30cm. How many blocks of soap
can be put inside it to be full completely if the dimension
of each block of soap are 8,5 and 3cm. cm
30
!
Solution 50 cm
The volume of the box = 50 x 40 x 30 = 60000 cm 3 8 notice the position of the block of
5 3 soap
!
The volume of are block of soap = 8 x 5 x 3 = 120 cm3
The number of blocks of soap = the volume of the box/ The volume of
6000
= = 500 block of soap
120
Example 4
A building worker used 1500 bricks to build a wall. Calculate the volume of the wall in m3 if the brick
is in the shape of a cuboid of dimensions 25, 12 and 6cm.
Solution
The volume of are brick = 25 x 12 x 6 = 1800 cm3
The volume of the wall = 1800 x 1500
= 2700000 cm3
i. e The volume of the wall in m3
2700000
= = 2.7 m3
1000000
Mathematics Sixth grade of primary 73
Geometry and mea
sure
Example 5
!
8400 cm3 of water is poured into a vessel in the shape of a cuboid
! 45 cm
with internal dimensions 20, 35 and 45 cm
Find :
8400 cm3
1- the height of water in the vessel.
2- The volume of water needed to be added for the vessel becomes ! cm
! 35 cm
!
filled with water completely. 20
Solution
The water poured in the vessel is in the shape of a cuboid.
i. e The volume of water in the vessel
= The base area x height
i. e 8400 = (35 x 20) x The height
8400
i. e The height of water = = 12 cm
35 x 20
2- The volume of water needed to be added for the vessel becomes filled with water completely
can be obtained by two methods
The first method
The volume of the whole vessel
= 20 x 35 x 45 = 31500 cm3
i. e The volume of the added water
= 31500 - 8400 = 23100 cm3
The second method :
We calculate the volume of the empty part of the vessel
The volume of the added water
= 35 x 20 x (45 - 12) - 35 x 20 x 33
= 23100 cm3
74 First Term Mathematics
The third unit
Exercise (3 - 4)
1 Which is greater in volume?
A cuboid of dimensions 70. 50 and 30 cm or a cuboid whose base area = 2925 cm2 and its height
= 35cm.
2 How many cm3 are enough to form a cuboid of dimensions 17, 13 and 11 cm.
The
3 Complete the following table
The dimensions of the cuboid The area of the base
volume
Length Width Height Cm2 Cm3
12 7 60
A Juice case in the shape of a
4 cuboid. 8
4
6
8 160
528
Its base is square shaped of side 21.5 365.5 4751.5
length 6cm and its height is 15cm
calculate the volume of juice which
fills the case completely.
A sweet case in the shape of a cuboid its internal dimensions are 21, 18 and 6 cm It is wanted to
5
fill it with pieces of chocolates each of them is a cuboid of dimensions 3, 3 and 1cm, calculate
the number of pieces of chocolates which fill the case completely.
A Truck for transporting goods.
6
Its dimensions are 3, 1.5 and 2metre. It is wanted to fill it with
cartoon boxes for mineral water bottles to distribute it to the
commercial shops. The dimensions of one cartoon box. Are
40, 25 and 25cm. calculate.
a- The greatest number of cartoon boxes of can be carried by
the truck.
b- The cost of transportian if the cost of transporting one
cartoon is 0.75 pounds.
7 A swimming pool, its internal dimensions are 30, 15 and
2metres. 405 metre cube of water are poured into it
Find :
a- The height of water in the swimming pool.
b- The volume of water which is needed to fill the swimming
pool completely.
Mathematics Sixth grade of primary 75
Geometry and mea
sure
5 The volume of the cube
!
Think and discuss
What will you learn from !
!
Fig (1)
!
this lesson?
- Through your active Fig (2)
!
participating you will come
to:
How to calculate the
volume of the cube by
different methods.
How to solve miscellaneous
applications on the volume
of the cube.
the fig.(1) is a cuboid consists of 4 layers, each layer has 3 rows
and each row has 3 cubes . what is the resulting solid . if we remove
the upper layer as in fig.(2)
Mathematic concepts
The volume of the cube
Notice that the resultant solid as you know is a cube because its
faces are congruent and its edges are equal in length.
That means that
The cube is a special case of the cuboid
when the length = the width = The height
i. e
The cube is a cuboid with equal dimensions
The volume of the cuboid = length x width X height !
The volume of the cube = The edge length x it self x if self
Example 1 !
Find the volume of a cube of edge length 4 cm .
Solution
4 cm
The volume of the cube
= edge length x it self x if self
= 4x4x4 = 46cm3
76 First Term Mathematics
The third unit
Example 2
The sum of lengths of all edges of a cube is 132cm calculate its volume.
Solution
The cube has 12 equal edges in length
132
i. e The edge length = = 11cm.
12
The volume of the cube = 11 x 11 x 11 = 1331 cm3
Example 3
The total area of a cube = 54cm2
Calculate its volume
Solution
The cube has 6 congruent faces
54
* The area of one face = = 9cm2
6
Since the area of one face = the side length x it self
9 = ? x? i. e 9=3x3
* The side length of the face = 3cm
* The volume of the cube = 3 x 3 x 3 = 27cm3
Example 4
A metallic cube of edge length 9cm It is wanted to be melted and convert it into ingots in the shape
of cuboids each of them has the dimensions 3, 3 and 1cm. calculate the number of ingots that are
obtained.
Solution
The volume of the metallic cube
= 9 x 9 x 9 = 729 cm3
The volume of one ingot = 3 x 3 x 1 = 9cm3
* The number of the obtained ingots
= the volume of the metallic cube/ the volume of one ingot
729
= = 81 ingots
9
Mathematics Sixth grade of primary 77
Geometry and mea
sure
Exercise (3-5)
1 Complete the following table
The Cube
The edge The perimeter The area f the The sum of The volume
length cm of the base cm base cm2 lengths of all cm3
edges cm
6 216
26
49
108
2 We have an amount of rice, its volume is 2700 cm3. It is wanted to put it in a cartoon box.
Show which of the following boxes is the more suitable and why?
a- A cuboid with dimensions 45, 40 and 15cm.
b- A cube, its internal edge length = 30cm.
3 A commercial shop shows a cubic case with edge length 12cm, it is filled with honey Calculate
the amount of money that a person pays for buying 3 cases of honey of one cm3 is sold for
0.05 pounds.
A box of cartoon in the shape of a cube. Its external edge length is 30cm
4
An antique made of glass is put inside it. And for protecting it from damage, the box is put
inside another box of carton in the shape of cube, its internal edge length is 36cm, the empty
part between the two boxes is filled with sponge form all over sides. calculate the volume of
sponge.
5 A cube of cheese, its edge length is 15cm It is wanted to be divided it into small cubes
the edge length of each is 3cm for presenting them through meals. Calculate the number
of the resulting small cubes.
6
An aquarium for fish is cube shaped It has a lid. The internal edge length of the aquarium
is 35cm. the aquarium is made of glass. Find the volume of the glass given that the
thickness of the glass is 0.5cm.
78 First Term Mathematics
The third unit
6 The Capacity
Think and discuss :
What will you learn from
this lesson? the capacity
Through your active Is the volume of the inner space for any hollow solid
participating you will come
to: In the case of vessels:
- The concept of capacity.
-The units of capacity. The capacity of the
- Solving miscellaneous vessel:
applications of calculating
the capacity. It is the volume of the
liquid which fills the
vessel completely
Mathematical concepts
- The capacity The capacity of vessel is
- The liter measured by a unit called
- The milliliter
the litre.
What is the litre?
The previous figure shows a mineral water bottle with capacity "1"
litre and an empty container in the shape of a cube of edge length
1dm (10cm) - As pouring the liquid from the bottle to the container
we find that it is filled completely.
From the previous we deduce that
The unit of measuring the capacity is the litre = dm3 = 1000 cm3
Notice That The milliliter is a common unit (a part of the litre) for measuring the
capacity.
The milliliter = cm3 and It is denoted by ml that means that 1 litre = 1000 milliliter.
Example 1
A box of milk of capacity 2 litres. And another box of capacity 200 milliliters.
How many boxes of the second kind are needed to be filled with the milk of the first box
completely.
Solution
The number of required boxes = the capacity of the large box/ the capacity of the small box
2000
= 200 = 10 boxes
Mathematics Sixth grade of primary 79
Geometry and mea
sure
The relation between the units of volume and the units of capacity
dm3 = 10cm x 10cm x 10cm = 1000 cm3 = 1 litre
m3 = 10dm x 10dm x 10dm = 1000 dm3 = 1000 litre
cm3 = 10mm x 10mm x 10mm = 1000 mm3 = 1 ml
Example 2
Convert each of the following to litres
(a) 5600 cm3 (b) 0.23 m3 (c) 9.52 dm3
Solution
(a) 5600 cm3 = 5600 x 1/1000 = 5.6 litre
(b) 0.23 m3 = 0.23 x 1000 = 230 litre
(c) 9.52 dm3 = 9.52 litre
Example 3
Convert each of the following into cm3
(a) 4.63 litre (b) 55 ml (c) 0.66 m3
Solution
(a) 4.63 litre = 4.63 x 1000 = 4630 cm3
(b) 55 ml = 55 cm3
(c) 0.66 m3 = 0.66 x 1000000 = 660000 cm3
Example 4
A swimming pool in the shape of a cuboid whose internal dimensions are 40m, 30m, 1.8m Find its
capacity in litres.
Solution
The volume of the swimming pool = 40 x 30 x 1.8
= 1200 x 1.8 = 2160m3
The capacity in litre = 2160 x 1000 = 2160000 litre.
80 First Term Mathematics
The third unit
Exercise (3 - 6)
1 Write the suitable unit from the units (m3, cm3, dm3, litre, ml) to measure the following.
- The capacity of a water tank on the roof of a house. ( )
- The volume of cereals container. ( )
- The capacity of oil bottle. ( )
- The volume of on amount of medicine in a syringe. ( )
- The capacity of a swimming pool in a sport club. ( )
- The volume of a box of carton of T. V set. ( )
2 A cube shaped vessel, its internal edge length is 30cm. it is filled with food oil.
a- calculate the capacity of the vessel.
b- If the price of one litre of food oil is 9.5 pounds calculate the price of all oil.
3 A container has 12 litre of honey. It is wanted to put them in smaller vessels (bottles) the
capacity of each of them is 400cm3 . calculate the number of bottles which is needed for
that.
4 A patient take a medicine spoon of capacity 3ml daily in the morning and at evening.
After how many days does the patient take 240 cm3 from this medicine.
5 A container in the shape of a cuboid, its internal dimensions are length = 25cm, the width
= 30 cm. The height = 42cm . An amount of solar is Put in it, its height = 1 the height
3
of the container. calculate
a- The volume of solar in the container
b- The total price of solar in the container if the price of one litre of solar = 1.2 pounds.
Mathematics Sixth grade of primary 81
Geometry and mea
sure
General exercises on the third unit
1 Write the name of the figure through the following descriptive statement.
No The descriptive statements for the figure The name of the figure
1 - The figure ABCD in which AB = BC = CD = DA, The two diagonals are perpendicular ……………………….
and not equal , m (∠A) ≠ m (∠B)
2 - The figure XYZL in which XY = ZL , YZ = Xl , XY ≠ YZ The two diagonals are ……………………….
equal.
3 - The figure DEFL in which DE = LF , EF = DL, DE ≠ EF, The two diagonals are not ……………………….
equal , m (∠D) ≠ m (∠E) .
4 - The figure ABCD in which AB = BC = CD = DA, The two diagonals are equal, and ……………………….
perpendicular.
2 In the opposite figure XYZL is a rectangle L X
in which XY = 5cm, YZ= 7cm, Show in
steps how can you to draw a square inside
5 cm
the rectangle such that XY is one of its
sides
- Write all the parallelograms which are
obtained in the figure. Z 7 cm Y
3 The opposite figure ABC is a right angled triangle at B in which AB = 5cm. Try to draw a
parallelogram in the following cases: A
a- A parallelogram such that AB is a diagonal of it.
b- A Parallelogram such that AC is a diagonal of it.
4 cm
C 5 cm B
82 First Term Mathematics
The third unit
A lorry for transporting building materials, the internal dimensions of the container are
4
5m, 1.8 and 0.6m. Its wanted to fill it completely by bricks of dimension 25cm, 12cm and
6cm, Calculate:
a- The greatest number of bricks can be Put in the container of the lorry.
b- The cost of transporting the bricks if the cost of transporting 1000 bricks is 35
pounds.
5 A swimming pool, its internal dimensions are 30m, 15m and 2m. 405m3 of water were
poured in it.
a- Find the eight of water which is poured in the basin.
b- Find the volume of water needed to be added to the basin to become filled with water
completely.
6 Which is greater in volume and why?
A cuboid whose dimensions are 12cm, 10cm and 8cm or a cube of edge length 10cm.
7 A tin in the shape of a cube, its internal edge length is 36cm, is filled with maize oil It is
wanted to put it in small tins in the in the shape of cubes, its internal edge length is 9cm.
Find the number of small tins needed to that.
8 The sum of all dimensions of a cuboid is 48cm and the ratio among the length of its
dimensions is 5: 4: 3 Find its volume.
9 A cuboid, its base is a rectangle whose perimeter = 40cm. the ratio between its length to
its width = 3 : 2.
Calculate its volume if its height is 10cm.
10 We have 6 pieces of soap, the dimensions of each of them are 3, 4 and 9cm, and we have a boxs
of cartoon its dimensions are 25, 20 and 15cm. Determine suitable method to put all the soap
bars in it.
11 A box of cartoon, its internal dimensions are 50, 40 and 30cm. It is wanted to fill it
with boxes of tea In the shape of cuboids, the dimension of each box are 7cm, 5cm and
12cm.
Calculate the greatest number of tea boxes can be put in the box.
Mathematics Sixth grade of primary 83
Geometry and mea
sure
Portfol
io
!
(1) from the opposite figure and using the geometric tools answer the following : ! !
! !
a- Write the greatest number of parallelograms you can draw in the figure.
b- Write the greatest number of trabeziums you can draw in the figure.
! !
! !
(2) from the opposite figure and complete :
A
!F !X ! B
- Three parallelograms
They are ………, ……….., ……….
- Three Trapeziums
! !
!E ! C
Z Y
They are ………, ……….., ……….
!D
- The number of triangles in the figure = …………
- Three triangles in the figure
They are ………, ……….., ……….
(3) The opposite figure is a rectangle the pattern is :
joining the mid points of the consecutive sides
a- Complete by drawing three internal figures due to this pattern.
b- Colour the obtained figure by different colours to get an art figure.
!
(4) The opposite figure is a regular pentagon the pattern is joining the
mid- points of the consecutive sides.
a- complete by drawing three internal figures due to the same pattern.
b- colour the obtained figure by different colours to get art figure.
84 First Term Mathematics
The third unit
A technological activity
Drawing geometric figures and solids using word programme.
What do you learn from his activity.
Using word programme to
- Draw a group of geometric figures (rectangle - square - parallelogram)
Draw a group of geometric solids (cuboid - cube)
Example
Using word programme draw the following geometric figures and solids
(a rectangle - a square - a parallelogram, a cuboid - a cube)
The procedure
1- Click (start) then select program then select Microsoft word. And open new document.
2- Press the symbol ِ at drawing tape below the screen. Then click by the mouse in an empty
region I the word page and through drawing and estimating the size of the rectangle and leaving out,
the rectangle will appear.
3- press second time the some symbol then click shift and go on pressing, during this press in an
empty region, then through drawing and leaving when you get the required square.
4- Select auto shapes which exists at the drawing tape, then select Basic shapes then select the figure
draw the parallelogram trough !
parallelogram , and
drawing and leaving out due to
you estimation.
5- to draw a cube and a cuboid.
Select Auto shapes then
select basic shaper then select
the shape to the solid , then
draw the cube and the cuboid
and leaving out due to your
estimation . yy will obtain the
following figure.
Mathematics Sixth grade of primary 85
Geometry and mea
sure
The unit test
(1) Complete the following
a- The rectangle is a parallelogram …………….
b- 120 dm3 = …………… = …………. cm3
c- 2580000 mm3 = …………. = ………….. m3
d- the volume of the cuboid = …………. × …………
e- 2.65 litre = ……….. = ………….. cm3
L X
(2) The opposite figure 35°
XYZL is a parallelogram in which
M (∠Y) = 118, m (∠LXZ) = 27 °
118
Find m (∠ L), m (∠XYZ) Z
Y
(3) Discover the pattern in each of the following cases, then describe it and complete its repetition
twice
a- !!??!!??................................................ (the pattern is ………)
b- ........................... (the pattern is ………)
!
(4) How many cm3 are enough to fill a box in the shape of a
cuboid, its internal dimensions are 50cm, 35cm, 20cm. 15 cm
(5) In the opposite figure
A cuboid of volume 6480 cm3 18 cm
Its height = 15 cm, its width= 18cm
Calculate its length.
(6) A box of milk in the shape of a cube of edge length 12cm. It is wanted to put a number of these
boxes in a box of cartoon in the shape of a cube of edge length 60cm. How many boxes of milk can
be but in the cartoon box?
(7) A vessel in the Shape of a cube with edge length 15cm is filled with honey.
a- calculate the capacity of the vessel.
b- If the price of one lire is LE 8. Calculate the price of honey.
86 First Term Mathematics
The Fourth Unit
Statistics
First lesson : The Kinds of statistics data.
Second lesson : Collecting the descriptive statistics data.
Third lesson: Collecting the quantitive statistics data.
Fourth lesson : Representing data by frequency curve.
General exercises on the unit.
technology activity.
portfolio
The unit test.
Statistics
1 The Kinds of Statistics data
What do you learn from this
lesson? Notice and deduce
Through your active
participating you willcome to: Hany is a pupil in sixth grade.
The Specialist Hospital
- The meaning of descriptive
Requisition for medical examination
He went with his mother
data.
- The meaning of quantitive
The name ................................................................. to the hospital for medical
The age.................................................................
data. Examination date / / 20 examination.
- Completing writing Sex male female
descriptive and quantitive The employee asked him to
The birthday / / 20
data. The birth place......................................................... complete the data in he sheets of
........
The address................................................................. medical examination.
The social case................................................................. Hany asked his mother about
The educational case....................................................
Mathematical concepts The kind of disease...................................................... the required data. His mother
The degree of disease...................................................
- descriptive data The tallness.................................................................
replied. There are some data
- quantitive data The weight................................................................. require writing digits as :
The temperature degree
- data sheet. Blood species age, the date of examination,
- data base. the birthday, the tallness, the
weight, the degree of temperature….. etc.
There are other data required writing words or Statement as:
The name, sex (male, female), social case (married, celibate),
educational case (not educated, educated), the birth place, the
address, blood species (O, A, B) ….. etc.
Through the discussion between Hany and his mother It is show
that:
The statistics data which we use in our daily life are two kinds.
1- descriptive data : they are data written in the form of discribtion to the case of the persons in
the society as : the favorite colour, favorite food, the birth place, the social case, the education case,
profession case….. etc
2 - Quantative data : they are data written in the from numbers to express a certain phenomenon as:
age , tallness, weight, the shoes size, number of sons, the student's mark in the examination …. Etc.
Drill (1) The opposite figure shows the sheet- model of requisition for one of your fellow to
join with a sport activity during the summer holiday in a sport club near to his house.
88 First Term Mathematics
The fourth unit
The Specialist Hospital
Requisition for medical examination Examine it well then answer the following.
The name .................................................................
The age................................................................. (a) There are in the sheet. Model a descriptive data as
Examination date / / 20 ……………
Sex male female (b) There are in the sheet- model a quantitive data as
The birthday / / 20
The birth place................................................................. ………..
The address................................................................. (c) Register your name in the card, then complete one of
The social status.......................................................... the descriptive data and one of quantitive data.
The educational case....................................................
The kind of disease......................................................
The degree of disease...................................................
The tallness.................................................................
The weight.................................................................
The temperature degree
Blood type
Notice that
The data requisition sheet is a sheet contains a set of data some of
them is descriptive and the other is quantitive belong to a certain
person or a thing.
Drill (2) MR. Khaled is the superior of a class in the sixth grade in a primary school. He
wanted to set up data base about his pupils. He designed the following table
Age Tallness
Series number The name Month year How to arrive to school Favorite activity
in cm
1 Ahmed Omar 6 11 147 Walking School broad casting
2 Adel Said 12 150 Bus Scouts
3 Nermeen Nabeel 7 11 141 Taxi School press
Look at the previous table and answer the following.
1- Determine which columns represents descriptive data and which one represents quantitive data.
2- Complete the two missed columns in condition that one of then for descriptive data and the other
for quantitive data.
3- Consider yourself one of MR. Khalid's pupils and register our data.
Notice that:
Data base is a set of descriptive data and quantitive
data belong to some persons or establishment or
administrations… or authorities …………
Mathematics Sixth grade of primary 89
Statistics
Exercise (4-1)
(1) Read the data on the box of milk then classify the data registered on it into descriptive data and
quantitive data.
- The descriptive data are ………………
- The quantitive data are ……………….
A personal card of pupil
(2) The opposite figure shows a model School name. ..............................................
sheet to one of personal cards of a pupil in Name ..............................................
Grade ..............................................
a school. Look at it well then and extract Personal Photo
Class: ..............................................
from it descriptive data and quantitive School year ..............................................
data. Birthday ............../........../........20..........
Blood type
Write you own personal data on this
Tel. house......................
sheet. mobile......................
(3) In the following the model sheet of data base to the members are participating in a sport club.
The date of Favorite Blood The Telephone
No The name Age
participating game species adress number
1
2
3
4
- Determine which columns represent descriptive data and which of them represent quantitive data.
- Consider yourself one of members of this club and register your name from today and complete the
data.
90 First Term Mathematics
The fourth unit
2 Collecting descriptive statistic data
What do you learn from
this lesson? Notice and deduce
Through your active
participating you will come to: A class contains 36 pupils. The superior of pupils
- How to put descriptive data in to register the hoppies which each of them prefers
frequency data table.
selecting it from five hoppies (singing, drawing,
- How to form a simple
frequency data table.
acting, reading, playing music) for making a
(descriptive data) Extracting competition concerned with these hoppies.
information's from data In a The data were as follows.
simple frequency table.
drawing - reading - playing music - singing - acting - reading
playing music - drawing - acting - reading - playing music -
playing music
Mathematical concepts acting - singing - reading - drawing - acting - drawing
- forming the tally frequency
singing - playing music - drawing - acting - drawing - reading
table.
- forming a simple frequency reading - drawing - acting - reading - drawing - singing
table. drawing - reading - singing - acting - drawing - playing music
How can you deal with these data? The tally frequency data table.
You may notice that all these data are The hoppy Tallies Frequence
descriptive data.. In order to collecting them Singing 5
we should use the tally frequencie data table. Drawing 10
As you studied in fifth grade as follow. Acting 5
Reading 7
If we take away the column of tallies
playingMusic 9
from the previous frequency data table we total 36
will get the distribution frequence table as
follow
The hoppy singing drawing acting reading music total
Number of pupils 5 10 5 7 9 36
This table represents the distribution of the pupils of a class in six the grade due to their hoppies.
Mathematics Sixth grade of primary 91
Statistics
The previous table is called the simple frequency table because all data which it contains are
distributed due to one description which is the preferable hoppy in this activity.
Through the previous table answer the following.
- What is the hoppy which the most pupils prefer ? and what is its percentage?
- What is the hoppy which is the least preferable? And what is its percentage ?
- What is your advice to the director of this school? And the superior of this class to do a bout
these hoppies?
One of schools collected data about the kinds of stories book which the pupils
Drill (1)
borrow them from the story corner in the school library in a month of the year.
Through examining the borrow sheets which were 36 sheets, the resut was as
follows.
drawing - reading - playing music - singing - acting - reading
playing music - drawing - acting - reading - playing music -
playing music
acting - singing - reading - drawing - acting - drawing
singing - playing music - drawing - acting - drawing - reading
reading - drawing - acting - reading - drawing - singing
drawing - reading - singing - acting - drawing - playing music
Form a simple frequency table for the previous descriptive data. Then answer the following
questions.
- What are the kinds of the stories which are the most attractive for the pupils? Express that
by its percentage?
- What are the kinds of the stories which are the least attractive for the pupils? Express that
by its percentage?
- What is your advice to the director of the library?
- What is your advice to your fellow pupils who go to the library repeatedly ?
92 First Term Mathematics
The fourth unit
Exercise (4 - 2)
1 The following table shows the distribution of the number of the foreign tourists in
millions who visited Egypt in 2009 due to their nationalities.
Nationality French German Britch Russian Italian total
Number of tourists
0.8 1.2 1.34 2.35 1.04 6.73
in million
a- What are the countries from which the most tourists visited Egypt? What is their
percentage?
b- What are the countries from which the least tourists visited Egypt? How many tourists from
these countries visited Egypt?
c- What is the number of German tourists? What is their percentage?
2 If the public score of 40 students in Arabic language in a university is as follows.
very good - good - pass - good - excellent - good - good
very good - good - very good - good - good
excellent - very good - excellent - excellent - pass
good - good - very good- good - pass
very good - very good - good - very good- pass - good
very good - good - pass - very good - excellent
pass - pass - excellent - good - pass
Form the Tally frequency table. Then form the frequency table for the previous results
then answer the following questions.
- What is the most common score of the students?
- What is the least score of the students?
- What is your advice to the students In this important educational stage?
Mathematics Sixth grade of primary 93
Statistics
3 Collecting The statistics quantative data.
Notice and deduce
What ate you learn from
this lesson?
Through your active Think and discuss. The scores of the pupils of a class of sixth
participating you will come grade in mathematics at the end of the year had been Collected for
to.
- putting the quantitive data in 42 pupils their marks were as follows given the fall mark is 60.
the tally frequency table.
- forming the frequency 36 – 32 – 42 – 38 – 45 – 28 – 42 – 57 – 20 – 41 –
table of equal sets from the
frequency table of quantitive 59 – 49 – 48 – 46 – 40 – 48 – 51 – 53 – 54 – 55 –
data .
36 – 33 – 44 – 57 – 54 – 46 – 52 – 26 – 37 – 30 – 34 –
- Extracting in information
table of equal sets 47 – 35 – 44 – 29 – 49 – 49 – 50 – 23 – 43 – 39 – 43.
These marks are called raw marks, That means the marks of pupils
Mathematical concept after correction to their exam. Papers as they are scattered.
The raw marks
For example .
The range
The frequency table of equal what is the number of excellent pupils ?
sets.
and what is the number of pupils of low level?
And what is the number of pupils of intermediate level?
Notice that
The only thing that can be extracted from these raw marks is the least mark
= 20 and the maximum mark = 59 that means that the marks of mathematics
of the pupils of that class are distributed in range = 59 - 20 = 39 marks.
In order to deal these marks by studying and analyzing we should put them in a frequency table.
That will be carried out through the following steps.
1 - Determine the highest and the lowest value.
In this example
The maximum mark = 59
The minimum mark = 20
94 First Term Mathematics
The fourth unit
2 – determine the range of this distribution it is = The maximum mark – the minimum mark
In this example the range = 59 – 20 =39
3 – Summarise these data by dividing it into a Suitable number of sets by determining a Suitable
length for each set say 5 marks in this example.
- We start with the smallest mark and finished at the greatest mark.
Then we obtain 8 sets. As follows
First set contains the marks of pupils from 20 marks to less than 25 marks it is expressed as 20-
Second set contains the marks of pupils from 25 marks to less than 30 marks It is expressed as 25-
The third set Contain the marks of pupils from 36 marks less than 35 marks
It is expressed as 30-
And so on till the last set which will be
The eighth set contains the marks of pupils from 55 marks to less than 60 marks
It is expressed as 55-
Notice that The number of sets can be calculated by the following relation
the range
The number of sets =
the length of set
In this example
39 4
The number of sets = 5 = 7 5 ~ 8 sets.
Sets Tallies Frequence
In this way. The sets contained all raw marks of the 20- // 2
25- /// 3
pupils
30- //// 4
4 – putting these data in a tally frequency table as in 35- / //// 6
the opposite table. 40- /// //// 8
45- //// //// 9
50- / //// 6
55- //// 4
Total 42
Mathematics Sixth grade of primary 95
Statistics
5 – we take away the tally column from the previous table to get the frequency table of equal sets as
in the following table.
It is call as thus because the data contained in it has been distributed into sets.
Therefore it is called
The distribution of the marks of the pupils in mathematics in a class of the school.
Sets of marks 20- 25- 30- 35- 40- 45- 50- 55- Total
Number of pupils 2 3 4 6 8 9 6 4 42
Answer the following questions.
- What is the number of pupils who get 50 marks or more? What is the percentage of them?
- What is the number of pupils who get the least marks as your point of view? And what is their
percentage?
What da you advise your fellow pupils in mathematics?
Drill (1) During a trip to a factory of clothes has been hold
by the pupils of shool in the governorate Hend
and Nabeela collected data about the wages of
the works weekly, the number of workers was 60
cooprative person. Hend and Nabeela registered these data in
learning
a frequency table of sets as follows.
The weekly wages 50- 60- 70- 80- 90- 100- 110- Total
Number of workers 4 7 12 18 11 5 3 60
The distribution of the weekly wages of the workers in the factory.
Read the table well with your group members then answer the following questions
- The least weekly wage which the worker gets.
- The weekly wage which the maximum number of workers obtain lies between …………….. and
…………………..
- The percentage of the number of workers who obtain the least weekly wage is …%
- The number of workers whose weekly wages are L.E 100 and more is ….
And their percentage is ……%
96 First Term Mathematics
The fourth unit
Exercise (4-3)
1 In a competition of an acceptance exam. for joining a sport college the tallnesses of 48
students who presents to the competition in cm were as follows
175 – 183 – 163 – 181 – 164 – 195 – 182 – 166 – 193 – 195 – 185 – 157 – 190 – 166
– 163 – 173 – 166 – 177 – 164 – 157 – 173 – 193 – 168 – 183 – 155 – 178 – 173 – 180
– 164 – 181 – 156 – 194 – 173 – 187 – 162 – 176 – 158 – 170 – 168 – 190 – 156 – 169
– 155 – 170 – 188 – 155 – 192
Form the frequency table of sets to the previous tallnesses, then answer the following
questions
- what is the number of students who have the highest tallnesses?
What is their percentage?
- what is the number of students whose tallnesses are less than 165 cm.
What is the percentage?
- what is your advice to those students
2 the following frequency table of sets show The shares of money in pound hold by the
pupils of a class in the project of building a hospital near to the school study it and answer.
The shares in pounds 20- 30- 40- 50- 60- 70- Total
Number of pupils 3 6 8 12 7 4 40
1 - what is the number of pupils who shared with an amount of money lies between 40 and 50
pounds?
2 - what is the number of pupils who shared with the least amount of money what is their
percentage?
3 - what is the number of pupils who shared with an amount of money = 60 pound and more ? what
is their percentage?
4 - what is the least share hold by the pupils? And what is their number in each case?
Mathematics Sixth grade of primary 97
Statistics
Representing the Statistics
4 Data by the frequency curve
What do you learn from
this lesson? Notice and deduce
-through your active
participation you will c:
- How to represent a Adel sat in the neighbor of his father who works at a hospital to
frequency table of sets receive the patients for two hours.
by frequency polygon.
- How to represent a He formed a frequency table of sets to the ages of patients whom
frequency table by a
frequency curve were registered to enter the hospital within this period.
-Extraction It was as follows.
information's from
frequency table and its
frequency curve. The age 10- 20- 30- 40- 50- 60- Total
Number of patients 6 8 12 15 10 9 60
When Adel show this table to his teacher of the class, he asked
Mathematical concepts
- The centre of the set him and from other pupils to draw a frequency polygon to represent
- The frequency polygon
- The frequency curve.
these data. (as what had been done in 5th grade) Adel graph the
following frgure.
When the teacher asked Adel How did he draw the
frequency polygon
Adel replied. 18
16
I followed the following steps.
14
1 - I draw the horizontal axis and the vertical axis. 12
10
2 - I divided each of them into equal parts which are 8
suitable for the given data. 6
4
3 - determined the centre of each set as follows. 2
10+20 set
The centre of the set (10 - ) is = 15 80 70 60 50 40 30 20 10
2
The centre of the set (20 - ) is 20+30 = 25
2
And so on till the set (60- )
60+70
Its centre is = 65
2
98 First Term Mathematics
The fourth unit
1 - the points where determind The point
on the lattice where for every set Number
The patient's which
of patients Centre of the set
there is an ordered pair which age sets represents the
frequencies
is (the centre of the set, its set
frequency) for example the set. 10 - 6 15 (15,6)
- (10 - ) , the point which 20 - 8 25 (25,8)
represents 30 - 12 35 (35,12)
It is (15,6) where 15 is the
40 - 15 45 (45,15)
center.
And 6 is its frequency. 50 - 10 55 (55,10)
- the set (20 - ) , the point 60 - 9 65 (65,9)
which Total 60
represents it is (25,8) ….. and
so an.
Then the frequency table
becomes as in the opposite
figure.
frequency
2 - using the pencil and the ruler I drew a line segment
joining each tow consecutive points of the determined
18
points by the previous steps thus I got the graph of the 16
14
frequency polygon. 12
The teacher : very well but if you and your fellow 10
8
pupils joined the points by the bencil with out lifting it 6
4
up the sheet without using the ruler then you will get
2
set
another graph. What is it?
80 70 60 50 40 30 20 10
If you got the red line in the previous graph the you
are correct and you got the frequency curve which frequency
passes through the most of points.
18
This new graph is called
16
The frequency curve which 14
12
Can by drawn directly new 10
As in the opposite graph 8
6
And it is another form 4
2
For representing the statistics data set
80 70 60 50 40 30 20 10
Mathematics Sixth grade of primary 99
Statistics
Drill :
Ola and Nargis registered the temperature degrees which are expected for 30 cities in one of
summer days through watching the news in television. They formed the following frequency table.
Temperature degree 24- 28- 32- 36- 40- 44- Total
Number of cities 3 4 7 9 5 2 30
Draw the frequency curve of the previous table.
Then answer the following questions.
(a) what is the number of cities whose temperature's degree are 40 degree and more? What do you
advice these cities' inhabitants.
(b) What is the number of cities which are suitable for summer season on that day?
(c) what are the number of cities whose temperature's degrees are mild on that day from your own view?
(Exercise (4-4)
1 the following table shows the extra money which 100 workers got in a month in a
factory . they are as follows.
The extra money 20- 30- 4- 56- 60- 70- Total
Number of workers 20 15 30 20 10 5 100
- what are the number of workers who obtained extra money less than 50 pounds.
- Draw the frequency curve of this distribution.
In a goodness party for orphan's day A group of contributors paid sums of money in pounds
2
as shown in the following table.
The sum 50- 60- 7- 80- 90- 100- 110- Total
Number of contributors 5 7 10 12 10 7 5
- what is the number of contributors by L. E 80 and more.?
- Represent the previous data by the frequency curve.
100 First Term Mathematics
The fourth unit
General exercises on unit 4
1 Examine each of the front envelope page of mathematic book and the last page of the art
features of the book , then extract from them at least three descriptive data and another three
quantitive data.
2 In a competition hold by sport's teacher for jumping in the place.
The number of jumps carried out by the pupils of a class were as follows.
30 - 18 - 21 - 25 - 14 - 19 - 7 - 8 - 11 - 26 - 22 - 16 - 17 - 35 - 33 - 16 - 27 - 6 - 30 - 26 - 16 -
21 - 14 - 20 - 18 - 9 - 15 - 31 - 21 - 18 - 15 - 29 - 26 - 12 - 28 - 9 - 25 - 8 - 10 - 15 - 36 - 23
(a) Form the frequency table of sets for the previous jumps.
(b) Represent these data using the frequency curve.
(c) Answer the following questions.
- What is the number of students of most number of jumps? What is their percentage?
- What is the number of students of the least number in jumps? What do you advice those
pupils?
The following table shows the number of air flights which done in Cairo airport in the
3 period from 12 at noon till 8 in the morning of the next day.
Time 12 p.m 4p.m 8 p.m 12 p.m 4 am Total
Number of flights 32 41 42 19 13 147
Represent these data by frequency curve then answer the following questions.
- In what time the Cairo air port is most crowded? Why?
- In what time the Cairo air port is the least crowded?
- what is the percentage of the number of flights comming to Cairo air port in the period from 12 at
noon till 4 p.m.
- what is the percentage of the number of flights comming to Cairo air port after 12 a.m?
Mathematics Sixth grade of primary 101
Statistics
A technologyical activity.
The activity's subject
Representing data by frequency curve through Excel program in the frequency
curve.
What do we learn from this activity?
- Inserting tabular data in cells. Of Excel program.
- Drowing the frequency curve of tabular data using Excel program.
Example
The following table shows the number of hours spent by a number of pupils dealing with
computers.
The required is representing these data by the frequency curve using Excel program
Number of hours 1- 2- 3- 4- 5- 6- Total
Number of pupils 8 11 15 6 4 2 46
The practical procedure
1 - Click start, select program then select Excel.
2 - Write the data of the first row in the previous table (number of hours) in cells of the column A.
3 - Write the data of the second row in the previous table (number of pupils) in cells of the column
B.
4- Determine the quantative data exist in the two columns A and B using the mouse.
5- from the menue (Insert) select chart then select custom types.
6- Write the number of pupils in the cell exsting down
7- Write the number of hours in the down cell then click next then finish
If the steps are correct the following graph will appear.
102 First Term Mathematics
The fourth unit
number of students number of hours
Port
folio
IIII
1- Read data registered on the national number card to one of your family (your father – your mother
– your brother – your sister) then extract from it descriptive date and quantative data.
2- Choose one of canned (food stuf) goods which your mother uses (oil – rice – suguar – tea –
detergent – butter - ….. etc) then extract from it describtive data and quantative data).
3- Carry out a study in the a live in which you live and collect data about the ages of persons who live
in this alive. Then form a frequency table of sets for the obtained data.
Ages 0- 10- 20- 30- 40- 50- 60- Total
Number of
persons
Represent these data by the frequency curve then answer the following.
1- What is the most common age in the alive?
2- what is the number of children whose age are less than 10 years?
3- What is the number of persons whose ages are 5 years or more?
Mathematics Sixth grade of primary 103
Statistics
The unit test
1- Classify the set of the following data into quantitive data and descriptive data age – the colours of
the nation's flag – Marks of the exam. In math – weight – social case – temperature degrees – tallness
– nationality – sex – score in science – the kind of the book that you real – the colour of school
uniform suit – the preferable hoppy – the number of sisters – the number of bages of Arabic book.
2- A samlpe is taken from a tourists group coming to Luxor in one day in winter the number of samlpe
was 33 tourists the nationalities of the tourists the nationalities of the tourists were as follow.
Rusian – American – English – Italian – French – American – English – Rusian – French – American
– Italian – Rusian – American – French – Italian – English – Rusuia – Italian – Italian – Rusian –
Rusian – American – Italian – English – Rusian – English – Italian – Rusian – American
* Form a simple frequency table for the previous descriptive data then answer the following
questions.
- Which nationality has the greatest number in this group? Express that by a percentage.
- Which nationality has the smallest number in this group? Express that by a percentage.
- What do you advice the responsible about tourism in Luxor.
3- In a competition for passing the acceptance exam. To a sport college., The weights of 40 student
presenting to this completion were as follow.
50 – 53 – 75 – 88 – 65 – 77 – 59 – 66 – 63 – 85 – 64 – 72 – 58 – 65 – 56 – 74 – 73 – 90 – 92 – 87 –
60 – 70 – 72 – 85 – 56 – 54 – 75 – 76 – 90 – 81 – 60 – 88 – 74 – 72 – 60 – 57 – 66 – 83 – 51 – 60
(a) Form the frequency table of sets for the previous weights
(b) Draw the frequency curve of the obtained table then answer the following questions .
- What is the number of the students who have the greatest weights? What is their percentage?
- What is the number of students whose weights are less than 60kg? What is their percentage?
104 First Term Mathematics
A model test for the first term
Answer the following questions :
First question :
Choose the correct answer from those between brackets in front of each item in each of the
following:
1
1- The ratio between the two numbers 3 , 9.6 = ………
5
( 1 ,3 , 1 ,2 )
6 2 3 3
2 x
2- If = then x = ………. (6 , 21 , 12 , 7)
7 21
3- The opposite data are descriptive except ………. (The favorite coloure, birthday – age – blood
species)
4- 4200000cm³ = ………m³ (42, 420 , 4.2 , 4200)
5- A cube, the perimeter of its base is 36cm, then its volume = cm³ (36 , 6 , 37 8 , 216)
6- 5cm³ = …….ml (0.5 , 0.05 , 0.005 , 5)
Second question :
Complete the following :
(1) The ratio between two numbers = ………..
(2) The two opposite angles are equal in measure in each of …….. , ……… , ………..
(3) The volume of the cube = …………
(4) The capactity of a vessel is …………..
(5) If the values of a frequency distribution lie between (20 , 60) then the range of this distribution =
…………..
(6) A class contains 40 pupils. 32 pupils are present in a day, then the percentage of the abscenteese
= ………….
The third question :
(a) If the ratio among the prices of three electric sets (Tv, Oven – refrigerator) is 4 : 5 : 8 and if the
price of Tv is LE 1200 calculate the price of each of the oven and the refrigerator.
(b) A minaret of height 22m, the length of its shade at a moment is 6 metre. How height is a house
neighbor to the minaret if the length of its shade = 3m at the same moment.
(c) A wooden box for transposing goods. It is cube shaped. It has a lid, its inner dimension is 150cm.
Mathematics Sixth grade of primary 105
مناذج االختبارات
Find the volume of wood of the box if the thickness of the wood is 6cm.
In the opposite figure:
(d) ABCD is a parallelogram in which AB = 6cm, BC = 7cm , BM = 3.8 cm , m (∠ C) = 70 ˚
! �! !A
Without using geometrical instrauments find:
°!
m (∠ BDC) , m (∠ A) , the perimeter of ∆ BCD. D
!M
! 3.8 cm ! 6 cm
! 70°
! !B
C ! 7 cm
Fourth question
3
(a) Three persons set up a commercial business, the first paid 4 what the second paid, the second paid
2 what the third paid at the end of the year the profit became LE 6240. Calculate the share of each of
3
them from profit.
(b) A man owns a piece of land its area is 48 kirat. He recommended the half of the area is specialized
for building a school. And the other half is divided among his two sons and his two daughters such that
the share of the boy is twice the share of the girl. Calculate the share of each of them.
The fifth question
The following table shows the number of hours which the pupils of a class spend daily in front of the
computer.
Number of hours 1- 2- 3- 4- 5- 6- Total
Number of pupils 7 11 15 6 4 2 45
Represent these data by frequency curve . then answer the following questions.
- What is the number of pupils who spend the greatest number of hours in front of computer what do
you advice those pupil?
- What is the greatest number of hours which the pupils spend in front of the computer?
- What is the percentage of the number of public who spend less than 3 hours in dealing with
computer?
106 First Term Mathematics
Guide answers for the general tests of the units and
the model of test of first term.
The first unit test (the ratio) Sets 50- 55- 60- 65- 70- 75- 80- 85- 90- Total
1- (20.5) 2- (10, 15, 20cm) 3- (5litre/ 3km) Frequency 4 5 6 4 7 4 2 5 3 40
4- (a) (1 : 2), (b) (2 : 3), (c) (6 : 5), (d) The answer of the model test
(1 ; 10) First question :
5- (8 : 15) 1- 1 / 3 2- 6 3-age 4- 4.5
5- 216 6- 5
The second unit test (proportion)
Second question :
1- ( - 12), 2- ( 33 , 1 , 3 ) 3- (192,
100 8 7 1- The first number / The second number
160, 228)
2- The parallelogram, the square, the
4- (LE 3740), 5- (6 metre), 6- (40 litre) rectangle the rhombus.
1- (a) one of its angles is right., (b) 12000 3- The edge length × itself × itself
cm3 4- The volume of the liquid which fills
(c) 0.00258 m3, (d) the base area x height the vessel completely.
(e) 2650 cm3 5- 60 – 20 = 40
2- 118, 35. 6- 8 / 40 = 1 / 5 = 20%
3- (a) the pattern is Third question :
(b) the patterns a) 1500 , 2400 b) 11 metre
4- 35000 cm3 c) = 8765 cm³ d)80 , 70 , 21 cm
5- the length = 24cm
6- 125 Fourth question :
7- 3.375 litre, 27 pounds a) 2880 , 1920 , 1440
The 4th unit test (statistics)
b) 8 kirats, 4 kirats
5th question :
2 pupils , from 3 – 4 hours 40 %
Nationality Rus. Ame. Ita. French Eng. Total
The number 9 7 8 4 5 33
Mathematics Sixth grade of primary 107
General QuestionsOn the subjects Of the math book
For primary 6
(1) The side length of a square = 3 cm then the ratio between it's side length and it's perimeter equals
...........
(a) 4 (b) 3
1 1
(c) (d)
4 3
(2) In any equilateral triangle , the ratio between it's side length and it's perimeter equals --------
(a) 3:1 (b) 3:2
(c) 1:3 (d) 2:3
1
(3) The ratio between 12 Kirat to1 Feddan equals ----------
2
(a) 12:1.5 (b) 4:1
(c) 1:3 (d) 2:3
(4) If of the attendees of a meeting for the parents in a school was females , In addition to the attend-
ees there are extra attendees 10 of them was males and 10 was females . Which of the following
statements is true ?
(a)The number of males is more than the number of females
(b)The number of females is more than the number of males
(c) The number of males is equal to the number of females
(d) The given data is not sufficient
(5)If the ratio among the measurements of the angles of a triangle is 1 : 2 : 3 then the measure for the
smallest angle equals ---------
(a) 10o (b) 30o
(c) 45o (d) 60o
(6)An irrigation machine irrigate 15 feddan in 10 hours , then the ratting work for this machine is
------ feddan/hour
2 3 5 5
(a) (b) (c) (d)
3 2 2 3
108
a c
(7)If = then which of the following statements is true ?
b d
a c
(a)a c=b d (b) =
d b
a-3 c
(c) = (d) ad = bc
b-3 d
2 x
(8) If = then x - 2 equals --------
5 20
(a) 8 (b) 6 (c) 4 (d) 2
a
(9) If a : b = 2 : 5 then , equals ----------
a+b
(a) 2 : 5 (b) 2 : 7 (c) 3 : 7 (d) 7 : 2
(10) 5 m3 = --------
(a) 5000 dm3 (b) 5000 cm3
(c) 500 dm3 (d) 5000 dm
(11) The volume of a cube equals 125 cm3 , then it's base area equals -----------
(a) 25 cm2 (b) 25 cm
(c) 5 cm 2
(d) 5 cm
(12) The volume of a cuboid equals =-----------
(a) the height perimeter of the base (b) Width base area
(c) the height base area (d) Length width height
(13) If the sum of the edges length of a cube equals 144 cm then it's volume equals ---------
(a) 1728 cm (b) 1728 cm3
(c) 144 cm3 (d) 144 cm2
First : Choose the correct answer from the given answers:
Second : Solve the following questions with steps
(1) if the length of a rectangle is twice its width .
Find : (a) the ratio between the length and the perimeter of it
(b) the ratio between the width and the perimeter of it
(2) The area of a rectangle = 64 cm2 and its width = 4 cm .
Find : (a) the ratio between the width and the perimeter of it
(b) the ratio between the length and the perimeter of it
109
General QuestionsOn the subjects Of the math book For primary 6
(3) A manufacture of clothes produces 800 pieces daily , if the ratio between what this manufacture
produce from the children's clothes to the adult's clothes 2:3 .find : the number of pieces for the chil-
dren's clothes produced in 3 days .
(4) If the ratio between the ages of Basma, Hanaa and Shereen is 2 : 3 : 5 and the difference between
the ages of Hanaa and Shereen is 4 years ,Find the age of each of them.
(5) A factory produce 8000 bottles of soft drink in 12 hours , What is the rate of production per hour?
x- 3 5
(6) If = , Find the value of X ?
2 3
(7) In the feast festival , one of the shops made a discount 15% for the price of a refrigerator which
equal 1750 pounds ,Find the price of the refrigerator after discount ?
(8) If the percentage of success for a school equal 85% and the number of the students in this school
equal 800 students . If the ratio between the number of boys and the number of girls equals 2:3 find
the number of succeeded girls in this school ?
(9) If the drawing scale for a map is 1 : 1000 , and the length of a road equals 5 K.metre .What is the
length of this road in the map ?
(10) The following table show the dates and the number of trips ( in one of the bus stations for the
governorates )
Dates 6 am 8 am 10 am 12 am 2 pm sum
Number of trips 30 41 40 16 13 140
Draw the frequency curve for this distribution ,then answer the following questions:
(a) What is the number of trips before 10 am?
(b) What is the percentage of the number of trips from 10 am till 12 am to the sum of trips ?
(11) If a quantity of sugar with volume 2700 cm3 need to can in a box ,Show which of the following
boxes is suitable ?
(a) A cuboid with dimensions 45 cm , 40 cm and 15 cm .
(b) A cube the length of its inner dimension equals 30 cm .
(12) A quantity of honey is needed to be distributed into small bottles the capacity of each of them 400
cm3 find the number of needed bottles ?
(13) Complete this pattern :
110
111
112
113
114
115
116
117
118
119
120 |
geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions. |
Not certain what level is right for your child? We have a Placement Test to help with the decision making process. You may also call 888-272-3291 and discuss your situation with our friendly and helpful customer service staff.
What is the Complete Elementary Kit?
This package has everything needed to teach RightStart™ Mathematics Level A through Level E first edition. This is perfect for multiple children going through the program.
The Complete Kit includes five Lesson manuals, Worksheets, Transition Lessons and Worksheets, Math Card Games book, along with all the manipulatives used in these five levels. Level G, RightStart™ Mathematics; A Hands-On Geometric Approach, is not included in this kit.
What about a High School curriculum?
We recommend VideoText Interactive for high school algebra, geometry, trigonometry, and pre-calculus. This program uses the same philosophy as RightStart™ Mathematics; students are taught to think mathematically and, consequently, develop an excellent understanding of the material.
VideoText comes in twelve modules, six in Algebra (includes pre-algebra, algebra I, algebra II) and six in Geometry (includes formal geometry, trigonemtry, and pre-calculus). All modules are available via DVD or online.
I wanted to thank you for your awesome products and sessions at the recent California Homeschool Network Conference. I had a great time talking with you and am excited to use the products I purchased. As a …
– Allison LeBaron |
Notations in Elementary Mathematics
ISBN 087548154X / 9780875481548 / 0-87548-154-X
Book summary
This classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, and its eventual decline or ultimate survival. Originally published in 1929 in a two-volume edition, this monumental work is presented here in a single volume. |
Written by Dan Celenti, Ph.D., this book covers arithmetic concepts such as integers, factors, proportions, and permutations; algebra; geometry; and additional topics such as probability and weighted average, offering students an in-depth look at the types of problems found on the test. In addition to the problem-solving experience and exposure to a wide range of math topics and degrees of difficulty, this holistic approach allows the students to get a glimpse into the "real thing" and experience the impact of time constraints on their performance |
MAT 2150 - 001 Calculus with Applications Summer 2008
Instructor Guo Wei
Time MTWRF 10:00-11:50am and TR 12:30-2:20pm
Classroom SCI 1256
Office Information SCI 1215, (910) 521 - 6582, guo.wei@uncp.edu
Office Hours MWF 1:00-2:30, TR 2:30-4:00, or by appointment
Textbook Lial et. al: Calculus & Its Applications, 9th ed.
Prerequisite MAT 1070 (College Algebra)
or MAT 1090 (Precalculus: College Algebra & Trigonometry) or equivalent
Course Links 1.
2.
3. (Academic Honor Code)
Description This course includes the study of functions of one variable: derivatives, integrals, and their
applications in other fields such as biology and business. Special attention will be given to exponential functions
with respect to growth and decay applications. Some selected topics on multivariable functions will be covered in
the course.
Mathematical Analysis (Calculus is the basic part), Topology (i.e., geometry of sets of points, developed from
geometric shapes of objects), and Abstract Algebra (Linear Algebra is part of, other parts include various algebraic
structures such as Group, Ring, Field etc) are three foundations of modern Mathematics. On the other hand, these
three branches of Mathematics are closely related and deeply interacted, and you will really realize this at the time
when you model and solve an application problem using Mathematics. Certain basic knowledge of Geometry is
necessary for better learning of Calculus (especially for multivariable functions), and basic methods and results
of Algebra become necessary tools for using Calculus solving application problems. These basic facts from
Geometry and Algebra are also fundamental at their own rights/roles in Mathematics.
Goal Introduce the concepts differentiation and integration as well as their computational methods in such a way
that is intuitive for students: an example – a theorem – an application. Guide students to read and review selected
materials of textbook. By completing all the homework assignments, students can better understand Calculus and
improve significantly their ability to solve applied problems using Calculus. All students need: read textbook
materials for each class prior to the class, attend every class on time and focus on the lecture throughout the class,
review the class notes immediately after the class, re-read the textbook and compare with the class notes, and finally
complete all the assignments timely and independently.
Objectives After the completion of this course, in addition to computational methods, students will
also understand the following:
Unlike Elementary Mathematics, in Calculus we study the relationship between variables, and the approach is
the consideration of various kinds of limits. Differentiation and Integration, two most fundamental
concepts/operations, originated in calculating the instantaneous velocity v(t) of a moving object given the position
function s(t) (or calculating the slope of the tangent line at a point of the graph of a function) and computing the
position s(t) given the velocity v(t) (or computing the area of a region in plane or the volume of a solid in space),
respectively. These two fundamental operations are inverses each other, and the internal connection between these
operations is characterized by the so-called Fundamental Theorem of Calculus.
Calculus includes two parts: Differential Calculus and Integral Calculus. Both have many wonderful and
successful applications in the modern sciences and technologies. For instance, the well-known Newton's Three Laws
can be described in the differential forms, and the famous Maxwell's Equations that represent one of the most
elegant and concise ways to state the fundamentals of electricity and magnetism are given in the differential and
integral forms.
General Education Objectives
The rationales of the course are described as follows:
To help students read analytically and think critically
To help students communicate effectively in writing and in speaking
To develop students' quantitative and scientific skills
To develop the ability to analyze, weigh evidence, and make statistical inferences
To demonstrate knowledge of the purpose, methods and principles of scientific inquiry
To demonstrate knowledge of effects of technology upon physical/human environment
To develop students' abilities in the statistical problem description; data collection, organization and analysis;
problem modeling; and problem solving
Remind If you miss without making-up even one class, you may find it extremely hard to catch up. The
study of this course requires continuous efforts throughout.
Content
Chapter R: Algebra References
Chapter 1: Linear Functions
Slopes and equations of lines, Linear functions, Least squares line Exam 1 (chap 0-1)
Chapter 2: Nonlinear Functions
Translation and Reflections of quadratic functions, Polynomial and rational functions,
Exponential and logarithmic functions, Growth and decay
Chapter 3: The Derivatives
Limits, Continuity, Rates of change, Derivative, Differential
Chapter 4: Calculating the Derivative
Techniques for finding derivatives, Product and quotient rules, Chain rule,
Derivatives of Exponential and logarithmic functions Exam 2 (chap 3-5)
Chapter 5: Graphs and the Derivative
Monotone functions, extrema, Higher derivatives, Concavity, Second derivative test,
Curve sketching
Chapter 6: Applications of the Derivative
Absolute extrema and applications, Business applications, Implicit differentiation,
Related rates, Linear approximation
Chapter 7: Integration Exam 2 (chap 6-7)
Antiderivatives, substitute method, Area and definite integral, Fundamental theorem,
Area between two curves, numerical approximation
*Chapter 8: Further Techniques and Applications of Integration
*Chapter 9: Multivariable Calculus
Homework There will be approximately 8 homework assignments. Before you work on any assignment, you
should spend enough time to read the textbook, review class notes, and visit course web sites. Everyone must work
out every assignment independently unless it is a group assignment or, when indicated, it allows discussions.
Homework and Lab assignments are critically important for a successful study of the course and must be completed
independently, on time and at your best efforts. You are required to check the course web site frequently and
regularly to get the assignments as soon as they are posted.
Exams
3 in-class exams (being noticed 3 days in advance) and the comprehensive final exam (Thursday, June 26,
10:00-12:00, SCI 1256).
Grading
HWs/Labs - 30%; In-class exams - 45% (15% each); Final exam - 25%;
Total score (= HWs/Labs + In-class exams + Final) = 100.
Attendance
Class attendance is mandatory and will be checked from time to time. Good attendance can earn up to 5%.
Example: if your Total score is 85 (which is a B) and your attendance is perfect (so you get 5 additional pts), your
overall course score will be 90 (which is an A-).
Course letter grade
A A- B+ B B- C+ C C- D+ D D- F
>=92 >=89 >=87 >=83 >=79 >=77 >=73 >=69 >=67 >=63 >=59 <59
The last day to drop with a "W" grade is Friday, June 13.
Note: Any student with a documented disability needing academic adjustments is requested to speak directly to
Disability Support Services and the instructor, as early in the semester (preferably within the first week) as possible.
All discussions will remain confidential. This publication is available in alternative formats upon request. Please
contact the Disability Support Services, DF Lowry building, (910) 521-6695. This publication is available in
alternative formats upon request.
University's Emergency Information Hotline: Phone (910) 521-6888 and Web site |
Basically, it works by allowing you to choose your "level of math" (which it uses to determine what tools it should provide to you) and then allows you to input a math problem which it then solves for you, and gives you detailed solutions (you have to try it, it's really cool).
I was wondering how it worked on two levels. First off, how would they parse the math problem (and all the sometimes foreign mathematical operators)? How do they get from text to numbers, variables, and operators?
Second, how do they generate the explanations? While you have to pay for the detailed solutions (which are explanations of how they solved the problem), I've seen their preview screenshots, and it looks very detailed. The explanations are given in full, accurate sentences. How would they generate something like that?
3 Answers
It first breaks it into tokens using a lexer. In an expression like 3 + 5, the tokens are 3, +, and 5. Those tokens are fed into a parser, which knows the context and the relationships between all the tokens, and can call the appropriate functions.
For example, when the parser encounters the expression 3 + 5, it sees the + token and looks up in a table that says it should call a function named add with the tokens of 3 and 5 as arguments, which does the math and returns an 8.
If you don't want to evaluate an expression, but maybe want to solve an equation, the add function will do something different. For example, in the equation x + 5 = 8, the add function might follow the rules we learned in algebra and subtract 5 from the right hand side.
As for generating the explanations, as part of the add function, it simply records what it is doing: "Subtract 5 from the right hand side." The computer has to take those steps in order, so writing it out in English isn't that much additional work.
Add a few thousand much more complex "add" functions and voilà, you have Mathway. Obviously, that's a vast oversimplification, but that's what computer science courses are for.
No software in the world can work all by itself until and unless it receives inputs from the user or another system. Once inputs are received, then they are processed into a form that is acceptable by the processor to process them further for the desired output. For example, data types are converted in other data types which we refer as casting. This is the answer to your question: How do they get from text to numbers, variables, and operators?
Also there is something what we call functional decomposition or stepwise refinement when analysing a certain complex process in programming. I would advise you to use the website further , jot down individual features, simplify them by breaking them up further and then research on those bits and pieces.
For performing Maths calculations, there are built-in maths libraries available for the said purpose. Also look into operator overloading. Have you ever tried adding two complex numbers in C++? |
Mathematics Courses
Note: Students must earn a grade of "C" or better in a mathematics course in order to continue in any mathematics sequence.
COURSES:
NCBM 0100. Non-Course-Based Mathematics
This is a 4-week class that meets 4 hours per week and is designed to provide first-time-in-college students with a review of mathematics skills necessary for success in college-level mathematics. Students who have scored between 346 and 349 on the TSI Assessment are eligible. F, S, Su
Students will use the My Math Test web site.
Institutional credit only. Topics Appropriate placement test score. Laboratory fee $35. F,Sp,Su (3201045119).
MATH 0306. Beginning Algebra (3-2-1)
Institutional credit only. A developmental course for those students who are in need of a review of basic algebra. This course includes operations with real numbers; simplifying algebraic expressions; solving linear equations and inequalities; the coordinate system and graphing; solving systems of equations; operations with polynomials and factoring; and applications. Prerequisite: MATH 0304 or appropriate placement test score. Math Lab attendance is required as arranged. (Taught in Fall, Spring, and Summer) Students will use the My Math Lab website.
MATH 0307. Modular Mathematics II
Institutional credit only. Topics Laboratory fee $35. F,Sp,Su (3201045119).
MATH 0308. Intermediate Algebra
Institutional credit only. After a brief review of topics from Beginning Algebra, this course will cover rational expressions; functions and graphing; solving inequalities; exponents and radicals; solving quadratic equations; and applications. Prerequisites: High School Algebra I and appropriate placement test score or MATH 0306. (Taught in Fall, Spring, and Summer) Students will use the My Math Lab website.
MATH 1314. College Algebra
This course is an in-depth study and application of polynomial, rational, radical, exponential and logarithmic functions, and systems of equations using matrices. Additional topics such as sequences, series, probability, and conics may be included. An instructor-approved graphing calculator will be required. Prerequisite: TSI complete. F, Sp, Su (2701015419)
MATH 1316. Trigonometry
In-depth study and applications of trigonometry including definitions, identities, inverse functions, solutions of equations, graphing, and solving triangles. Additional topics such as vectors, polar coordinates and parametric equations may be included. An instructor-approved graphing calculator will be required. Prerequisite: MATH 1314 or appropriate score on an additional test required by the mathematics department. F, Sp, Su (2701015319)
MATH 1324. Finite Mathematics
The application of common algebraic functions, including polynomial, exponential, logarithmic, and rational, to problems in business, economics, and the social sciences are addressed. The applications include mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value. The content level of MATH 1324 is at or above the level of college algebra, MATH 1314. An instructor-approved graphing calculator will be required. Prerequisite: TSI Complete F, Sp, Su (2703015219).
MATH 1325. Calculus for Business and Economics
This course is the basic study of limits and continuity, differentiation, graphing and optimization, and integration of elementary functions, with emphasis on applications in business, economics, and social sciences. This course is not a substitute for MATH 2413, Calculus I. Prerequisites: MATH 1314 or MATH 1324 or special permission of the department chairperson. Sp, Su (2703015219).
MATH 1333. Mathematical Topics
A study of sets, the real number system, algebra, functions and graphs, geometry, measurement, mathematics of finance, and probability and statistics. Prerequisite TSI complete. (Taught in Fall, Spring, and Summer) Students will use the My Math Lab website.
This course is for elementary education majors and includes the study of sets, functions, numeration systems, number theory, and properties of the natural numbers, integers, rational and real number systems with an emphasis on problem solving and critical thinking. Prerequisite: MATH 1314 or an appropriate score on an additional test required by the mathematics department. (Taught in Fall and Summer) Students will use the My Math Lab website.
MATH 1351. Mathematics for Elementary Teachers II
This course is for elementary education majors and includes the study of geometry, probability, and statistics, as well as applications of the algebraic properties of real numbers to concepts of measurement with an emphasis on problem solving and critical thinking. Prerequisite: MATH 1314 or an appropriate score on an additional test required by the mathematics department. (Taught in Spring and Summer) Students will use the My Math Lab website.
An introductory course in differential equations that includes the study of first and second order equations, linear equations, linear systems of equations, series solutions of nonlinear equations, the Laplace transform, and applications from a variety of fields. An instructor approved graphing calculator will be required. Students will utilize MAPLE software to solve selected problems. Prerequisite: MATH 2414. (Taught in the Summer)
MATH 2412. Precalculus
In-depth combined study of algebra, trigonometry, and other topics for calculus readiness. An instructor-approved graphing calculator will be required. Prerequisite: TSI complete and four years of college-preparatory mathematics including trigonometry. F (2701015819).
MATH 2413. Calculus I
A study of limits, continuity, differentiation and integration of algebraic, trigonometric, logarithmic, exponential and inverse functions; applications of the derivative. An instructor approved graphing calculator will be required. Students will utilize MAPLE software to solve selected problems. Prerequisite: MATH 1314 and MATH 1316 or MATH 2412 or an appropriate score on an additional test required by the mathematics department. (Taught in Fall, Spring, and Summer)
MATH 2414. Calculus II
A study of applications of integration, techniques of integration; sequences and series, conic sections, parametric and polar equations. An instructor approved graphing calculator will be required. Students will utilize MAPLE software to solve selected problems. Prerequisite: MATH 2413. (Taught in Fall and Spring)
MATH 2415. Calculus III
A study of vectors, vector-valued functions, functions of several variables, partial differentiation, multiple integration, and vector analysis. An instructor approved graphing calculator will be required. Students will utilize MAPLE software to solve selected problems. Prerequisite: MATH 2414. (Taught in the Spring)
MODULAR COURSES:
MATH 0305. Modular Mathematics I (3,2,2)
Institutional credit only. Topics time for material that is new. Prerequisites: Appropriate placement test score. Laboratory fee $35. F,Sp,Su (3201045119).
MATH 0307. Modular Mathematics II (3,2,2)
Institutional credit only. Topics Laboratory fee $35. F,Sp,Su (3201045119).
MATH 0309. Modular Mathematics III (3,2,2)
Institutional credit only. Topics similar to MATH 0308 High School Algebra I and an appropriate placement test score or MATH 0306 or MATH 0307. Students must be eligible to enroll in READ 0308. Laboratory fee $35. F,Sp,Su (3201045219).
INSTRUCTIONAL FORMATS:
The mathematics department offers a variety of instructional formats in addition to the traditional lecture format.
These include:
Lecture with Arranged Lab Format:
Format: A 3-hour weekly lecture meeting for 50 minutes 3 times per week or 80 minutes twice a week. A 2-hour weekly mandatory lab component is a part of the class requirement for Math 0304 and Math 0306. One hour of lab is required each week for Math 0308. The lab component takes place in the Math Learning Center in the Engineering Science Building, with student access to 40 computers and experienced math instructors and student tutors. Lab time is arranged at the student's convenience. The MLC lab is open from 8am -8pm, Monday through Thursday, 8am -2pm on Friday.
Advantages: The lecture component of the class is delivered in a traditional format that is familiar to most students. The lab component gives the student a quiet place to complete homework and on-line assignments, while having access to math instructors and student tutors. The MLC operating hours allow the student to have some degree of flexibility in scheduling their lab time.
Disadvantages: The primary disadvantage to this traditional "lecture with arranged lab" setup is that the student must conscientiously plan their lab time.
Target Students: This course will benefit students who need some flexibility in scheduling their lab time.
Courses Offered: Math 0304 and Math 0306, and 0308
Combined Lecture with Lab Format:
Format:
Math 0304 and Math 0306
course designed with a short lecture followed by a longer lab period in a computer lab during which students do online homework and quizzes. For classes meeting two days a week, the class period is two hours and 20 minutes per meeting day. For classes meeting three days a week, the class period is one hour and 30 minutes per meeting day. M Math 0308 meets 4 hours per week either 2 hours on MW or TTH.
Advantages: Required lab-time is built into the course; students are not required to attend a lab outside of class. Material retention will ideally be higher given that students do their daily assignments immediately following the delivery of the material. The course instructor is available to answer students' questions during lab. giving students support and consistency in instruction.
Disadvantages: Students need to be aware of scheduling conflicts given that these courses meet for a longer period than normal courses. Students must also be prepared to focus on their work for the full length of each class meeting.
Target Students : This course will be beneficial to students needing structure.
Courses Offered : MATH 0304, MATH 0306, and MATH 0308
Fast Track Instructional Format:
The fast track instructional format is used for MATH 0304, MATH 0306, MATH 0308, and Math 1314. With this format, the course is completed in an eight week semester with six lecture hours per week. Classes meet Monday through Friday. Math 0304 and Math 0306 are offered in the first eight weeks of each 16 week semester. Math 0306 and Math 0308 are offered in the second eight weeks of each 16 week semester. Math 0308 is offered the first eight weeks followed by Math 1314 the second eight weeks.
Due to the fast pace of the coursework, only students who are self-motivated and disciplined should consider taking fast track classes. Recommended placement guidelines for the fast track classes are as follows:
Course
Level
Test Scores
TASP/THEA
ACCUPLACER
OR
Math
0304
150-179
≥50 on Arith
Math
0306
200-229
≥55 on Elem. Alg.
B or higher in Math 0304
Math
0308
250-269
70-76 on Elem. Alg.
B or higher in Math 0306
Web-Based Instructional Format:
The web-based instructional format is used for MATH 0308, MATH 1333, MATH 1342, MATH 1314, MATH 1316, MATH 1350, and MATH 1351. With this format, the same course one would take in a traditional classroom setting is completed online over a regular 16 week semester using My Math Lab Software through
Most testing will take place at an approved testing center. Also, some assignments will be submitted to the instructor via e-mail, fax or US mail. Communication between the student and instructor is primarily via e-mail. The role of the instructor will be one primarily of facilitator.
The instructor will be available to answer questions, provide learning/testing materials, and monitor the student's progress. Students who cannot attend classes on campus should consider taking a web-based math class.
Because the majority of the coursework will be completed on the student's schedule while meeting due dates, only students who are self-motivated, disciplined, and have a strong mathematics background should consider taking web-based courses. Also, only students who have access to a relatively new computer with high speed internet should consider taking an on-line course.
Modular Format
The mathematics department offers all three levels of developmental mathematics in a modular format. These courses are Math 0305, Math 0307, and Math 0309 which have similar content to Math 0304, Math 0306, and Math 0308, respectively. Course material is divided into small modules. Students take a pre-test over a module. If they score below 75% on the pre-test, they work through the topics in the module by watching and taking notes on a video and completing the homework at 80% mastery level. After completing all the topics, students then take a post-test over the material. They must score 75% to be able to progress to the next module. If they don't score 75%, they talk to their instructor and complete a study plan in order to retake the post-test. Students will take a mid-term and final exam that will each count 20%.
Advantages: Students may complete modules at a faster rate if the material is familiar and take more time in modules that are more difficult. Students could complete more than one course in a semester. Should students need to repeat a course, they are able to carry over the modules that they have completed (the previous semester) and work on only the modules that they need.
Disadvantages: Although students will have a weekly schedule and contact with the instructor to help them stay on track, if students lack the discipline to work on the course and complete the modules, they will not be successful in the course.
Targeted Students: Students who need a quick review can work through the courses at a fast pace while students that struggle with math will have the opportunity to slow down (within reason) to master the content. Students that are repeating a course would benefit from taking a modular course. |
interconnections of the subject to geometry, algebra,... more...
Now in its third edition, Mathematics in the Primary School has been updated to reflect recent mathematics curriculum documentation and revised standards for QTS.
Key areas include:
The role of talk in learning maths
Teacher questioning
Development of children?s reasoning
Creative engagement with maths
Assessment for learning and
Develops the statistical approach to inverse problems with an emphasis on modeling and computations. The book discusses the measurement noise modeling and Bayesian estimation, and uses Markov Chain Monte Carlo methods to explore the probability distributions. It is for researchers and advanced students in applied mathematics. more... |
Gary Rockswold teaches algebra in context, answering the question, "Why am I learning this?" By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Introduction to Functions and Graphs; Linear Functions and Equations; Quadratic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra For all readers interested in precalculus. |
on compact sets, continuous functions are uniformly
continuous and have maxima and minima
differentiable functions are continuous
method for prooving from first principles that a
given function is continuous or differentiable at a given
point
the student must be able to solve concrete problems and
write clear and coherent mathematical arguments incorporating
these techniques and concepts.
Expected outcomes
Students should be able to demonstrate through written
assignments, tests, and/or oral presentations, that they
have achieved the objectives of MAT 401.
Method of Evaluating Outcomes
Evaluations are based on homework, class participation,
short tests and scheduled examinations covering students'
understanding of elementary topology, real analysis, and
related topics that are covered in MAT 401.
Text
Advanced Calculus, by R. Creighton Buck.
McGraw-Hill, 1978.
Table of contents
1. Sets and Functions
1.1. Introduction
1.2. R and R^n
1.3. Distance
1.4. Functions
1.5. Topological Terminology
1.6. Sequences
1.7. Consequences of the Monotonic-Sequence
Property
1.8. Compact Sets
2. Continuity
2.1. Preview
2.2. Basic Definitions
2.3. Uniform Continuity
2.4. Implications of Continuity
2.5. Limits of Functions
2.6. Discontinuities
2.7. Inverses for Functions of One Variable
3. Differentiation
3.1. Preview.
3.2. Mean Value Theorems and L'Hospital's Rule
3.3. Derivatives for Functions on R^n
Grading Policy
Students' grades are based on homework, class participation,
short tests, and scheduled examinations covering students'
understanding of the topics covered in MAT 401. The instructor
determines the relative weights |
Math and Metrics
Session Format:
8 Hours Total (Two 4-Hour Sessions)
Introduction
It is essential that most employees in the production process understand basic mathematical
concepts. For individuals planning to attend a statistical process control training
session, it is a necessity. Furthermore, knowledge of metric units is needed by many
such employees.
Objectives
The participant will learn: (1) the decimal number system, (2) correct rounding procedure,
(3) percentages, (4) relative size, (5) concepts of squares and square roots, (6)
the names, symbols and prefixes of metric units, (7) comparisons and conversions between
metric and U.S. customary units, and (8) illustrations and applications to business
and industry.
Content Outline
Numbers and numeration
Rounding procedures
Squares and square roots
Calculator computations
Percentages
Metric units of length, volume, weight, temperature, and pressure
Who Should Attend
This seminar is intended for all individuals who desire to learn the metric system,
or those entering the SPC program. |
College Trigonometry 6e
9780618825073
061882507X
Summary: Accessible to students and flexible for instructors, "College Trigonometry," Sixth Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses th...at allow the option of using graphing calculators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs.The authors' proven "Aufmann Interactive Method" allows students to try a skill as it is presented in example form. This interaction between the examples and "Try Exercises" serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition, "Review Notes" are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts."Updated!" End-of-chapter exercises--"Assessing Concepts"--have been revised to include more question types including fill-in-the-blank, multiple choice, and matching."Revised!" "Prepare for This Section" exercises, formerly "Prepare for the Next Section," have been moved from the end of each chapter to the beginning of each chapter and afford students the opportunity to test their understanding of prerequisite skills about to be covered."New!" "Calculus Connection" icons have been added to indicate topics that will be revisited in subsequent courses, laying the groundwork for further study."New!" AQuantitative Reasoning feature demonstrates math solutions to real-world problems and is compliant with MAA Guidelines and AMATYC 2006 Crossroads Revisited."Applications" require students to use problem-solving strategies and new skills to solve practical problems. Covering topics from many disciplines, including agriculture, business, chemistry, education, and sociology, these problems demonstrate to students the practicality and value of algebra.Noted by a pie chart icon, "Real Data" examples and exercises require students to analyze and construct mathematical models from actual situations.Appearing throughout the text, "Integrating Technology" notes offer relevant information about using graphing calculators as an alternative way to solve a problem. Step-by-step instructions allow students to use technology with confidence."Exploring Concepts with Technology," an optional end-of-chapter feature, uses technology (graphing calculators, CAS, etc.) to explore ideas covered in the chapter. These investigations can be used in a variety of ways, such as group projects or extra-credit assignments. Together with "Integrating Technology" tips, this feature makes the text appropriate for courses that allow the use of graphing calculators.
Aufmann, Richard N. is the author of College Trigonometry 6e, published 2007 under ISBN 9780618825073 and 061882507X. Six hundred sixty four College Trigonometry 6e textbooks are available for sale on ValoreBooks.com, one hundred twenty nine used from the cheapest price of $83.15, or buy new starting at $103061882507X BRAND NEW. We are a tested and proven company with over 900, 000 satisfied customers since 1997. Choose expedited shipping (if available) for much faster delivery. [more]
061882507X |
Fórmulas Matemáticas is the Spanish version of the Math Formulary App that covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic betterBest mathematical tool for school and college! If you are a student, it will help you to learn algebra!
Note: Polynomials appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in algebra and algebraic geometry revealed |
'I Did It' Mathematics- 2nd Edition Teacher's Manual 3
(Paperback)
The textbooks 'I Did It' Mathematics for Classes 1 to 5, prepared in conformity with the latest NCERT syllabus and the National Curriculum Framework (2005), encourage students to understand the interrelationship between different topics. 'I Did It' Mathematics Teacher Manuals, besides providing additional resources for teachers, would serve as a useful guide for teaching mathematics in classrooms.
Key Features
* Introduction to help teachers understand the concept of 'mathematics laboratory'
Popular Searches
The book 'I Did It' Mathematics- 2nd Edition Teacher's Manual 3 by Sudha Mahesh
(author) is published or distributed by Cambridge University Press India [, 9788175966574].
'I Did It' Mathematics- 2nd Edition Teacher's Manual 3 has Paperback binding and this format has 32 |
Engineering Mathematics
Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, ...Show synopsisThrough previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Advanced Engineering Mathematics features a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets, incorporating the use of leading software packages. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Partial Differential Equations, Complex Analysis, and Probability and Statistics |
Foundations of Algebra
by Lynn Marecek and MaryAnne Anthony-Smith
Hi! We are excited to introduce Foundations of Algebra with Strategies for Success and Prealgebra with Strategies for Success to you!
Foundations of Algebra with Strategies for Success is a manuscript being used right now in the Prealgebra classes at Santa Ana and Santiago Canyon Colleges. It provides students with a bridge between arithmetic and beginning algebra. Student understanding of algebraic concepts is supported through the use of manipulative activities called Manipulative Mathematics. Students' literacy in written English and fluency with mathematical vocabulary are addressed through Links to Literacy activities. And every lesson in Foundations of Algebra with Strategies for Success includes a pro-active study skills activity, which we call Strategies for Success.
Designed with a heavier emphasis on arithmetic concepts and procedures, Prealgebra with Strategies for Success can meet the needs of college students in their first developmental mathematics course. Manipulative Mathematics, Links to Literacy, and Strategies for Success are integrated throughout Prealgebra.
Foundations of Algebra with Strategies for Success and Prealgebra with Strategies for Success will be available in early 2014 from Pearson Higher Education.
The Strategies for Success student workbook is now available from Pearson Higher Education. Check their website ( PearsonHigherEd ) for information about ordering it as a standalone workbook or as part of a textbook package.
Click on the Manipulative Mathematics, Links to Literacy, or Strategies for Success links on the menu bar above to learn more about these unique features of Foundations of Algebra with Strategies for Success and Prealgebra with Strategies for Success.
12 responses to Foundations of Algebra
I really seem to go along with everything that is put into writing throughout "Foundations of
Algebra | Prealgebra with Strategies for Success". I am grateful for pretty much all the
information.I appreciate it-Curt |
Permadi.com - F. Permadi
Java and Flash applets: logic games, drawing and pattern-making programs, Conway's Life, and more arcade-style offerings. Also includes tutorials in using Flash and a graphics gallery.
...more>>
Plane Geometry Web Pages - David Jaffe
Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity;
...more>>
Please Excuse My Dear Aunt Sally - Robert Owens
A step-by-step introduction to the mathematics behind the PEMDAS mnemonic. With examples, quizzes, and puzzles illustrating order of operations. A Wired@School project of The Franklin Institute Online Museum Educator program.
...more>>
Poliplus Software
Educational computer algebra, geometry, trigonometry, calculus software for Windows and Macintosh, and Java. Formulae 1 (F1) is a computer algebra system designed for the teaching and exploration of Mathematics. EqnViewer is a Java applet that allows
...more>>
Practical Money Skills for Life - VISA
For educators, parents and students to practice better money management for life. Available online or in a binder format, the free classroom curriculum consists of a teacher's guide, student worksheets and quizzes. Teacher's Guide lessons cover topicsProbability Tutorials - Noel Vaillant
An online course on measure theory, lebesgue integration and probability, with tutorials (in PDF format) designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved theorems, as well as clear definitions, are
...more>>
Professor Freedman's Math Help - Ellen Freedman
A mixture of sound, animation, humor and personal advice dealing with math anxiety for the adult student and community college learner. The site includes tutorial lessons, math assignments, study skills tips, information on learning styles, an on-line
...more>>
Rational Number Tutorial - Joseph L. Zachary
A tutorial that explores the nature of rational numbers, the significance of the minimum and maximum integers in a rational number system, and the meaning of overflow. Includes a Java applet that opens in a separate window, for use alongside the tutorial.
...more>>
Rick Durrett's Home Page - Rick Durrett
Research in the general area of probability theory, and more specifically in stochastic spatial models and their applications to ecology and genetics. Publications organized into books and papers, as well as s3 (stochastic spatial simulator) and stochastic
...more>>
Roman Numerals 101 - Oliver Lawrence
The Romans used only seven letters; the combination of a letter and its position could represent any number. They also used a line above the letter, so the numbering system actually represents our own very closely, with fourteen different symbols. The
...more>>
Shelley's Mathematics Articles - Shelley Walsh
"Little self-contained articles [that] write up more than you can normally fit in a lecture, and ... hopefully put together enough explanation so that there's something for a great variety of different ways of thinking." Organized into Geometry; Analytic
...more>>
SketchMad - Nathalie Sinclair
An archived resource, not currently updated: A resource center devoted to using The Geometer's Sketchpad in the classroom. Includes tips, strategies, lesson plans, and sketches for beginning and intermediate Sketchpad teachers, stories from the classroom
...more>>
Snowflakes - Kenneth G. Libbrecht
"Your online guide to snowflakes, snow crystals, and other ice phenomena." Snow activities include instructions for using everday objects and dry ice to make your own snowflakes; for using glue to make plastic snowflake replicas ("snowflake fossils")
...more>>
Software Carpentry - Software Carpentry
Basic computing skills for scientists through self-paced online instruction or short, intensive workshops ("boot camps" at universities and research facilities in the US, UK, and Canada). See, in particular, the free outlines and video lectures on MATLAB,
...more>>
Solving-Math-Problems
Type up your math questions for free help or see step-by-step instructions on solving problems that involve sets, equations, exponents, roots, or real numbers, such using the number line to compare two decimals or using direct comparison (equivalence)
...more>>
Solving Quadratic Equations - Prakash Sukhu
Introduces the general form of the quadratic equation, and shows how to solve the quadratic equation step by step. Includes methods of factorisation and completing the square, questions to test your knowledge, and an online equation solver with which
...more>>
The SPSS Decision Maker - Maurits Kaptein
This is a website that guides you through a number of steps to select a statistical technique. Developed for those who do know the basic concepts of research statistics and experimental design but need help determining the final test.
...more>>
Statistical Assessment Service (STATS)
STATS is a non-profit, non-partisan resource on the use and abuse of science and statistics in the media. Its goals are to correct scientific misinformation in the media and in public policy resulting from bad science, politics, or a simple lack of information
...more>>
Statistics How To - Stephanie
A resource which includes step-by-step instructions for undergraduate statistics students for specific problem types, reference tables, and visual calculators that actually explain how computations are performed using the student's own inputted data.
...more>> |
Functions and graphs, rational, trigonometric, exponential functions, composite and inverse functions, limits and continuity, differentiation and its applications, integration and its applications. Prerequisites: MATH 120 (or four units of high school mathematics including trigonometry, or MATH 110 and MATH 125, or MATH 202). |
Derwood ACT MathAlgebra is the most useful of the math disciplines we learn in school. We think algebraically about many problems without realizing it. Many students just have some difficulty translating what they already know into x and y language. |
Addition, subtraction, multiplication, and division of common fractions and mixed numerals. This module includes solving equations and word problems and the order of operations. Skills prerequisite: MAT 011. Skills corequisite: ENG 010. |
Theory, Methods and Practice
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in...
Compared to the traditional modeling of computational fluid dynamics, direct numerical simulation (DNS) and large-eddy simulation (LES) provide a very detailed solution of the flow field by offering enhanced capability in predicting the unsteady features of the flow field. In many cases, DNS can...
Computational Tools in A Unified Object-Oriented Approach
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding...
Theory and Applications
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and...
A Thorough Overview of the Next Generation in Computing
Poised to follow in the footsteps of the Internet, grid computing is on the verge of becoming more robust and accessible to the public in the near future. Focusing on this novel, yet already powerful, technology, Introduction to Grid Computing...
Known for its versatility, the free programming language R is widely used for statistical computing and graphics, but is also a fully functional programming language well suited to scientific programming.
An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to...
Collects the Latest Research Involving the Application of Process Algebra to Computing
Exploring state-of-the-art applications, Process Algebra for Parallel and Distributed Processing shows how one formal method of reasoning—process algebra—has become a powerful tool for solving design and...
This textbook presents a variety of applied mathematics topics in science and engineering with an emphasis on problem solving techniques using MATLAB®. The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book...
An Introduction to Experimental Mathematics
Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples... |
Mathematics and Technology for
Talented Youth
Welcome!
Mathematics is one of the few
disciplines that teaches us about the power of thought as distinct from
the power of authority. It is not necessarily dependent on our physical
observations of the world, and yet it constantly provides models for
our observations. Such models—usually studied in applied
mathematics—may have relevance in traditional sciences such
as physics, biology, or chemistry. Topics studied by mathematicians,
such as chaos theory or dynamical systems, often serve as models for
economics, neuroscience, or predictors of fluctuations in the stock
market.
Students majoring in
mathematics take courses in the logical foundations of mathematics, the
calculus sequence, matrix algebra, and discrete mathematics. Majors
choose from a concentration of applied, traditional, or actuarial
mathematics. Both the B.A. and the B.S. in mathematics will allow entry
to advanced studies or career opportunities as diverse as the fields to
which mathematics is applied. The metro region of Washington, DC is a
particularly fertile area for related job opportunities, including
consulting, teaching, and government.
About
George Mason
Since it was founded in 1972,
George Mason University has grown into a major educational force and
earned a reputation as an innovative, entrepreneurial institution. Just
minutes from Washington, D.C., George Mason has a growing and diverse
student body and an exceptional faculty of enterprising scholars. At
the center of the world's political, information, and communications
networks, George Mason is the university needed by a region and a world
driven by new social, economic, and technological realities.
Department
of Mathematical Sciences
4400
University Drive, MS: 3F2
Exploratory Hall, room 4400
Fairfax,
Virginia 22030
Main
Phone Number: 703-993-1460
Fax
Number: 703-993-1491
News and Events
Mathematics Colloquium on Apr. 18
The Mathematics Colloquium will meet on Friday, Apr. 18 at 3:30 pm in Room 4106, Exploratory Hall. James Shook of NIST will talk on Matrix scaling: A new heuristic for the feedback vertex set problem.
Combinatorics, Algebra and Geometry Seminar on Apr. 18
The next meeting of
the CAGS Seminar
will be Friday, Apr. 18 at 12:30 pm in Room 4106, Exploratory Hall.
James Shook of NIST
will speak on
Threshold digraphs.
Alexandra Zeller is going to the White House!
Alexandra was selected to represent the state of Virginia at the Posters on the Hill conference. She will present her URCM research. |
books.google.ca - Students,... geometry from an advanced standpoint
Elementary geometry from an advanced standpoint |
Algebra 1
9780078651137
ISBN:
0078651131
Pub Date: 2005 Publisher: Glencoe/McGraw-Hill School Pub Co
Summary: A flexible program with the solid content students need "Glencoe Algebra 1" strengthens student understanding and provides the tools students need to succeed--from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests.
Holliday, Berchie is the author of Algebra 1, published 2005 under ISBN 9780078651137 and 0078651131. Eight hundred ei...ghty two Algebra 1 textbooks are available for sale on ValoreBooks.com, seven hundred seventy five used from the cheapest price of $7.34, or buy new starting at $45.00.[read more]
NOTE! This is the Virginia Edition with some additional state-specific material, otherwise the text is identical to the national edition. Book is heavily worn. Cover corners [more]
NOTE! This is the Virginia Edition with some additional state-specific material, otherwise the text is identical to the national edition. Book is heavily worn. Cover corners bumped. No markings noted on pages. Multiple copies available. Your purchase benefits world-wide relief efforts of Mennonite Central Committee.[less |
Secaucus GeThe laws of exponents are extended to the cases of zero, negative and fractional exponents. The idea of a function and its inverse is introduced. Extensive use is made of exponential and logarithmic functions, including graphing and solving equationsPlease feel free to contact me with any specific questions, comments, or concerns. I assure you that you will receive a prompt response. TonyIn college, the emphasis of my studies was on ancient philosophy, particularly Plato and Aristotle. |
Copies of the 2011 Facilitator Guide and StudentWorkbook will be available for download from the ... RT-130. Core content is ... at Questions and Additional Information
130, 145, 200, 241 Math 222 or ... Orientation Workbook ~ 29 CSM STUDENT EDUCATIONAL PLAN THIS IS YOUR WORKSHEET. KEEP A RECORD OF YOUR COURSE WORK AND PLANS. ... a student's and educational goals. Should be monitored each semester and revised and modified
If the hours are a minimum versus recommended they will be ... In both the Instructor Guide and StudentWorkbook, Appendix A includes optional readings. Read through these articles before conducting the class so you have a good
Firefighter Training, S-130 Fire Exercise Day INSTRUCTIONS TO THE INSTRUCTOR Exercise set up and logistics: ... Student demonstrated proper travel procedures (vehicle, foot, etc.) en route to and from an incident. Yes _____ No_____ If no is ...
StudentWorkbook This class is a requirement of 310-1 and CICCS for Company Officers. When: April 7th to 9th, 2010 ... (I-100, L-180, S-190, S-130, S-131, S-133) Pre-Course Work There is pre-course work that is required to be completed prior to the class.
• This StudentWorkbook correlates with the Show What You Know® on the OAA for Grade 7 Mathematics,Teacher Guide (sold separately). $16.95 StudentWorkbook ... full-length Mathematics Practice Tests with over 130 OAA-style questions.
Show What You Know® on STAAR for Grade 4 Mathematics, StudentWorkbook includes many features ... H 130 calories J 113 calories 23 The fourth grade classes at Pinedale Elementary School are going on a field trip to the natural history museum.
The Glencoe Parent and Student Study Guide Workbook is designed to help you support, monitor, and improve your child's math performance. ... If she spent $130.29, what is a reasonable estimate for the cost of the third book? A $30.00 B $35.00 C $40.00 D $25.00
StudentWorkbook. ii TO THE STUDENT ... each section of the Student Edition, you are alerted to key terms, asked to draw ... Study Guide 2 Russia's People and Culture 130 Study Guide 3 The Republics Emerge 135 Birthplace of Civilization
... student achievement. This workbook, along with many other resources including videos of classroom instruction, pre- and post-conferences ... ... demonstrates familiarity with each student's background knowledge and experiences, ...
The All-in-One StudentWorkbook, available as both on-level and adapted for special needs, ... ongoing student support o Teacher's Edition – Provides comprehensive support for planning, ... 130-134, 153, 537-538, 540-545, 553 |
books.google.ca - Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later, a new series Erg... |
Chapter 6: CK-12 Algebra Explorations Concepts, Grade 4
Introduction
In these concepts, you will continue to develop eight key concepts of algebra and will practice your problem solving skills. There are eight concepts, and each one focuses on a key algebraic thinking strategy. You will focus on describing, identifying your job, planning, solving, and checking your thinking.
Chapter Outline
Chapter Summary
Summary
In these concepts we used proportional reasoning when we interpreted map scales and bar graphs and when we determined better buys. We thought about equality and inequality and wrote equations when we interpreted and reasoned about pictures of pan balances. We saw variables as unknowns when we solved for the weights of blocks on scales and for the unknowns in circles and arrows diagrams. We also saw variables as varying quantities when we completed tables for functions. In all of the concepts, we practiced interpreting representations of mathematical relationships when we looked at pan balances, circle and arrow grid diagrams, tables of values, weight scales, weigh equations, better-buy signs, maps, and bar graphs.
Image Attributions
Description
Writing and solving equations, functions and function tables, and interpreting maps and graphs |
Resources
Information
Mathematics
Enjoy working with numbers, looking for and recognizing
patterns, manipulating mathematical symbols, and solving logic
puzzles and brain teasers? If so, a mathematics major may be for
you.
The mathematics major at CMU is designed to prepare students
to work in areas which require critical thinking skills and the
ability to work with mathematical concepts. Problem solving is
needed in every field imaginable, which is one reason for the
diversity of jobs held by mathematicians. |
An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)
Book Description: "Written in an admirably cleancut and economical style." — Mathematical Reviews.This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented.The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations.Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems |
Delmar's Math Review Series for Clinical Practice : The Basics of Fractions
9781439058350
ISBN:
1439058350
Pub Date: 2011 Publisher: Delmar Cengage Learning
Summary: Ellsbury, Roger is the author of Delmar's Math Review Series for Clinical Practice : The Basics of Fractions, published 2011 under ISBN 9781439058350 and 1439058350. Four hundred sixty seven Delmar's Math Review Series for Clinical Practice : The Basics of Fractions textbooks are available for sale on ValoreBooks.com, one hundred eight used from the cheapest price of $3.00, or buy new starting at $20.52Delmar's Math Review Series for Health Care Professionals is the ideal resource for students, those just entering the health care field, and for practicing health care profes [more]
Delmar's Math Review Series for Health Care Professionals is the ideal resource for students, those just entering the health care field, and for practicing health care professionals who need to review mathematical concepts and take their basic arithm.[less] |
Lesson 10: Functions and Level Sets
by Matthew Leingang, Clinical Associate Professor of Mathematics at New York University on Feb 27, 2008
5,552 views
A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, ...
A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, it's like a topographical map of the surface |
Elementary Linear Algebra: Enhanced Edition - 6th edition
Summary: The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors? clear, careful, and concise presentation of material?written so that users can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data ...show moreand applications also reflect current statistics and examples to engage users and demonstrate the link between theory and practice. This Enhanced Edition includes instant access to WebAssign�, the most widely-used and reliable homework system. WebAssign� presents over 500 problems, as well as links to relevant book sections, that help users grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this book. This guide contains instructions to help users learn the basics of WebAssign quickly. ...show less
Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000115.96 +$3.99 s/h
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Algebra in 15 Minutes a Day
BDPacked with short and snappy lessons, Algebra in 15 Minutes a Day makes learning algebra easy. Fun facts help students build each lesson one step ...Show synopsisBDPacked with short and snappy lessons, Algebra in 15 Minutes a Day makes learning algebra easy. Fun facts help students build each lesson one step at a time, and valuable memory hooks and shortcuts help students retain what they are learning. This book helps students understand: Linear equations,Inequalities and absolute values,Systems of linear equations,Powers, exponents, and polynomials,Quadratic equations and factoring,Rational expressions and proportionsoAnd mor |
Combinatorics Topics, Techniques, Algorithms
9780521457613
ISBN:
0521457610
Pub Date: 1995 Publisher: Cambridge University Press
Summary: A textbook in combinatorics for second-year undergraduate to beginning graduate students. The author stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter. The book is divided into two parts, the second at a higher level and with a wider range than the first. More advanced topics are given as projects, and there are a number of exercise...s, some with solutions given.
Cameron, Peter J. is the author of Combinatorics Topics, Techniques, Algorithms, published 1995 under ISBN 9780521457613 and 0521457610. Six hundred forty Combinatorics Topics, Techniques, Algorithms textbooks are available for sale on ValoreBooks.com, one hundred sixty one used from the cheapest price of $41.00, or buy new starting at $78.67 |
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, �Calculus Derivatives 2� and �Calculus Derivatives 2.5 (HD).� Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Students construct the graph of derivatives using a tangent line. In this construction of a graph of a derivative lesson, students use their Ti-Nspire to drag a tangent line along a graph. Students graph the slope of the tangent line. Students discuss the similarities and differences between the original graph and its derivative.
Twelfth graders explore the concept of limits. In this calculus lesson, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
In this capacitance learning exercise, students solve 19 problems about capacitance, voltage, electric charge and Ohm's Law. They use calculus to solve some of the problems and they are given equations used to solve different capacitance problems.
Students investigate an article on local linearity. In this calculus lesson, students read about the application of math in the real world. They gain insight from the teachers view of how to teach and relate the topic to the real world.
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, "Calculus Derivatives 2Ó and "Calculus Derivatives 2.5 (HD).Ó Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Twelfth graders investigate derivatives. In this calculus lesson plan, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The lesson plan requires the use of the TI-89 or Voyage and the appropriate application.
In this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Students use online resources, including animations,to define the slope of a curve and how to calculate the slope. They solve 8 problems online, using the definition of the derivative of a function at a point to calculate slope of the curve.
Twelfth graders assess their knowledge of trig functions and their properties. For this calculus lesson, 12th graders take a test on derivatives, trig functions, and the quotient rule. There are 2 different versions of the same test available.
Students review derivatives and equations for their test. For this calculus lesson, students review average rate, parametric equations, tangent line to a curve and value of a derivative to prepare and show mastery on a chapter test. They show proficiency on rig derivatives and differential equations.
Students review integrals and how they apply to solving equations. In this calculus lesson plan, students assess their knowledge of derivatives, rate of change, and lines tangent to a curve. This assignment contains two version of the same test concept.
Students analyze graphs and determine their general shape. In this calculus instructional activity, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answers.
Using the TI-89 calculator, students explore the statistical, graphical and symbolic capabilities of the TI-89. Students investigate topics such as solving systems of equations, finding inverse functions, summations, parametrics and trigonometry.
Students investigate exponential functions. In this Algebra II/Pre-calculus lesson students find an exponential model from a set of data. Students investigate the affects of changing parameters have on the graph of an exponential function. |
9780321442321
ISBN:
0321442326
Edition: 9 Publisher: Pearson
Summary: Addison Wesley Staff is the author of Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover, published under ISBN 9780321442321 and 0321442326. One hundred nineteen Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover textbooks are available for sale on ValoreBooks.com, fifteen used from the cheapest price of $5.37, or buy ne...w starting at $175Textbook-Sound copy, mild reading wear. May or may not have untested CD or Infotrac. May contain highlighting, underlining or writing in text. No international shipping. Purc [more]
Textbook-Sound copy, mild reading wear. May or may not have untested CD or Infotrac. May contain highlighting, underlining or writing in text. No international shipping. Purchasing this item helps us provide vocational opportunities to people with barriers to employment1442321
ISBN:0321442326
Edition:9th
Publisher:Pearson
Valore Books is the top book store for cheap Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover rentals, or used and new condition books available to purchase and have shipped quickly. |
Course Listings
Math
MATH 102X Problem-Solving (.25)
The course will offer students the opportunity to solve challenging mathematical problems unlike standard homework problems in any course. Class time will be spent studying problems, discovering solutions, writing up solutions formally, and discussing the important ideas of each solution. Most problems will be of the kind appearing on the Putnam Exam, an annual international mathematics competition. This course may be repeated for credit.
Offering: Fall
Instructor: Staff
MATH 130 (QA*) Contemporary Mathematics (1)
A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics. MATH 130 may not be taken for credit after any Mathematics course numbered above 140 has been completed.
MATH 141 (QA*) Calculus I (1)
A first course in calculus-differential and integral calculus of algebraic and exponential functions, with applications. (MATH 141 counts for only .5 credit if the student has completed MATH 139 Brief Calculus.)
MATH 142 (QA*) Calculus II (1)
A second course in calculus: review of differential and integral calculus via trigonometric and logarithmic functions, techniques and applications of integration, polar coordinates and parametric equations, infinite series.
MATH 220 (QA) Mathematics for Elementary Teachers (1)
The objective of the course is to present mathematics in a format that prepares teachers to teach elementary school mathematics. Teachers need a firm foundation in the theory of mathematics as it pertains to the elementary school curriculum. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. Topics to be covered will include problem solving, mathematics as a method of communication, mathematics as a method of reasoning, and specifics of elementary school mathematics such as whole number operations, geometry and spatial sense, measurement and estimation, fractions and decimals, and patterns and relationships.
MATH 251 (W) Foundations of Advanced Mathematics (1)
This course is intended as the first course after calculus for those students intending to major or minor in mathematics. It provides an introduction to logic and the methods of proof commonly used in mathematics. Applications covered in the course are the foundations of set theory, the real number system, elementary number theory and other basic areas of mathematics.
MATH 325 (QA) Mathematics for Teachers (1)
The objective of this course is to present mathematics in a format that prepares teachers to teach mathematics in the public schools. Teachers need a firm foundation in the theory of mathematics as it pertains to their particular curricula. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. The course will emphasize mathematics as a method of communication and reasoning. Topics selected to be relevant to elementary, middle, and/or high school curricula will depend on the interests of the students, but will have a strong problem-solving emphasis. The course will require an extensive early field experience in the public school classroom.
MATH 366 (QA) Applied Mathematics: Optimization (1)
Formulation of problems in mathematical terms, solutions of the problems, interpretation and evaluation of the solutions. Topics will be chosen from inventory problems, growth and survival models, linear programming, scheduling, Markov chains, game theory and queuing problems.
MATH 446 Advanced Calculus (1)
A study of the concepts of calculus from an advanced standpoint. Includes the real numbers, real valued functions, differentiation and integration, vector valued functions, line and surface integrals. Other topics may be chosen from point set topology, measure and integration, differential geometry and calculus of variations.
MATH 486 Topics in Mathematics (1)
This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Cryptology, Differential Geometry, Vector Analysis, Topology.
Offering: On demand
Instructor: Staff
MATH 490 Independent Research (.5)
Directed research to investigate topics of special interest under the guidance of a faculty member. Topics chosen on the basis of the background and interests of the individual student.
Prerequisite: Consent of instructor
Offering: On demand
Instructor: Staff
MATH 491 Advanced Independent Study (.5)
A course of directed research designed to enable the exceptional student to continue the investigation of topics of special interest under the guidance of a faculty member.
Prerequisite: Consent of instructor
Offering: On demand
Instructor: Staff
MATH 499 Seminar in Mathematics (1)
Study selected in consultation with the mathematics faculty and presented to the class. The seminar serves as the Senior Year Experience and involves oral and written presentation of research and reading topics. Required for Mathematics majors. |
Lessons Include: Ratios, Unit Rates, Proportions, Solving Proportions, Fractions and Percents, Decimals and Percents, Find the Percent, Percent of a Number (Finding the Part) Finding a Number When the Percent is Known, Discount, Markup, Percent of Increase, Percent of Decrease
Lessons Include: Area of a Triangle, Area of a Parallelogram, Area of Similar Figures, Area of a Trapezoid, Area of a Rhombus or Kite, Area of a Circle, Area of a Sector of a Circle, Area of Regular Polygons, Area of an Irregular Shape, Comparing Area and Perimeters, Using Trigonometry to Find the Area of a Triangle, Geometric Probability
Lessons Include: What is a Polynomial? Adding Polynomials, Subtracting Polynomials, Multiplying a Polynomial, Multiplying Binomials, Squaring a Binomial, The Difference of Two Squares, Finding the Greatest Common Factor for Variable Terms, Factoring a Binomial, Factoring a Polynomial, Factoring Trinomials in the Form x² + bx + c. Factoring Trinomials in the Form ax² + bx + c
Lessons Include: Graphing Quadratic Functions, Properties of a Graph of a Quadratic Function, Writing a Quadratic Function from its Graph, Quadratic Function in Intercept Form, Solving Quadratic Equations Using Square Roots, Solving a Quadratic Equation by Completing the Square, Quadratic Formula, Solving a Quadratic Equation by Factoring, Using the Discriminant, Methods for Solving Quadratic Equations, Writing an Equation of an Ellipse, Foci of an Ellipse
Lessons Include: Raising a Power to a Power, Raising a Product to a Power, Raising a Quotient to a Power, Dividing Powers with the Same base, Simplifying Rational Expressions, Multiplying Rational Expressions, Dividing Rational Expressions, Finding the ICD of a Rational Expression, Adding Rational Expressions, Subtracting Rational Expressions
Lessons Include: Relations and Functions, Types of Functions, Direct Variation, Inverse Variation, Slope-Intercept Form, Point-Slope Form I, Point-Slope Form II, Linear Parametric Equations, Writing a System of Equations as a Matrix, Using Matrices to Solve a System of Two Equations, Cramer's Rule
Math (Grades 4-6 2-3 K-1 |
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Overview
This is an easy-to-follow tutorial on the most popular text processing system used in the academic community. It explains formatting fundamentals and the more complex techniques for typesetting mathematical formulas. It is useful as a resource for those with access to the previous version (LATEX 2.09) who want to update themselves on the latest version - LATEX 2.
The book is aimed at anyone interested in text processing and in particular those wanting to use LATEX to produce high quality documents. LATEX 2e is suitable for people with no previous LATEX experience.
Written from the users point of view, this edition features many entirely new commands, replacing obsolete material as well as an appendix describing the main differences between old version LATEX 2.09 and the new version. There is also a glossary of all basic LATEX 2 commands.
Many of the typesetting examples from the book are coded as templates and are available on the accompanying Website |
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Linear Algebra And Its Applications 3rd Edition By David C. Lay solutions ebook |
Carnegie Learning develops textbooks that support a collaborative, student-centered classroom. Our classroom activities address both mathematical content and process standards. Students develop skills to work cooperatively to solve problems and improve their reasoning and sense-making skills.
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Supplemental & Intervention Solutions
Some students will need additional support and intervention to meet the high expectations of state standards. Carnegie Learning can help you implement tiered interventions in mathematics. In addition to the core instruction we provide in our textbooks, we provide interactive math instruction in our Cognitive Tutor software.
Our Algebra Readiness curriculum is a one-year course designed to remediate students who have completed a middle school math sequence of instruction but still exhibit gaps in their math knowledge and skills. The course covers the five major NCTM strands: Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability.
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I think Carnegie Learning curricula is helping students by allowing them to take an active role in their work and set their own goals. Many have become responsible learners, taking on initiative to do better for themselves. I love the independence this program has fostered in my students. |
Product Information for the Carnegie Learning Math Series
Our goal is to support your team of teachers, coaches and leaders to obtain the results that your students deserve.
The Carnegie Learning Math Series contains textbooks and MATHia software for grades 6-8. Together these instructional materials provide formative assessments, relevant problem-centered activities to develop mathematical reasoning and sense making skills, and technology to personalize learning.
The primary goal of the Carnegie Learning Math Series is to get students to think! We recognize the responsibility of providing instruction that respects the research on how students learn mathematics and believe in a continuous improvement model. Research can be difficult to implement in a practical way. Research shows that there is no magic bullet - there are no shortcuts; learning math requires mental effort. Our materials are designed to provide students with the appropriate tools to think deeply about mathematics and fluently
execute the procedures.
Since the middle grades are critical for students to obtain mastery of mathematics, the courses were developed to align to the Common Core State Standards for Mathematics. Students who complete the series will have a solid foundation to be successful in high school mathematics.
Carnegie Learning Math Texts help students make connections among different math concepts and understand mathematical relationships. Students build on prior knowledge and obtain new knowledge by solving real-world problems that relate to their interests in sports, business, environmental science, the arts and more.
Carnegie Learning is working side-by-side with schools and districts implementing our curricula, and we are dedicated to partnering with you to increase teacher effectiveness and student achievement in mathematics. As you work with our professional services team to build a standards-based, student-centered classroom and effectively integrate technology to inform data-driven instruction, your district will build the capacity you need to raise and sustain student achievement.
The Carnegie Learning Math Series includes MATHia software, which offers personalized mathematics instruction using the most precise methods of differentiated instruction available. The built-in assessments, engagement features and reports make it a perfect fit for your intervention model. Carnegie Learning offers a three-tiered approach to RI for middle school math students. |
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THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Algebra 2 is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
Empower Teachers and Students in the 7th Grade Math Classroom Built around the Common Core Accelerated 7th GradePathway,Glencoe Math Acceleratedsupports eachteacher's unique teaching style and each student's uniquelearning needs like never before. Get your students excitedabout math with this all new program that is interactive,flexible, and highly customizable. Empower Teachers to: Plan Your Waywith preloaded lesson plans,resources, and presentations which can be customizedto match unique teaching styles or add your ownresources for a personal touch Teach Your Waywith interactive whiteboad lessons,games, presentations, and point of use activities that engage students and helps them stay on task Assess Your Waywith choices for diagnostic,formative, and summative assessment available inready-to-use print assessment masters or create yourown tests online with McGraw-Hill's eAssessment tool Empower Students to: Learn Their Wayby establishing strong study andorganizational skills for the transition to algebra andhigh school math with the Interactive Study Guide Learn in Their Worldwith online resources such as engaging apps, animations, games and videosThe Glencoe Math Interactive Student Editions allowGlencoe Algebra 1 strengthens students/learners understanding and provides the tools students need to succeed from the first day your students/learners begin to learn the vocabulary of algebra until the day they take final exams and standardized tests.
A flexible program with the solid content students need Glencoe Algebra 2 strengthens student understanding and provides the tools students need to succeed--from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests |
Using And Understanding Mathematics A Quantitative Reasoning Approach
9780321458209
ISBN:
0321458206
Edition: 4 Pub Date: 2007 Publisher: Addison-Wesley
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics ...engage students while underscoring the practical, essential uses of math.
Bennett, Jeffrey O. is the author of Using And Understanding Mathematics A Quantitative Reasoning Approach, published 2007 under ISBN 9780321458209 and 0321458206. One hundred twenty Using And Understanding Mathematics A Quantitative Reasoning Approach textbooks are available for sale on ValoreBooks.com, fifty three used from the cheapest price of $1.30, or buy new starting at $18Everything about this book was absolutely useful and helpful in working on my assignments and doing homework. I was able to highlight key elements in the book as well to help me prepare for my tests. The diagrams and examples were very self explanatory. I would highly recommend this book to anyone I know that is taking a general college math course. I actually bought this book so I can use it as a reference when working towards my bachelors degree in the near future.
I took a MAT106 class which was a general math course that I had to take towards my degree. I found purchasing this book very helpful and plan to keep it for further reference and to continue working on problems to have a complete understanding of mathematics. |
The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ???see the math??? through its focus on visualization and technology. These books continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications.
With the Fifth Edition, visualization is taken to a new level with technology, and students find more ongoing review. In addition, ongoing review has been added with new Mid-Chapter Mixed Review exercise sets and new Study Guide summaries to help students prepare for tests |
Discrete Mathematics For Computer Science
9781930190863
ISBN:
1930190867
Pub Date: 2005 Publisher: Key College Publishing
Summary: "Discrete Mathematics for Computer Science" is the perfect text to combine the fields of mathematics and computer science. Written by leading academics in the field of computer science, readers will gain the skills needed to write and understand the concept of proof. This text teaches all the math, with the exception of linear algebra, that is needed to succeed in computer science. The book explores the topics of bas...ic combinatorics, number and graph theory, logic and proof techniques, and many more. Appropriate for large or small class sizes or self study for the motivated professional reader. Assumes familiarity with data structures. Early treatment of number theory and combinatorics allow readers to explore RSA encryption early and also to encourage them to use their knowledge of hashing and trees (from CS2) before those topics are covered in this course.
Bogart, Kenneth P. is the author of Discrete Mathematics For Computer Science, published 2005 under ISBN 9781930190863 and 1930190867. One hundred twenty two Discrete Mathematics For Computer Science textbooks are available for sale on ValoreBooks.com, eight used from the cheapest price of $10.19, or buy new starting at $16.74 |
Fractal Music Composer is a powerful music editor. Students build their own musical phrases out of notes from their choice of...
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Fractal Music Composer is a powerful music editor. Students build their own musical phrases out of notes from their choice of multiple keys and musical scales. Compositions are built from notes and phrases playing on assorted instruments. Fractal editing operations create self-similar sequences across different time and sound scales. Students can save MIDI output of their creations, which can play their music on almost any computer.
A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata;...
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A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata; Iterated Function Systems (deterministic, random, data-driven, and with memory); Pascal's Triangle; Circle Inversion; Limit Sets of Circle Inversion. The online course materials that go with this applet series is at . This course is taught to high school math teachers as well as university students. |
During this level course, students gain proficiency in solving linear equations, inequalities, and systems of linear equations. New concepts include solving quadratic equations and inequalities, exploring conics, investigating polynomials, and applying/using matrices to organize and interpret data. Students will also investigate exponential and logarithmic functions |
Volume 8, Number 3
20 January 2003 Vol. 8, No. 3
THE MATH FORUM INTERNET NEWS
Math Lessons for Math Teachers - Picciotto
The Math Projects Journal | Michigan Teacher Network | NSDL
MATH LESSONS FOR MATH TEACHERS
by Henri Picciotto
Picciotto links to or references lessons which he has used
to help middle school and high school teachers develop more
depth of understanding of pre-college math. Most of the
lessons are based on ideas that are accessible to students,
though not at the same depth.
Concept Analysis
Look at familiar material from unfamiliar angles, in order to
increase depth of understanding.
- Function Diagrams
- Iterating Linear Functions
Problem Analysis
Start with a problem that can be posed to students, and end with an
analysis at a deeper level, generally by seeking generalization
and/or proof.
- Staircases (PDF)
- Pattern Block Trains (PDF)
Formal Development
Put pre-college mathematics in a more formal framework.
- Abstract Algebra
- Geometry of Linear Graphs (PDF)
-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-
THE MATH PROJECTS JOURNAL
Edited by Greg Rhodes and Chris Shore
The Math Projects Journal is a bimonthly publication
offering tips and lesson plans for math activities,
discussions on relevant topics, and contributions from
teachers around the world. The purpose of the newsletter
is to create a network of math project enthusiasts and share
engaging, classroom-tested ideas for teaching mathematics,
especially for algebra and geometry.
Each issue of MPJ is twelve pages long and consists of
articles, discussions and, most importantly, projects
(usually two or three of them). Since collaboration is one
of their main goals, every issue includes a Site License,
which allows you to reproduce and distribute any part of the
journal within your school.
Subscriptions cost $30 per year (6 issues). Order back
issues for $5 per issue.
Browse descriptions of back issues:
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MICHIGAN TEACHER NETWORK
The Michigan Teacher Network (MTN), providing access to K-12
education-related Web resources, is one of the featured
collections of the recently launched National Science Digital
Library.
The sites listed on the Michigan Teacher Network have been
evaluated for quality, relevance, and effectiveness. MTN
describes thousands of resources that can be used with
students in the classroom, with teachers for professional
development, and by educators for planning and problem solving.
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THE NATIONAL SCIENCE DIGITAL LIBRARY (NSDL)
NSDL is a comprehensive, online source for science,
technology, engineering and mathematics education. The NSDL
mission is to both deepen and extend science literacy through
access to materials and methods that reveal the nature of the
physical universe and the intellectual means by which we
discover and understand it.
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Mathematics – Mrs. Martin
Course Description:
This course is designed for the jr. high student. Students will maintain
previously acquired skills while extending their knowledge and thinking skills in
problem solving, percent, measurement, equations, and other mathematic essentials and
applications.
There will be homework and a warm-up quiz nearly ever day. Homework is
important! It helps the student learn the material. Please support and encourage your
students in this area. If a student has difficulty, extra help is available before and after
school.
In order to guarantee your student and all the other students in class the excellent
educational climate they deserve, I ask that each student comply with the following rule:
1. Students are expected to bring textbook, notebook with paper, a sharpened
pencil and completed assignment and be in their seats when the tardy bell
rings.
2. Notes should be taken daily.
3. Students are expected to correct the mistakes that they make on tests,
homework, quizzes, and other assignments so that they can learn from their
errors.
4. Students must keep hands, feet, and objects to themselves.
5. No swearing, rude gestures cruel teasing or put-downs.
6. Students are encouraged to ask questions and take part in class discussion.
Grading Scale:
Grades are based on mastery of the material presented and may not reflect true ability or
effort.
Grades are computed on a percentage basis. The teacher reserves the option to
compensate grade percentages for particularly difficult material. The breakdown is as
follows:
94-100 = A 73 - 76 = C
90 - 93 = A- 70 - 72 = C-
87 - 89 = B+ 67 - 69 = D+
83 - 86 = B 63 - 66 = D
80 - 82 = B- 60 - 62 = D-
77 - 79 = C+ Below 60 = F
Grades are posted weekly for students to check their current status. They are also
uploaded nightly at midnight to the portal. If you would like to know how your student is
doing I welcome your calls.
Citizenship grades will be earned according to the school citizenship policy. A copy of
this may be found in the folder received during the first week of school. Additional
copies are available in the office.
Thanks for all you do, I am looking forward to a great year!
Mrs. Martin
PRE ALGEGRA/INT. ALGEBRA
7th / 8th / 9th
STUDENT
NAME______________________________________PERIOD____________
Please Print
I have reviewed Mrs. Martin's disclosure statement for Pre Algebra/Int. Algebra. I am
aware of, and will support the academic grading standards, citizenship grading standards,
and class policies and expectations as described. I am keeping the descriptive portion of
the statement for future reference.
___________________________ ___________________________ __________
Student Signature Parent |
CS 208 Discrete Mathematics Green, Kathleen3) If you are looking for an equation editor, you can tryMath Equation Editor, 30-day free trial version found in MathTypeenables students to export or save the symbols into .gif or .jpg format. You can then insert the .gif/.jpg file in the assignments for submission.
You can also write your equations in hardcopy paper, scan your work, and save the file in .gif or .jpg format, and then insert the .gif/.jpg file in the assignments for submission My educational philosophy is one of inter-activeness based on lectures, readings, dialogues, examinations, internet, videos, web sites and writings. I will engage each student to encourage the lively exploration of ideas, issues, and contradictions. School should be fun not a chore. Anyone who works at it with diligence and courage can learn to think more clearly, accurately, and efficiently and express ideas with clarity and poiseStudents should visit the discussion area at least three times each week or a minimum three hours per week, or participate at class. Making sure that you post your discussion in the proper format, is of great importance. We will post as:
PROBLEM: Section # [student will post, at a minimum, one problem]
ANSWER: Section # [student will answer another student's problem, not their own problem]
RESPONSE: Section # [student will response to the student who answered their problem]
·There is no credit given if a student does not participate in the Class Discussion during the week assigned or does not post in the correct manner as stated above.
Homework Assignments & Quizzes:
·All assignments and quizzes should be completed on or before end of day Sunday. Homework must be done independently. Students will place completed assignments in the dropbox. Do not post answers to quizzes or assignments in the discussion threads. Note that weekly QUIZ 1 is to be taken on or before end of day on Friday of the academic week to receive full credit (i.e., 4 points) for each correct answer. Between Saturday 12:00am Mountain Standard Time and Sunday 11:59pm Mountain Standard Time, each correct answer in weekly quiz 1 is worth 3 points.
Weekly QUIZ 2 does not have this restriction.
Grading:
You will be able to track your average exactly throughout the course. The grading scale is as follows:
A = 90%-100%; B = 80%-90%; C = 70%-80%; D = 60%-70%; F = 0-60%.
You will know in advance the standards for each assignment. My goal is to give you prompt, clear, and useful feedback to help you to succeed in this class. Each student is responsible for:
Completing Weekly Reading assignments
Completing Weekly Discussions
Completing Weekly Homework assignments
Completing Weekly Self Checks
Completing Weekly Quizzes
Completing a Final Examination. This step is essential!
Completing a Online Survey of Student Opinion of Teaching
Proctored Examination:
Final Examination - An examination will be taken in person during the 8th (or 16th) week of instruction at one of the Park University sites around the country or at an alternative location approved by the University where Park University sites are not available. It will be the responsibility of the student to arrange for a proctor, by the 6th week, who will be accepted and approved by the instructor. Guidelines for selecting an acceptable proctor can be found at the Park University website (or submit your final project for some online graduate courses) will result in an automatic "F" grade. Some graduate courses may not require a proctored final examination.
The following table shows the score distribution.
Assessments
Points earned each week
Number of Weeks
Total Points
Percentage (%)
Course Home Introduction
4
1
4
0.3%
Course Home
Self Check
15
1
15
1.3%
Weekly Discussion
12
7
84
6.9%
Weekly Homework
12
7
84
6.9%
Weekly Self Checks
30
7
210
17.3%
Weekly Quizzes
80
7
560
46.2%
Final Exam
256
1
256
21.1%
Total
1213
100%
Course Grading Scale:
This subsection should list the grading scale and weighting for all of the graded work during a course. The grading scale must use the following scale below, and point totals for each letter grade must be included (see example below).
Letter
Points
Percentage
A
1091-1213
90-100 %
B
970-1090
80-89 %
C
849-969
70-79 %
D
727-848
60-69 %
F
Below 727
Below 60 %
Late Submission of Course Materials:
All assignments and quizzes must be completed by 11:59 pm Central Time on Sunday of the academic week.
There will be 20% penalty for each day that a homework is turned in late. Students are not allowed to take a quiz that is scheduled beyond its due date.
Classroom Rules of Conduct: On-Line Participation
·This course is offered on-line, over the Internet, using the eCollege course delivery system. Students are expected to devote a minimum of three hours per class week logged on to the computer discussion area-the same amount of time you'd spend in the physical must I began teaching and tutoring for Park University at the Mountain Home AFB, Idaho Campus in 1993. Until April 31, 2005, I was also the Testing Center Supervisor for LaserGrade Computerized Testing (Yes, one of those "official" proctors). I watched the Park University Online Program grow from a handful of instructors and students to its present day size. As an online instructor I have been required to take several online instructional courses, and have also received my PhD in Adult Education, specializing in Online/Distant Learning. I have developed many courses in various fields of study, for example: Advanced Aerodynamics, Algebra, and Accounting, just to name a few. So you might say I have experienced the online program from the viewpoint of a student, a proctor, an instructor, course developer, and in a limited way, an administrator! During the continual growth period there have been numerous changes and improvements. Please read more about me in my introduction posting.
I pledge to do my best as your instructor. Will you do the same as my student? If so, let's work together and hopefully we will all learn something new.
Kathleen Green |
I use Robert Taylor's book to tutor Classical Mechanics. As precalculus is a prerequisite for taking calculus, I took this subject as a high school junior and still use the fundamentals from this subject in classes such as calc 1,2,3 and physics classes. As a person who learned English as secon...
...It too consists of verbal and mathematical sections. The math sections also include information about learning sequences. The verbal reasoning section is about half straight definitions, and the other half are sentence completion. |
What's New
Version 4.4.29: Release notes were unavailable when this listing was updated.
As a teacher of English and history who teaches a junior maths class (yes, Australian spelling), I find Geogebra indispensable. I can sit students in front of it and help them to create in concrete form what is otherwise an abstract concept. We can change angles on the fly, add measurements, make calculations, create number lines and work on Cartesian coordinates.
Another major benefit is that I can create shapes (e.g. triangles for trigonometry) and then export them in graphics formats that I can import into MS Word and other apps. Terrific for creating information sheets, worksheets and quizzes.
Overall, a very powerful tool and well worth the time to learn to use.
well as functions, and change them dynamically afterwards. Furthermore, GeoGebra allows you to directly enter and manipulate equations and coordinates. Thus you can easily plot functions, work with sliders to investigate parameters, find symbolic derivatives, and use powerful commands like Root or Sequence. |
Description: This collection of articles discusses the following topics: Abacus vs Calculators, Prime Factorization on the Abacus, Using an Abacus and the Counting Method, Courses Available to Learn Abacus, and Abacus Internet Site Packet.
Description: This book has been designed as an easily assimilated presentation of the special symbols and complex rules and procedures laid down in the Nemeth Code for Mathematics and Science Notation. The homework exercises in this manual are designed to prepare certified literary braillists for the Library of Congress examination leading to certification in braille mathematics transcribing.
Description: TSBVI has produced a 15 part series in learning how to use the APH braille/print protractor. The series is taught by Susan Osterhaus, a leader in the field of math for the visually impaired.
Description: This kit brings together informal checklists, suggestions for format; assessment materials that you may want to buy, informal reading inventories, and assessments of compensatory skill areas.
Description: Design Science offers MathType, which is a powerful interactive equation editor for Windows and Macintosh that lets you create mathematical notation for word processing, web pages, desktop publishing, presentations, elearning, and for TeX, LaTeX, and MathML documents. It can be used with Duxbury to produce Nemeth Code.
Description: 'Evaluation of students with VI is a complex, multi-faceted process of gathering info. using appropriate tools & techniques. Informal evaluation should be considered an essential supplement to the use of formal measures and published instruments. In order to determine curricular focus and plan effective instructional programming for students, the staff must know a student's levels of functioning in all areas of academic and unique need.'
Description: This curriculum covers math, science, social studies, physical health and vocational skills (elementary to high school) for students with moderate to severe disabilities. (Not VI specific)
Description: Tuition free correspondent courses available to students, family members, etc. for instruction in areas specific to visual impairments, including parents, early childhood, and assistive technology.
Description: From the catalog, 'Mathbuilders is a supplementary math program separated into eight units by content standards and grade level. This allows the teacher to focus on specific standards or provide remedial materials for individual students.'
Description: This book is one of the most popular and important instructional resources for primary teachers and provides a complete range of activities essential for primary students' development of mathematical understanding. (Not VI Specific)
Description: This chapter provides detailed instructional strategies for teaching mathematics to visually impaired students. It also contains specific information regarding the creation of tactile graphics for the instruction of mathematics skills.
Description: TSBVI offers one week courses during the regular school term for intensive training in specific areas of a student's IEP. Some programs are specific to a particular subject and some programs are specific to having a visual impairment.(Texas students only)
Description: This group of documents include: Collaborative/Inclusive Strategies, Challenges in Teaching Mathematics to the Visually Impaired, Arithmetic Calculation Using the Braillewriter, Solving Quadratic Equations, Solving Systems of Equations in Three Variables, Linear Measure, Perimeter, and Area, Transformations, Line Symmetry, and Tessellations, Geometric Constructions, Teaching a blind student how to graph on a coordinate plane and No tech, low tech, and high tech tools.
Description: This book is a comprehensive resource for the classroom teacher who is working with a visually impaired child as well as a systematic overview of education for the specialist in visual disabilities.
Description: Publication for instuctors and families of visually impaired children including those with deafblindness and multiple disabilities. It contains current and relevant information for various topics from school to community to home. (Downloadable)
Description: Designed to be used by blind individuals to learn to read and write the Nemeth Code for Braille mathematics, or to refresh skills using this code. Download available for the Braille Lite 40, 2000, M20 and M40.
Description: A fully accessible app for iPod Touch, iPhone and iPad. ViA has been designed to help identify apps that are useful for adults and children who are blind or have low vision, including those with additional disabilities. Users can easily sort through the apps in the App Store and locate those that were built specifically for, or provide functionality to the user with a visual impairment." |
Algebra in the 8th grade?
This link will take you to CPM's position paper and additional resources about accelerating students in middle school. Click here for the timelines, pacing guides, and course outlines for two pathways to Algebra 1 in 8th grade.
Users of Making Connections 1 & 2, High School Connections
- How to Supplement Current CPM Texts
The first editions of the Connections books (2006, 2007, 2009, 2011) can be supplemented to meet the CCSS content standards.
- Content and Practices Correlations
Detailed correlation between the CCSS content standards and their location in
the corresponding CPM text.
Announcements Get the latest news, addenda, and errata for current users of Core Connections 1-3 or the CCSS Supplement Booklets.
About the Common Core State Standards (CCSS)
The Common Core State Standards for Mathematics (CCSS) were released in June 2010. In addition to specifying the mathematics to be taught for each grade (K-8) and high school, the standards include "mathematical practices" that foster understanding. Students will be expected to make sense of problems, persevere in their solutions, use appropriate tools strategically, be precise, reason abstractly and qualitatively, construct arguments to support their work and the reasoning of others, model using mathematics, and look for and make use of structure. States participating in the CCSS will begin using common national assessments in the 2014-15 school year. For more information, go to: |
Course Descriptions
Precalculus (MAT 1013)
This course provides the essential mathematical background needed to take calculus. Students should have had three to four years of college preparatory high school mathematics. The emphasis is on developing the concepts that play a central role in calculus by exploring ideas from graphical, numerical, algebraic, and oral perspectives. Prerequisite: Placement at Level 4 or permission of the instructor. 3 credits.
Introduction to Statistics (MAT 1015/ELA 1101)
This course explores the basic concepts of statistics: measures of central tendency, variation, estimating and inference. The focus of this course is on data analysis and making students better consumers of statistics. Exploration of these topics will make use of computer technology. Prerequisite: Placement at Level 4 or permission of the instructor. 3 credits.
Calculus I: Applications in Environmental Issues (MAT 1031)
This course presents the fundamentals of calculus through the modeling real world examples. Data from biology, medicine, ecology, education and social sciences is interpreted and modeled with mathematics. Calculus topics are taught in relation to the data sets and the context in which the data set arose, highlighting concepts and applications as they arise in different fields of research. This course emphasizes the role of technology in modeling and analyzing data by using calculators. Topics include rates of change, functions and graphs, differentiation, limits, accumulation functions, and integration. Prerequisite: C- or better in MAT 1013 Precalculus or placement at Level 4 or 5. 3 credits.
Calculus II (MAT 1032)
Topics include applications of integration, including use of integration in biology, business and statistics. In addition, multivariate calculus, including partial rates of change and multivariate optimization with and without constraints will be studied, as well as differential equations and numerical estimations. Prerequisite: C- or better in MAT 1031 Calculus I. 3 credits.
History of Mathematics (MAT 2001)
In this course the development of mathematics in a historical context will be studied. The evolution of mathematical ideas and the different views of mathematics held by different cultures at different times will be explored. 3 credits.
Topics in Mathematics (MAT 3000)
A seminar course in advanced mathematical topics such as fractals and chaos, geometry, number theory, or graph theory. Prerequisite: Permission of instructor. 3 credits.
Mathematical Modeling I (MAT 3100)
The course is an introduction to the art of modeling and mathematical modeling. This course links the study of mathematics together with the applications of mathematics to various fields. Topics include: the modeling process, model fitting, discrete dynamical systems, deterministic and stochastic models, optimization, and systems of differential equations. Offered alternate fall semesters. Prerequisite: MAT 1031 Calculus I with a grade of C- or better or permission of instructor. 4 credits.
Seminar in Mathematics (MAT 3500)
This is a seminar style course used to investigate one or more areas of mathematics. Students will read through various journal articles, gaining an understanding of the underlying mathematical theory along with an appreciation of the utility of mathematics. Topics will be selected to reflect the interests of the students and the instructor. Offered on demand. 1 credit. |
This text from the author team of Aufmann and Nation offers the same engaging style and support for students as the Aufmann College Algebra series, all in a brief format that covers the entire course in a single semester. Interactive learning techniques incorporated throughout the text help students better understand concepts, focus their study habits, and achieve greater success.In this First Edition, the authors have also integrated many components into the textbook to help students diagnose and remediate weak algebra skills. Prerequisite review in the textbook and supporting materials allows students to fill in gaps in their mathematical knowledge, and keeps instructors from having to spend time on review. Extra support also comes from the Aufmann Interactive Method, featuring Try Exercises that allow students to practice math as it is presented and to more easily study for tests artists who need a quick and efficient way to join this brave new world will want 3D for Graphic Designers. |
Thomas H. Wolff was a leading analyst and winner of the Salem and Bôcher Prizes. He made significant contributions to several areas of harmonic analysis, in particular to geometrical and measure-theoretic questions related to the Kakeya needle problem. Wolff attacked the problem with awesome power and originality, using both geometric and combinatorial ideas. This book provides an inside look at the techniques used and developed by Wolff. It is based on a graduate course on Fourier analysis he taught at Caltech. The selection of the material is somewhat unconventional in that it leads the reader, in Wolff's unique and straightforward way, through the basics directly to current research topics. The book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The first few chapters cover the usual background material: the Fourier transform, convolution, the inversion theorem, the uncertainty principle, and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics, and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensure that both graduate students and research mathematicians will benefit from the book. |
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