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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
Content MathML
Summary: A short introduction to writing Content MathML by hand. It covers
tokens, prefix notation, and applying functions and operators. In
addition it introduces writing derivatives, integrals, vectors, and
matrices.
The authoritative reference for Content MathML is Section 4
of the MathML 2.0 Specification. The World Wide Web
Consortium (W3C) is the body that wrote the specification for
MathML. The text is very readable and it is easy to find what
you are looking for. Look there for answers to questions that
are not answered in this tutorial or when you need more
elaboration. This tutorial is based on MathML 2.0.
In this document, the m prefix is used to
denote tags in the MathML namespace. Thus the
<apply> tag is referred to as
<m:apply>. Remember all markup in
the MathML namespace must be surrounded by
<m:math> tags.
The Fundamentals of Content MathML: Applying Functions and
Operators
The fundamental concept to grasp about Content MathML is that
it consists of applying a series of functions and operators to
other elements. To do this, Content MathML uses prefix
notation. Prefix notation is when the operator
comes first and is followed by the operands. Here is how to
write "2 plus 3".
There are three types of elements in the Content MathML
example shown above. First, there is the apply
tag, which indicates that an operator (or function) is about
to be applied to the operands. Second, there is the function
or operator to be applied. In this case the operator,
plus, is being applied. Third, the operands
follow the operator. In this case the operands are the
numbers being added. In summary, the apply tag applies the
function (which could be sin or
ff, etc.) or operator (which
could be plus or minus, etc.) to the elements that follow it.
Tokens
Content MathML has three tokens: ci,
cn, and csymbol. A
token is basically the lowest level element.
The tokens denote what kind of element you are acting on.
The cn tag indicates that the content of the
tag is a number. The ci tag indicates that the
content of the tag is an identifier. An
identifier could be any variable or function;
xx,
yy, and
ff are examples of identifiers.
In addition, ci elements can contain
Presentation MathML. Tokens, especially ci and
cn, are used profusely in Content MathML.
Every number, variable, or function is marked by a token.
csymbol is a different type of token from
ci and cn. It is used to create a
new object whose semantics is defined externally. It can
contain plain text or Presentation MathML. If you find that
you need something, such as an operator or function, that is
not defined in Content MathML, then you can use csymbol to
create it.
Both ci and csymbol can use
Presentation MathML to determine how an identifier or a new
symbol will be rendered. To learn more about Presentation
MathML see Section 3
of the MathML 2.0 Specification. For example, to
denote "xx with a subscript 2",
where the 2 does not have a more semantic meaning, you would
use the following code.
The ci elements have a type attribute which
can be used to provide more information about the content of
the element. For example, you can declare the contents of a
ci tag to be a function
(type='fn'), or a vector
(type='vector'), or a complex number
(type='complex'), as well as any number of
other things. Using the type attribute helps encode the
meaning of the math that you are writing.
Functions and Operators
In order to apply a function to a variable, make the
function the first argument of an apply. The second
argument will be the variable. For example, you would use
the following code to encode the meaning, "the function
ff of
xx". (Note that you have to
include the attribute type='fn' on the
ci tag denoting
ff.)
There are also pre-defined functions and operators in
Content MathML. For example, sine and cosine are
predefined. These predefined functions and operators are
all empty tags and they directly follow the
apply tag. "The sine of xx" is
similar to the example above.
<m:math>
<m:apply>
<m:sin/>
<m:ci>x</m:ci>
</m:apply>
</m:math>
This will display as
sinxx.
You can find a more thorough description of the different
predefined functions in Chapter 4 of the MathML specification.
In addition to the predefined functions, there are also many
predefined operators. A few of these are plus
(for addition), minus (for subtraction),
times (for multiplication), divide
(for division), power (for taking the
nnth-power of something), and
root (for taking the nnth-root
of something).
Most operators expect a specific number of child tags. For
example, the power operator expects two children. The first
child is the base and the second is the value in the
exponent. However, there are other tags which can take many
children. For example, the plus operator merely expects one
or more children. It will add together all of its children
whether there are two or five. This is referred to as an
n-ary operator.
Representing "the negative of a variable" and explicitly
representing "the positive of a variable or number" has
slightly unusual syntax. In this case you apply the plus or
minus operator to the variable or number, etc., in question.
The following is the code for "negative
xx."
<m:math>
<m:apply>
<m:minus/>
<m:ci>x</m:ci>
</m:apply>
</m:math>
This will display as
−xx.
In contrast to representing the negative of a variable, the
negative of a number may be coded as follows:
<m:math><m:cn>-1</m:cn></m:math>
This will display as -1-1.
To create more complicated expressions, you can nest these
bits of apply code within each other. You can create
arbitrarily complex expressions this way.
"aa times the quantity
bb plus
cc" would be written as
follows.
The eq operator is used to write equations. It
is used in the same way as any other operator. That is, it
is the first child of an apply. It takes two (or more)
children which are the two quantities that are equal to each
other. For example, "aa times
bb plus
aa times
cc equals
aa times the quantity
bb plus
cc" would be written as shown.
Integrals
The operator for an integral is int. However,
unlike the operators and functions discussed above, it has
children that define the independent variable that you
integrate with respect to (bvar) and the interval
over which the integral is taken (use either
lowlimit and uplimit, or
interval, or condition).
lowlimit and uplimit (which go
together), interval, and condition
are just three different ways of denoting the integrands.
Don't forget that the bvar, lowlimit,
uplimit, interval, and
condition children take token elements as well.
The following is "the integral of
ff of
xx with respect to
xx from 0 to
bb."
Derivatives
The derivative operator is diff. The derivative
is done in much the same way as the integral. That is, you
need to define a base variable (using bvar). The
following is "the derivative of the function
ff of
xx, with respect to
xx."
To apply a higher level derivative to a function, add a
degree tag inside of the bvar tag.
The degree tag will contain the order of the derivative. The
following shows "the second derivative of the function
ff of
xx, with respect to
xx."
There are also operators to take the determinant and the
transpose of a matrix as well as to select elements from
within the matrix.
Entities
Note:
The use of MathML character entity references in Connexions content is deprecated.
MathML defines its own entities for many special characters used in mathematical notation. While the entity references have the advantage of being mnemonic with respect to the characters they stand for, they also entail some technical limitations, and so their use in Connexions content is deprecated. Please use the UTF-8-encoded Unicode characters themselves where possible, or, failing that, the XML Unicode character references for the characters. At some time in the future, the Connexions repository system will likely convert entity references and character references silently to the UTF-8-encoded Unicode characters they stand for. See 6.2.1 Unicode Character Data from the XML Specification for more information. The MathML specification contains a list of character entities with their corresponding Unicode code points.
There are character picker utilities available to help you select and paste UTF-8 characters into applications like Connexions. If you are running Microsoft Windows, the Windows accessory Character Map can help you. The "Lucida Sans Unicode" font seems to have a good selection of mathematical operators and special characters. Under Linux, the charmap utility and GNOME applet provide access to all Unicode characters.
Other Resources
There is a lot more that can be done with Content MathML.
Especially if you are planning on writing a lot of Content
MathML, it is well worth your time to take a look at the MathML
specification |
Book summary
This book presents a treatment of principal topics of linear algebra and illustrates the importance of the subject through a variety of applications. The topics include vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, canonical forms. In addition there are applications to differential equations, economics, geometry, physics and probability. The second edition uses Gaussian elimination instead of Gauss-Jordan method, reduces the dependence of direct sums, shortens and reorganizes the coverage of diagonalization, develops unitary diagonalization via Schur's theorem as opposed to the more abstract invariant subspaces, interchanges canonical forms and inner product spaces, and features a new subsection which develops motions in the plane. [via] |
PLEASE NOTE: THE SPECIAL ORDER TAKES 4-5 BUSINESS DAYS TO SHIP OUT. free upgrade to 1st class shipping with tracking. (8-14 days to arrive.)
1. ID # 6007
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3. the listing contains no books. it's only a TEACHER'S CD ROM. contents on it:
=====HARDCOVER TEACHER'S EDITION. FULL ANSWERS FOR EVERY PROBLEM IN THE STUDENT TEXTBOOK, EVEN AND ODD.
=====whole set teaching resources, workbook answer key, quizzes tests with answers.
4. THE ITEM IS USED TO THE FOLLOWING STUDENT TEXTBOOKS:
===0030700523 (2004)
===003066053X (2003)
===0030522196 (2001)
THE STUDENT TEXTBOOK IS NOT INCLUDED |
Course Description: Students will engage in real world and hands-on problem solving while using their developing skills in algebra. Students will learn new material through animations, videos, reading, manipulatives and guided practice. The topics covered in this course include: real numbers, algebraic expressions, graphing to solve inequalities and absolute value, graphing to solve linear equations, systems of equations, factoring polynomial equations, relations and functions, quadratic equations, radical expressions and rational equations.
Before you take the quiz, either watch the first two videos on this Khan Academy list or spend ten minutes working on the first two exercises, whichever you prefer as your way to review, by listening and watching or by doing. The two topics are combining like terms and combining like terms with distribution. Here are the two exercises: onetwo.
Don't worry about the video on the page or the stuff at the bottom of the page.
Take the quiz. If it says "quiz group" but you don't see the quiz, click on those words and it should appear. Record your quiz score.
Even though you aren't recording scores for these other types of practices, they will still count toward your grade for completing them. They will also help you do better on your quizzes and tests, so I suggest always doing your best. In fact, do ALL things as unto the Lord.
You don't have to become proficient in these, just see if you can figure some of them out, more writing expressions.
Day 16
Remind yourself about inequalities by reading this page and by clicking on next and reading that page, just two pages.
You can draw the graphs on paper or on an online tool (choose -5 to 5).
Answers to the graph problems (open circle on -2 and line to the right; dot or closed circle on five with line to the left)
Take the test at the bottom of the lesson list. Record your score out of 18. (It tells you at the very bottom after you submit.)
Note: This gives you the chance for 2 points of extra credit.
Day 17
Complete all of the parts of this lesson on solving for a specific variable. (You can skip the worked examples if you can get all of the practice problems correct.)
Don't forget the "topic text."
Day 18
Do the Get Ready, Learn (several pages), and Practice parts of this lesson on solving equations.
Whenever you use this site, you have to login (down on the right). The login is easypeasy and allinone .
Day 19
Complete all of the steps of this gas price project. To complete the chart, you need to find gas prices. The link is outdated. Here's the new link.
Record ten points for completing steps 1 through 3 and following all of the directions.
There are three questions in number 4. The first question also asks you to explain. Add two points for each question you answered correctly, including the explanation. (Total 8 points for that section)
This is the end of the first quarter. If you are using a paper version, you will add up 128 for your scores for the first quarter would give you an A so far.
Day 4: Create your poster and present it. Keep in mind that there is a grade for presentation.
This is just a sample schedule. If you need lots of time to write, then you should design your roller coaster on the first day to leave two days for writing. If you don't finish in four days, you will lose lots of points. You will score poorly. You'll also have to finish over the weekend! No getting behind.
Use the rubric to score your project out of 8.
Add 10 points for completing on time.
Add 5 points for your paper having a clear intro, at least three points and a conclusion. Take off a point for each of those things that are missing.
You can print the test or just read the questions online. The answers are in number three. Why shouldn't you look at them? That would be cheating. Cheating is wrong. In school you would get a zero on your test and could be kicked out of school. Cheating is always a temptation when it comes to tests, but God not only sees what you are doing, He promises a way out when there is a temptation. If it's too much of a temptation, print out your test and do it away from the computer. The more you resist temptation the stronger you will become. Don't let sin rule over you like Cain did.
Check your answers when you are done. Number 4 has an error on the answer key. See the explanations for the correct answer.
The SATs are a test you'll take in 11th grade. It is required by colleges. You will need a good score to show the college of your choice that you will be a good student. A good score also shows that you've been learning something and not just home playing video games.
In 10th grade you can take a practice test called the PSATs. Some schools give full scholarships to students who score very high. That could save your parents $100,000! So do your best
When you take the PSATs or SATs, you need to know how to play the game. It's a bit of a game and knowing the rules will help you win.
You get one point for each correct answer. You get zero points for anything left blank. You lose a quarter of a point if you get one wrong. So it's not a good idea to just guess. If you can eliminate at least one answer, then your odds of guessing the right one increase and statistically speaking, it's in your favor to guess. If you can eliminate two or more of the answers, then you really should guess at the answer. Of course it's best to know the answer!
Here's another reason not to cheat. The truth has a way of making itself known. If your PSAT/SAT scores don't match up with your grades, everyone will know something is up. Just copying answers won't help you learn anything and it will eventually show if you aren't learning.
The PSAT and the SAT are also timed tests. You have to stop when time is up. Give it a try.
This is the end of the second quarter. If you are using a paper version, you will add up all of 96 for your scores for the first quarter would give you an A so far.
(*) Take the chapter test. NOTE! On number 6, the second exponent looks like an 8, but it's not. It's a 6. You don't have to print this. You can read it online, but you might want a sample for your portfolio.
Complete this activity from NROC. You will select three rectangular locations to measure. After measuring the length and width of each location, you will use the Pythagorean Theorem to calculate the length of the diagonal. Then you will measure the actual distance of the diagonal. How accurate were your calculations compared to your measurements.
You can choose something like a table or door. If you have access, why not try a football field or some other larger rectangle. Make sure you are able to measure the diagonal. (You could use string to measure and then measure the string at home.)
Completing the homework for lesson 5 is optional, but advisable. In high school I had a math class where only tests counted. Homework didn't get checked, but I did it every day. Why? If you don't, you won't be prepared when it's time for the test. It may make sense when you are looking at an example in a lesson done for you, but you don't know if you can do it until you try it for yourself. It's smart to complete your homework, check it and fix mistakes to make sure you understand.
The homework is optional, but highly recommended. In fact, you should do it, but I'm trying to train you to make the diligent choice, not the lazy choice. If it's easy, great, you can finish it quickly. Do as much as you need to to make sure you got it.
This is the end of the third quarter. If you are using a paper version, you will add up your scores and divide, your score total/total score. It should be a decimal. Multiply that decimal by 100. That number can be translated into a letter. How are your grades? What do you need to do?
You have 15 minutes to take this test. This is PSAT/SAT practice. Remember, incorrect answers count against you. If you have no idea, skip it. If you can eliminate at least one answer, it's in your best interest to guess.
Get the timer ready and then begin.Your Score equals the total Correct minus one fourth of the number Incorrect. S = C – .25I You can use a calculator to find your score.
Then you will follow the directions for part 2, but you only need to find two people. You can use three people, but you don't have to. Choose an activity. Some ideas are setting the table or cleaning up the legos. There are more ideas on the page. Each person has to do the same activity. You don't need pictures. Record their times.
Solve for rate as directed in part 3.
For part four, have everyone whom you timed in part 2 work together to do the same activity and time yourselves. Calculate your percent error.
Answer the questions in part 5. Compare your results to the result of your equation. State your conclusion.
You will stop at part five and not go beyond that in the directions.
You get two points for each of the five parts that you completed. (up to 10 points)
Day 165
Before we review for the final exam of the course, we are going to have a mini course on probability.
Get the timer ready and then begin.Your Score equals the total Correct minus one fourth of the number Incorrect. S = C – .25I You can use a calculator to find your score.
Record your score out of 15.
Day 171
Choose a project to complete by Day 179. Follow the directions. You won't be working with classmates, but follow the directions in ways that make sense. You will be doing the final presentation project, creating a website, poster, etc. as described in the directions. Present your project to your family/friends at the conclusion. You can send something from your project (link, photo, video) to me to post on the hall of fame if you like!
You are responsible for finishing this on time. Make a plan of action as to when you need to be finished with each portion of the project.
Scoring
You get 10 points for finishing on time.
You get 15 points total for following directions and completing each problem section. Lose 5 points for any section skipped.
Were you able to make yourself clear? Did your audience understand the problem, solution, and why you came to that conclusion? If so, give yourself 15 points. Lose 5 points each if you did not make clear the problem, solution or why.
You get up to 10 points for how nice your project looks. Did you take care to do your best? Have someone else judge!
Day 172
Here is a study packet for your final. You don't have to print it. It is a summary of the lessons from the course. On Day 180 you will be taking a final exam. It has 50 questions. Figure out how many lessons you should look through each day to go through them all by Day 180.
Things you are unsure of, take out a pencil and try the example problem.
You might to read the lesson summaries out loud to help you remember them, or pretend you are teaching the material to someone else.
These are study techniques. In college you will be taking tests. Before the test you will study, review the material, to remind yourself of what you've learned.
Today, study.
Don't forget your project.
Day 173
If you want more videos to go over any specific material, this is a good place to look for them. They are listed as "watch" under the topics on the right under Algebra 1 A and B.
Continue to review the packet of lesson summaries and use the videos as needed.
Record your score out of 30. (I always give you leeway on the timed tests. That won't happen at the real thing. I do it because I don't have an official time guideline to go by and because you haven't learned from the course that the test is from. I didn't teach to test, as they say.)
Day 179
Today you must finish and present your project. Grade it along with your parents. The scoring is detailed in Day 171.
Figure your course grade. Enter on your fourth quarter grading sheet your total score for each quarter. Divide by the total score from all four quarters. That can be your grade, but I also think you can award up to half of the grade for completing the daily assignments. Then you would take the grade you just calculated, divide it in half and add it to 50, or whatever grade you deem appropriate. Example of the scoring calculation:
four quarters total: 126 + 115 + 110 + 233 = 584
dividing by total possible 584/ 669 = .87*100 = 87%
dividing in half for being worth half the grade: 44%
100% completion of daily assignments, readings, homework, etc.
Half of that 100% for being worth half of the final grade: 50%
Final grade would be: 50 + 44 = 94%, A
Summer School: If you want to practice for the PSATs, here is one place to do it.
Disclaimer
The assignments, the collection of links, the structure of the curriculum and the files created by this site all belong to this blog owner and may not be copied and published to another site or used for any commercial benefit.
Copyright 2012 Lee Giles
All Rights Reserved |
This site is an interactive unit on Graphing Linear
Equations at the algebra 1 level. You will see math on the Internet
like you have never seen before. Come see the high school classroom of
the future. |
Algebra and Trigonometry
2nd
Algebra and Trigonometry book by James Stewart
Choose the algebra textbook that's written so you can understand it. ALGEBRA AND TRIGONOMETRY reads simply and clearly so you can grasp the math you need to ace the test. And with Video Skillbuilder CD-ROM, you'll follow video presentations that show you step-by-step how it all works. Plus, this edition comes with iLrn, the online tool that lets you sign on, save time, and get the grade you want. With iLrn, you'll get customized explanations of the material you need to know through explanations you can understand, as well as tons of practice and step-by-step problem-solving help. Make ALGEBRA AND TRIGONOMETRY your choice today.
Buy Algebra and Trigonometry book by James Stewart from Australia's Online Bookstore, Boomerang Books.
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Hi gals and guys I would really cherish some help with combinations and permutations problems for elementary school on which I'm really stuck. I have this test on math and don't know how to solve conversion of units, factoring expressions and powers . I would sure value your suggestion rather than hiring a math tutor who are pricey.
If you can give details about combinations and permutations problems for elementary school, I could provide help to solve the algebra problem. If you don't want to pay for a math tutor, the next best option would be a proper computer program which can help you to solve the problems. Algebrator is the best I have come across which will explain every step of the solution to any algebra problem that you may copy from your book. You can simply represent as your homework . This Algebrator should be used to learn math rather than for copying answers for assignments.
My parents could not afford my college fees, so I had to work in the evening, after my classes. Solving problems at the end of the day seemed to be impossible for me at those times. A friend introduced Algebrator to me and since then I never had any problem solving my questions.
Thank you, I will check out the suggested program. I have never studied with any software until now, I didn't even know that they exist. But it sure sounds amazing! Where did you find the program? I want to get it as soon as possible, so I have time to prepare for the test.
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Mathematics
Grade 9: content well emphasize on linear relationships. Students will have a chance to utilize the graphing calculator.
Grade 10: content will emphasize on the quadratic relationships, further analysis of these relationships can be explored using graphing calculators or computer softwares.
Grade 11: students begin to explore more specialized functions such as trigonometic and exponential. This will prepare them to further their Math study in their final year.
Math, Science & Technology departments are working together to create the M2ScT program begining 2003-2004 school year. This program is for high achievers in the 3 areas.
Course Content
Grade 9
MFM1P Foundations of Mathematics, Applied
This course enables students to develop mathematical ideas and methods through exploration of applications, the effective use of technology, and extended experiences with hands-on activities. Students will investigate relationships of straight lines in analytic geometry, solve problems involving the measurement of 3-dimensional objects and 2-dimensional figures, and apply key numeric and algebraic skills in problem solving. Students will also have opportunities to consolidate core skills and deepen their understanding of key mathematical concepts.
MPM1D Principles of Mathematics, Academic
This course enables students to develop generalizations of mathematical ideas and methods through the exploration of applications, the effective use of technology, and abstract reasoning. Students will investigate relationships to develop equations of straight lines in analytic geometry, explore relationships between volume and surface area of objects in measurement, and apply extended algebraic skills in problem solving. Students will engage in abstract extensions of core learning that will deepen their mathematical knowledge and enrich their understanding.
Grade 10
MFM2P Foundations of Mathematics, Applied
This course enables students to consolidate their understanding of key mathematical concepts through hands-on activities and to extend their problem-solving experiences in a variety of applications. Students will solve problems involving proportional reasoning and the trigonometry of right triangles; investigate applications of piecewise linear functions; solve and apply systems of linear equations; and solve problems involving quadratic functions. The effective use of technology in learning and solving problems will be a focus of the course. Recommended Preparation: Foundations of Math, Grade 9, Applied
MPM2D Principles of Mathematics, Academic
This course enables students to broaden their understanding of relations, extend their skills in multi-step problem solving, and continue to develop their abilities in abstract reasoning. Students will pursue investigations of quadratic functions and their applications; solve and apply linear systems; solve multi-step problems in analytic geometry to verify properties of geometric figures; investigate the trigonometry of right and acute triangles; and develop supporting algebraic skills. Recommended Preparation: Principle Mathematics, Grade 9, Academic
Grade 11
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MCR3U Functions and Relations, University Preparation
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MBF3C Mathematics of Personal Finance, College Preparation
This course enables students to broaden their understanding of exponential growth and of important areas of personal finance. Students will investigate properties of exponential functions and develop skills in manipulating. Prerequisite: Principles of Mathematics, Grade 10, Academic
MEL3E Mathematics for Everyday Life, Workplace Preparation
This course enables students to broaden their understanding of mathematics as it is applied in important areas of day-to-day living. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Prerequisite: Mathematics, Grade 9, Academic, Applied, or Essential Recommended Preparation: Mathematics, Grade 10, Essential
Grade 12
This course builds on students' experience with functions and introduces the basic concepts and skills of calculus. Students will investigate and apply the properties of polynomial, exponential, and logarithmic functions; broaden their understanding of the mathematics associated with rates of change; and develop facility with the concepts and skills of differential calculus as applied to polynomial, rational, exponential, and logarithmic functions. Students will apply these skills to problem solving in a range of applications. Prerequisite: Functions end Relations, Grade 11, University Preparation, or Functions, Grade 11, University/College Preparation
MAP4C College and Apprenticeship Mathematics, College Preparation
This course equips students with the mathematical knowledge and skills they will need in many college programs. Students will use statistical methods to analyze problems; solve problems involving the application of principles of geometry and measurement to the design and construction of physical models; solve problems involving trigonometry in triangles; and consolidate their skills in analyzing and interpreting mathematical models. Prerequisite: Mathematics of Personal Finance, Grade 11, College Preparation, or Functions, Grade 11, University/College Preparation (or Functions and Relations, Grade 11, University Preparation)
MGA4U Geometry and Discrete Mathematics, University Preparation
This course enables students to broaden mathematical knowledge and skills related to abstract mathematical topics and to the solving of complex problems. Students will solve problems involving geometric and Cartesian vectors, and intersections of lines and planes in three-space. They will also develop an understanding of proof, using deductive, algebraic, vector, and indirect methods. Students will solve problems involving counting techniques and prove results using mathematical induction. Prerequisite: Functions and Relations, Grade 11, University Preparation
MDM4U Mathematics of Data Management, University Preparation
This course broadens students' understanding of mathematics as it relates to managing information. Students will apply methods for organizing large amounts of information; apply counting techniques, probability, and statistics in modeling and solving problems; and carry out a culminating project that integrates the expectations of the course and encourages perseverance and independence. Students planning to pursue university programs in business, the social sciences, or the humanities will find this course of particular interest. Prerequisite: Functions and Relations, Grade 11, University Preparation, or Functions, Grade 11, University/College Preparation
MCT4C Mathematics for College Technology, College Preparation
This course equips students with the mathematical knowledge and skills needed for entry into college technology programs. Students will investigate and apply properties of polynomial, exponential, and logarithmic functions; solve problems involving inverse proportionality; and explore the properties of reciprocal functions. They will also analyze models of a variety of functions, solve problems involving piecewise-defined functions, solve linear-quadratic systems, and consolidate key manipulation and communication skills. Prerequisite: Functions, Grade 11, University/College Preparation (or Functions and Relations, Grade ll, University Preparation) |
1, algebra 2 and calculus 1, algebra 2 and geometry algebra 1, algebra 2 and calculus |
ons Included
None of the lesson in this series have been reviewed.
Below are the descriptions for each of the lessons included in the
series:
Alg 1: Systems of Equations 1 - Graphing
This lesson covers the idea of graphing systems of equations. Students
For more on this topic from including practice problems, multiple-choice self-tests, printable worksheets, and more, click the following link:
Alg 1: Systems of Equations 2 - Addition
This lesson covers the idea of system of equations. Students learn to solve a system of linear equations by addition. To solve a system of equations by addition, the goal is to cancel out one of the variables by adding the equations together. Students may need to multiply one or both of the equations by a number in order to set up a situation where one of the variables will cancel out when the equations are added together.
For more on this topic from including practice problems, multiple-choice self-tests, printable worksheets, and more, click the following link:
Alg 1: Systems of Equations 3 - Substitution
This lesson covers the idea of solving systems by substitution. Students learn to solve a system of linear equations by substitution, by first isolating one of the variables in the system, then substituting its value for the corresponding variable in the other equation.
For more on this topic from including practice problems, multiple-choice self-tests, printable worksheets, and more, click the following link: |
Sample Review: The Algebra of Inequalities -- SAT, GRE, GMAT
Many of my students preparing for the SAT, GRE, and GMAT have decent algebraic intuition when it comes to EQUATIONS, but most are much weaker when it comes to INEQUALITIES.
On the one hand, this is entirely natural: inequalities capture less information than equations -- they establish merely a relation between two quantities, rather than their equivalence -- so they are inherently trickier to think about. But on the other
hand, it's crucial to have a very solid grasp of how inequalities work to do well on the SAT, GRE, and especially the GMAT (which tends to love data sufficiency questions that deal with tricky inequalities).
To test yourself to see how up-to-speed you are, try to decide whether the following statements are true or false. (I have intentionally made the problems very abstract and seemingly confusing to see if you really know what's going on, so DON'T WORRY IF
YOU'RE TOTALLY LOST OR INTIMIDATED!)
1. If a+b=c+d and e+f=g+h, then a+b+e+f=c+d+g+h.
2. If a+b=c+d and e+f=g+h, then a+b-e-f=c+d-g-h.
3. If a is less than b and c is less than d, then a+c is less than b+d. (WyzAnt won't let me use the greater and less than symbols on this blog!)
4. If a is less than b and c is less than d, then a-c is less than b-d.
Here's a hint -- one and only one of these statements is false! Do you know which one it is? The amazing thing is that although these problems LOOK scary, they are extremely simple if you know the basic rules for handling equations and inequalities.
To find out which one is false, send me an email & start preparing to ace the SAT, GRE, or GMAT today! |
I don't know the title or author, the professor hasn't posted anything about it yet. It's the book for Math 2420, right? It's most likely the same book, I don't think they switch math texts very often. |
Mathematics
The study of Mathematics is like climbing up a steep & craggy mountain ; when once you reach the top, it fully recompenses your trouble, by opening a fine, clear & extensive prospect.
Mathematics syllabus in SPSS is not only confined to the theoretical approach but also towards the practical as well as activity based approach.
Activity based teaching from lower classes onwards, have developed an interest for the subject amongst the students, thus making learning permanent. SPSS, has one of the best Mathematics laboratories in Kota City.
Mathematics is a way of organizing our experiences of the world. It enriches our understanding & enables us to communicate & make sense of our experiences. It also gives us enjoyment. Through the subject, students are able to solve a range of practical tasks & real life problems.
With these efforts of Mathematics department, SPSS students are able to develop scientific aptitude & reasoning skill. Building up will power & creating interest amongst the students for the subject has encouraged the students to participate & secure positions in National Mathematical Olympiad.
Thus, with these teaching learning process, SPSS Mathematics department have tried to remove Maths phobia amongst the students, thus making learning more interactive and exciting. |
UMBC's new Math Gym provides students with training in foundational skills.
Previous Profiles:
Pumping Up Their Math Muscles
Coach Sory Kante, moves quickly across the gym. One of his students working out needs help. But what's stumped the student isn't a 220 pound bench press or a complicated yoga move. It's a calculus problem.
Kante is a coach in UMBC's newest type of gym: The Math Gym. One recent evening, dozens of students lined up for the gym, knowing that rather than hitting the treadmill, they'd be tackling a regimen of worksheets and quizzes specifically designed for them. The gym provides students with training in foundational skills, skills they've supposedly already learned, but have now faded into distant memory. And, on this particular night, more than 40 students, working with as many as 7 coaches, spill out of the seminar room and into the corridors of the math department.
Math Gym is the first of the projects funded by the inaugural Hrabowski Fund for Innovation grants to get off the ground. The fund invests in creative faculty initiatives that reimagine our students' learning experiences.
Nagaraj Neerchal, professor and chairman of the department of mathematics and statistics, came up with the idea for Math Gym. "It's something Freeman Hrabowski inspired," he says.
Math Gym is a departure from traditional tutoring in focusing on crucial, yet basic skills—rather than a specific topic that's stumping a student in a current class. "Tutoring is like going to the clinic when you're sick," says Neerchal. "Working in Math Gym is like working out to stay fit so you won't get sick. We need both."
The custom workout begins with QuizZero, a quiz Neerchal and his colleagues designed to test students' understanding of prerequisite material before classes start. It's administered through Blackboard and evaluates students' preparation in the foundational classes, such as algebra, pre-calculus, calculus I and calculus II. Students who score below the median of the class are notified they should brush up on their skills. About 1800 students every semester take the test.
More than half of the freshman entering UMBC each year don't place into pre-calculus. Those that do may be lacking in foundational skills. "Almost all of them have taken algebra in high school," says Neerchal, "they just forget."
The solution, he says: come to Math Gym and get fitted for a "custom workout." Last semester, nearly 800 students whose QuizZero performance indicated they could use a refresher were invited to participate. Of those, over 500 came to Math Gym.
"If students are taking a class, any class," says Neerchal, "and if they are unable to do well in class, it's because they've lost their foundational math skills."
Once a student completes QuizZero, they can come to the Math Gym and have their "workout" customized. The Math Gym coaches and manager have a spreadsheet that they can check to find out what students have to work on. They pass out worksheets and the students are ready for their "workout."
As the semester progresses the gym rats develop their foundational skills and they can begin to move on to working on their current class, says Chris Harris, Math Gym manager.
And Math Gym appears to be working. "This semester, I saw a dramatic increase in student exam grades in applied calculus as compared to last year of approximately twenty points," says instructor Elizabeth Stanwyck. "We are tracking the progress of those students who have come to Math Gym versus those who have not," says Neerchal.
And students say that Math Gym is helping them in their classes. Take Aaron Good, a junior, majoring in physical therapy. Good is taking trigonometry and pre-calculus. "I noticed that my test scores and everything significantly improved," since the opening of Math Gym, he says. Good says that he hopes to make around a B in his class.
Other gym rats, Nnamdi Onyioofor, a senior, and Caleb Zhou, a freshman, are at Math Gym one evening to work on Calculus I. "I've been here for the past week every day," Zhou says.
Professors also offer extra credit for students who regularly go to Math Gym. But Nicole Lentz, a freshman, says it's not just the extra credit that keeps her coming back.
"The people here are really helpful too," she says. "Whenever I have a question they just sit down and help you work it through. They don't just tell you how to get it so it really makes me understand everything a lot better."
What's next for Math Gym? Neerchal and Harris are looking to target a wider range of courses, including those in disciplines beyond mathematics and statistics. They would like to build relationships with other departments and colleges so that students could come to work on math skills relevant for their subjects, such as chemistry, physics and economics. No matter the subject, the underlying math skills are the same.
And the key to mastering them, Neerchal says, "is doing reps. It's all about repetition just like at the gym." |
Editorial Reviews
Booknews
Designed to provide engineers with readily accessible mathematical formulas for their specialties, this handbook proceeds from algebra and geometry through such advanced topics as Laplace transforms and numerical methods and concludes with basic discussions of plane curves and space curves. This edition (last, 1987) incorporates new information on such topics as electronic hand-held calculators and their advanced problem-solving capabilities; engineering economics calculations; Mollweide and Freudenstein equations; trigonometry and mensuration procedures; new measuring systems; logarithms; cubic and quartic equations; and maxima and minima equations 2003
Excellent, Consise, & Comprehensive
This book provides a very comprehensive and excellent handbook or reference on the subject of engineering mathematics. I've use the handbook through it many editions since 1974 and still recommend it a concise reference.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
Foundation Mathematics for Edexcel is the perfect preparation for the two-tier GCSE from Edexcel. This course has been written especially for Edexcel students and their teachers, and comprises student textbooks, teacher's resources, and homework books as well as digital resources. |
Quick Calculus: A Self-Teaching Guide
calcul...more calculus with a preliminary review of algebra and trigonometry. Emphasizes technique and application. Includes many numerical exercises on the pocket calculator and microcomputer.(less)
Paperback, 276 pages
Published
November 11th 1985
by John Wiley & Sons
(first published October 28th 1985)
Community Reviews
...more a graph. Page 1, a concept is introduced. Page 2 is an example. Page 3 is an easy problem. Page 4 gives you the answer. Did you get the problem right? the book asks. If not, and you need more help understanding this concept, try the second example on Page 5 which may help. Otherwise, skip to Page 6 for the next concept. Page 20 reviews concepts 1,2,3.
This book is a very good introduction to calculus. But it contains "very simple" examples. You may want to refer some other books for variety of questions. Many useful books are mentioned in the suggestions for further reading. |
Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of...
see more
Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of math topics." The math topics covered include 1) Precalculus Tutorials 2) Calculus Tutorials and Problems 3) Geometry Tutorials and Problems 3) Trigonometry Tutorials and Problems for Self Tests 4) Elementary statistics and probability tutorials 5) Applications of mathematics in physics and engineering. And much more, including many applets.
Develop your transformations skills. You will be able change shapes using rotations, reflections, translations or...
see more
Develop your transformations skills. You will be able change shapes using rotations, reflections, translations or enlargements The focus of these resources are the five areas, rotations, reflections, translations, enlargements and combinations of them, covering the High School curriculum. There is also a section on vectors and animations and an advanced section. Each area contains 40 tasks arranged in 4 groups of 10. Each task is numbered and uses some form of interactive feedback. The final 10 in each area use elements of geometric construction, which require use of special interactive buttons.
You can alter the geometric construction dynamically in order to test and prove (or disproved) conjectures and gain...
see more
You can alter the geometric construction dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand. Requires Java Plug-in 1.3 or higher. Please be patient while the applet loads on your computer. If you are using a dial-up connection, it may take a few minutes but is well worth the wait.
QuasiTiler draws Penrose tilings and their generalizations. This document explains the interesting geometryinvolved in the...
see more
QuasiTiler draws Penrose tilings and their generalizations. This document explains the interesting geometryinvolved in the processes. The concepts involved are surprisingly simple. The only apparent hurdle that wehave to overcome is working in spaces with more than 3 dimensions. However in the next section we startwith examples in 2 and 3 dimensions where our intuition is useful. Then we extend the same concepts tomore dimensions. I hope that you get some insight on the geometry of higher-dimensional spaces by readingthis document and by experimenting with QuasiTiler. Includes interactive applet. |
Algebra in Mathematics
Algebra in Mathematics
This free online course offers a comprehensive introduction to algebra and carefully explains the concepts of algebraic fractions. It guides you from basic operations, such as addition and subtraction, up to simplifying quadratic equations and more. It applies maths to real-world problems. This course is ideal for students looking for extra help, or even for a different approach to learning maths.
Learn about algebra fractions such as addition, subtraction and more
Learning Outcome
After completing this course you will have a good understanding of algebraic notation.You will be able to use algebra to calculate the cost of renting a car, the speed of a car, and temperature conversions. You will gain a good knowledge of simplifying, verifying, expanding, adding and subtracting algebraic expressions. You will be aware of the Distributive Law. This course will teach you algebraic fractions. You will learn binonial expressions, quadratic trinomials and many more algebraic concepts.
DAVID BENCOMO - United States of America
-
Course Module: Algebraic Expressions 1 Course Topic: Simplifying algebraic expressions without using algebra blocks Comment: It would be nice if you had a little bit more clearer explanation of what you are supposed to be doing,,,the interacting part of this course is really lacking
Tom Norman - United Kingdom
-
Why does it not give you the answers? How am I supposed to check if I'm right or not? Quite annoying...
Dale Foster - United States of America
-
Very throrough but also easy to understand
Imeh Brown - Nigeria
-
algebra have been my favorite during my days in high school
gerri wilmer - United States of America
-
math is one of the hardest courses for me to learn and I don't know why. |
24 SOUTHERN BRANCH
SUBJECTS OF INSTRUCTION.
MATHEMATICS.
MR. LEWIS.
MR. BURGESS.
Algebra a. This course affords a thorough and complete treatment of elementary algebra; including quadratic equations, equations in quadratic form; simultaneous quadratic equations, theory of quadratic equations; ratio, proportion, and variation; arithmetical, geometrical and harmonical progressions; logarithms.
Wells' The Essentials of Algebra is the text-book used.
Five hours per week throughout the year.
Algebra b. Review of algebra a, and a brief course in advanced algebra.
Two hours per week throughout the year.
Plane Geometry. This course covers the five books in plane geometry. It aims to familiarize the student with the forms of rigid deductive reasoning, and to develop accuracy of statement and the power of logical proof. Considerable time is devoted to the demonstration of original theorems and to the solution of practical problems.
Two hours per week throughout the year.
Solid Geometry. Wentworth's Solid Geometry. Three hours per week throughout the year.
ENGLISH.
MR. DRIGGS.
English a. This course consists of a thorough study of the more, advanced principles of English grammar. It also includes the |
The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu.
PROFESSOR STRANG: Alright. So this is Lecture 15. It's the last topic, today and Friday, like just 15 and 16, trusses within Chapter 2. The last topic we'll do for discrete systems. Then it's a lot of fun. I wanted to say a few words first about last night's exam. Several words first. Overall, I'm sure it's going to be fine. Ramis is grading the first two problems, he'll pass them to Peter for the next two. And I'll get them back. I'm pretty sure it'll be next week. I felt it was a fair exam, except I should have done a better job in helping you with the matrix A. Especially in problem one. I'm glad that hint was there, the matrix A_0, that goes with free-free to sort of say what kind of matrix to be looking for. And I thought I'd just repeat, make the connections that I should have made earlier. So we all see the point about these. These A's and the A transpose A's. So if I take, for that A_0, free-free one. Everybody sees that this, and this connects of course with our graphs.
Our graph is just this simple graph with well actually is that how many, is it five nodes? I guess there are five. Because as it stands I have one, two, three, four, five columns, I've got five u's, u_0 down to u_4. And if I take A_0 transpose A_0, that would be the free-free matrix. What size would it be? And what matrix would it be? Just if we do that multiplication, this is a first difference matrix. When I do A_0 transpose A_0 I'll get one of our second difference matrices. So it'll be one of our special ones. Which special one would it be? B. It'll be the matrix B that has both ends free. And what size will it be? I guess it'll be five by five. That's right; that would be five by four times A_0, which is four by five. So it'll be the five by five matrix B. Can I call it B_5? OK. So that was there as a hint. That isn't the correct matrix for problem one because problem one was fixed fixed. Let's get there in two steps. Suppose it's fixed free. So suppose I make u_0=0. So I ground the top node, I support the top node - oh no, shall I do u_0? Yeah. I'll do u_0. So that would knock out this one. If I say fix u_0, say, at zero or whatever.
Now I've got, the next a, I won't call it A_0 anymore. So now four by four, now if I do A transpose A, which of our special matrices am I going to get? t. It'll be T. It'll be the one that has the first 1, 1 entry will only be a one. So that'll be the fixed free matrix. It'll be of what size? Four. Now I've only got four unknowns. u_1 to u_4. OK, that still is not what problem one is. Problem one was fixed fixed. So as I did in the review, that would knock out both of these columns. So this now is the matrix that I was looking for in problem one, and I wish I had emphasized these steps in advance. I apologize. OK, so what fixed-fixed if, without the C part in it. Just focusing on the A, what fixed-fixed matrix would I get? Which one of our guys would it be? K of size three. And while we're at it, what would be the story, how would I get one of these circular ones, which is sort of on our special list. For Fourier it's the really special guy. So a circular one I'm going to connect u_4 back to u_0.
So I'm going to put these guys back in. And what else would change, if u_4 was connected back to u_0, now I'm aiming for this circulant. What matrix A is going to give me the circulant? So again, these guys are the A transpose A's. This over here was the A, and over here is the A transpose A. And now I want to fix A, and then I want to see that A transpose A. So suppose I give you that graph, then. Oops, I should have, well. Just connect the whole guy. So fifth node coming back to the first. So that's my circle of nodes. That's a simple graph. What's the a circulant now? So this would be the A for the circulant case. So it's got that back in. That shouldn't be erased, that shouldn't be erased. And what else is it got? If I ask you for the incidence matrix, now I'm in Section 2.4, like I've given you a graph, or you can think of masses and springs in a circle. So I've got five masses, five springs. What's my matrix A missing? It needs another row. We just put in another edge, it needs another row. That edge went the node back to the first node. So we've got a fifth row.
So you see, now it really is circulant. I would call this one also a circulant matrix. The diagonals are constant. That what I and MATLAB and everybody else would call a templates matrix, and the command templates could create this. That diagonal is constant. That diagonal is constant. The other diagonals are constant. But more than that, what's additional here in the circulant, which is the thing that makes Fourier happy? The diagonal circles around. That diagonal has only got four entries in it, but it circles around sort of periodically to its fifth entry. So that's more than templates. It's circulant because it's coming around again. This we'll see in the discrete Fourier transform. It's really all good stuff. And now there is my a circulant. And what would be my A transpose circulant A circulant? What would be A transpose A if I take that five by five matrix? C. Finally I've created, so I've already got B, I've got T, I've got K, all those three special guys. And now the A transpose A for this circulant, so that's a first difference matrix for a periodic problem. And A transpose A will be a second difference matrix for a periodic problem; c_5, I guess. It'll be five.
OK. I hope that brings together what I, if I was on the ball, I would of brought it together before the quiz. Can I just say a few words about the quiz and grades? They come out fine. Really they do. I've been doing this a long time. And just, enjoy October. I'm sorry to give you any exam at all, but it's a chance for you yeah, I'm working on this stuff. I'm learning it. Everybody doesn't it first time. I don't learn it first time, every time I teach the course I learn something more. And if you're learning from this course then I'm totally happy. And I believe that's the case. So I am entirely happy. And I hope the quiz, some points of it I wish I'd prepared better. But I feel pretty good about it. I feel good about it, let me just say. So, and I'm happy to have any comments, email or in person. But allow me to go forward with trusses. However, I'm ready always for a comment. Yeah. OK. Anyway, enjoy trusses. Enjoy life. Yeah.
And this should have been in the book, this page. So if I wasn't too late I would paste it in. Because this connects A transpose A to a special matrices, and the way I had in my mind but I didn't put it on the board until just now. OK, so I'll cover that up and ready to go with trusses. OK. So trusses, we want to know what's up. We want to get the setup right. Once we get the setup we'll know we're looking for. OK, so a truss is a bunch of elastic bars with pin joints connecting them. Now, what do I mean by a pin joint? I mean that stretching the bars takes force. Turning around the pin joint doesn't take force. So the pin just lets them turn, so we'll have forces in those bars. So it's like masses and springs. Exactly like masses and springs. But yet we have a 2-D problem. So it's a two dimensional problem with masses and springs. And we could certainly have a 3-D truss, but 2-D makes all the important points. And then I can count the bars. One, two, three, four, five. And I can count the nodes. There happen to be five here.
But now comes the moment. I have to tell you, what are the unknowns? What are the u's. Because of course, you know that I'm going to go from u's to e's to w's, to forces. f. And you know that a matrix A is going to do that. A matrix C is going to do that. A matrix A transpose is going to do that. You're all ready, we need to know what's the setup. What are these matrices. OK, and how many. So let me explain the setup. Typical node, node one. we have forces in these bars, so that node one could have a force. We're in the plane. So we have a horizontal force and a vertical force. Together, that would produces a force in any direction whatever. So this is the key point. That there is a horizontal force. f, horizontal one. The one being the force on node one. But there's also a vertical force. And let me take horizontal to the right, positive to the right. Vertical positive upwards. Just to have a convention. So how many f's have I got? Well, the point is I now have two per node. That's the difference. I have two per node, two forces. and I have two displacements per node. Because that point under, there will be more forces. Some maybe pulling this way, whatever. Maybe let's look at node two.
So node two could have a couple of forces on it. F H two, and F V two. And it moves like the other nodes. So now I'm introducing the unknowns. u is the movement. u, again horizontal, and again, now we're talking about node two. And it moves up. Or doesn't, or moves down. But that's an unknown. u, a displacement, a vertical displacement of node two. Do you see the setup? Two forces per node. Two displacements per node. So that's like, the number of unknown is like double. Like, doubled, and that produces an interesting situation. I've marked supports here. So let's just speak about supports. So what's happening at the supports? At the support there's no movement. The whole that point is pinned. So this is telling me that u horizontal five is zero and u vertical, sorry that was four and it'll be the same for five. u vertical five is zero. It's like grounding a node in the electrical case. We just see this pattern over and over. And we want to see OK, what does it look like for trusses? So here's a support that fixes those. So those are not unknowns. And similarly, they're not unknowns there. Still saying five when I mean four.
So those are boundary conditions, n conditions, whatever. And similarly here. So how many unknowns are there? Now look at this picture, how many unknown displacements are there in this truss? Six. Six, right? Two here, two here, two here and none there. So the number of actual unknowns is six. My idea would be that it's twice the number of nodes minus the number of fixed things, that R would be four in this case. I've got two fixed here and two fixed here, so this would be two times five. Ten possible displacements but R counts the number of fixed displacements, four, and leaves us with six. OK. So my matrix A will now be, it's always m by n. My matrix A will be five by six. OK. Now you're going to ask what is that matrix. But let me hold that off for a little moment. I want to just see its shape first. So you could now do this for a large truss, right? You count the bars, and you could count the nodes. And then you could count the unknown displacements, u. So there are six u's here. And there are five e's. And there are five bar forces. And there are six equilibrium, balance, force balances. Six, six for the node count, for the unknowns count, five, five for the bars count.
OK, now here's a point about this particular truss. It's not safe to get on it. Right? And I want to say why is it not safe. So this is a feature that comes into the truss question that makes it a little new and more interesting. A little twist compared to the previous examples. That bar, that truss, I wouldn't stand on it. Now, why not? Well, purely for linear algebra reasons. Of course. The matrix A is five by six. So now what do we know about a matrix that's five by six? So A is five by six. Five rows, as always the m; six columns, because now we have six unknowns. And what do I know about any five by six matrix? I want to ask about the equation Au=0. So I want to ask about it in linear algebra language and then I want to ask about it in physical language. And the beauty is the thing that makes trusses sort of fun is, these matrices, A, get pretty big fast. Because when I put a few more nodes on, the book has a picture of a sort of treehouse. Then A is growing. And I don't, all the time, write down the matrix A. I haven't written it down here. What I've written down it's just its size, because that's enough to tell us something about this set of equations Au=0.
What's the story Au=0? Well of course it has the solution u=0. Nothing moving. If I have no displacement, if the u's are all zero, then I have no stretching. The e's are stretching. Elongation, as before. How far does the bar stretch? OK. So if I have zero u's and zero e's, but what other possibility am I going to have here? I'm going to have probably one solution to this system that isn't zero. I'm probably going to have one set of displacements u, look what's happening here. This is Au is the e. So I'm going to have at least one and probably in this case it will be one, there will be one, the neat word for it is a mechanism. And what does that mean? A mechanism is a solution to Au=0. So that, a mechanism is a movement of the bar. So it's going to be non-zero. The bars are going to move a little. Sorry, the nodes are going to move a little. The nodes will move a little bit. In this u, because it isn't zero. But the bars won't stretch. So tells us we've got instability here. If there's a solution to that, that's always telling us that A transpose A is singular. So let me just put that A transpose A, or A transpose C A, C couldn't save it. Will be singular. It's just like our free-free thing in being singular, but the picture doesn't look free free, does it? It's got supports in here, just not good enough. And I believe that if you look at this truss, you could describe, you could tell me, and you could draw, a movement of that truss in which there is displacement but no stretching.
Let me ask you how to draw that. And I believe, everybody understood why was there a solution. It was because we have six unknowns and we only have five equations. So this was five equations. Any time you have five equations with a zero on the right hand side, so five homogeneous equations, whatever you want to say when that's zero on the right and six unknowns. Six u's. Then you're going to have solution. You can't help it. You've got that many degrees of freedom, you've only got that many constraints, there's going to be solution. OK, tell me how to draw that. Let me put in the truss now. What's the solution? So this is the fun part in a particular example at the start. How could that move without stretching bars? Let me see. What could happen? What do you mean now, who's going to move where? What's the movement here? And I want to draw it over there. So you give the answer by drawing it as well as by telling me the six unknown u's. So what can happen at this thing? So you're going to say the truss could, these bars could, turn a little? And notice that word a little. We're talking small displacement, small stretches all the time here. I'll show you why we're always making that linearity assumption, or small assumption. OK, those move a little. And what happens to that triangle at the top?
It sort of just moves along, right? So the picture you would draw would be that you started there. And it moved along a little, I'll make it a larger displacement than I really have in mind. These guys of course are here. So they come out and the rest of the truss, the top of the truss just kind of goes with it. Goes with the flow. That would be the answer that I would be looking for, to draw the mechanism. That would show it. And if I wanted to write down the u that goes with it, what would it be? Let me again number these guys; this is one, two, and this is three. So what are the displacements of nodes one, two, and three? I'll always write u_1 horizontal before vertical. Can we make an agreement? So I want to know about the horizontal movement then the vertical movement of node one, then node two, then node three. So I'll have six numbers there. And what could I put in for those six numbers?
So the horizontal, let me suppose that first guy, I'll put a one. Really that's a bigger number than I should put, but it's a convenient number. So I'll just take it to be one even so I really have in mind. Let's say that's one angstrom, or one tiny little person. OK, so what about the rest? What's the vertical cool, oh yeah this is a key point here, what's the vertical movement. This movement to me is horizontal. I'm going to say that the vertical moment is zero. Of node one, just moves over. And node two does the same. And node three does the same. So that's my solution. . That's a simple movement, a simple set of displacements, think most to the right. I have not written down the matrix A, but probably won't even do it until next time. But you will see that when we do the matrix A for this particular truss will have this particular u as a mechanism. In linear algebra, u is in the null space of A. Au=0, that's all that means. OK, do you see more or less what's up? But now there's one little thing that may be bothering you. Which is what? If I come back to the zero, zero, zero there, you could correctly say wait a minute, if those bars didn't stretch, if they just rotated as you told me to do, then this was mostly across but a little bit down, right? And I'm saying no. I'm saying zero. OK, how do I get away with that? So I'm saying in 18.085 it's a zero. And why?
So this is like a little time out just to focus in on, let me focus in on node two. So here's the bottom node four, so it used to be vertical up to two. This was node two and this was number four. And then it rotated a little, to there. To this position. So it went, if this angle was, let's say, theta, then what is that actual position? So let's say this was, let's say the bar had length one. This is the origin, zero, zero. This is the point zero, one above it, OK? And now, that's before it moved. Then it moved a little bit. It moved to an angle theta. What's the position of that bar? Of that node? What's the new position of the node, and then we'll look at the difference and we'll see the movement u, the displacement. So how far did it move? What's the x coordinate? How far did it go across? If I put in that line you'll know. So the movement across was, sin(theta)? Good. sin(theta). And the movement down, well, yes, so let's find its position and then we'll take the difference. So what's the vertical new position for that guy? It moved by, it moved across by sin(theta). And down by 1-cos(theta). Are you agreed with that? Because here is cosine theta, right there. And here's the little bit it moved down. OK. So these are exactly correct. Yeah this is in the position of sin(theta), cos(theta), and the difference was the 1-cos(theta).
OK, so now here comes the key point. Approximately sin(theta) is approximately, if theta is small and now here comes the smallness, sin(theta) is approximately theta. sin(theta)'s approximately theta. And 1-cos(theta) is approximately what? Now, this is the important point. So theta is like the first term. If I expand, I mean, the exact term would be theta minus theta cubed over six, dot dot dot. But I'm only keeping that term. And 1-cos(theta), now what's the formula for cos(theta)? This is like worth, just should? It's a one, because of course cos(0) is one, and then you subtract what? Theta squared over two. And so on. And then plus theta fourtg over 24 or whatever. OK, so the ones cancel as we expect. And I'm getting theta squared over two. And this, here was theta to the first power. Theta cubed was, we didn't care. And we don't care about theta squared. So that's why it's zero. Because it's a second order movement. If theta is small, as I'm going to assume, small displacement, theta squared would, if I allowed theta squared and cos(theta) in here, I'd have a non linear problem. And I don't want that. And I don't need it. I mean, finite elements, structures, bridges, whatever. Your first hope and expectation and calculation is small theta linear problem. So to a linear person theta squared is zero. That's why those guys are zero.
OK, so that's an assumption we'll often see, so it kind of was. There are two kinds of non-linearities in structures and elasticity. One would be to allow this geometric non-linearity. Theta's large displacements, theta large enough so that you can't neglect theta squared. That's a tough one. If you allow geometric non-linearity in, as finite element codes have to do. If you have ABAQUS is a code that does major finite element calculations, nonlinear ones. I mean they, at the beginning they were studying what happens, what are the stresses on cables under the Atlantic. I mean, those are fascinating problems. Or I mention car crashes. I mean, car crashes, the geometry changes, you have big displacements. But we're talking here about linear small displacement cases. OK, so don't forget that part. That when the truss gets more complicated, the principle stays the same. That we distinguish between the thetas that matter and the theta squareds that don't.
OK, so now what? Now I guess I'm ready to complete this picture a little more. OK. So let me, so we've understood what the idea of a mechanism. Oh, how could I prevent a mechanism? In other words, if I stood on this truss, the slightest bit of wind would crash it down, right? So that's unstable. That's an unstable truss. How could I make it stable? I mean if you were designing this thing, what would you do? Add another edge. You'd stick in another bar. Maybe stick in a bar there. What would happen now? Would it now be stable? You'd have to answer that question. You couldn't just put in bars, whatever. You want to put bars that do the job. OK, now how many bars? We've now got six bars. So m is now up to six. The matrix A is six by six now, whatever that matrix may be. We have six bars, six displacements. We can hope that we now have a six by six, well, we do have a six by six matrix, whatever it looks like. And we can hope that it's not singular. We can hope it's invertible, we can hope that that mechanism is killed. And you see it is killed. The six by six, that truss is now stable. No mechanism there, right? Again I haven't written down the matrix, but I'm really calling for engineering intuition here. That this truss is now stable, and of course I can make it even more stable by adding a seventh edge. A seventh bar. So when it was six I had square matrices, A transpose and then C and then A would have been square.
Now I've got seven bars and, so now I've put in a seventh guy. m is now up to seven. My matrix a would now be seven by six. Mechanism will be gone because I've now got, what, seven equations. Same six u's. So we begin to get a feel of, are there solutions or not? What I'm saying is I can't tell just from the count that a is not singular. I could have a lot of bars and still be unstable. Invent a truss for me. Just because, how could you invent a truss that had, maybe it has seven bars. With those seven bars, those diagonal guys, that did it. That made it stable. Our eye tells us that before we do any linear algebra. Tell me a seven by, a thing. Well, yeah. OK, so here would be, shall we support both of these? I'll start out the same, OK. Now, yeah, how could I, let's see, I've haven't prepared. How could I get a whole lot of bars. I might not get seven by six exactly, but how could I have plenty of bars and still unstable? Well, suppose I do this. Oh yeah, that's a good example. That's not stable, right? OK. Every let's practice with that one. That's just my idea, and problems in the book just ask you to practice with things like that. Tell me the count, first. What is m, the number of bars? Six. What is n, the number of unknowns, little n, the number of unknowns? What's the shape of my matrix here? A is, it's got six bars and how many unknowns? Eight. Eight, right? two here, two, two, two. None here. Six by eight.
OK. And how many mechanisms am I now expecting? Probably two. Probably two, there would be two independent mechanisms here. Can you tell me what they look like? Draw them. What would they look like? What would be two different things that could happen, could go wrong with that truss? You see it, right? This could turn. As in our example with the top part moving with it. Or, second one possibility would be the top part goes. And the bottom part stays. Or any combination. So the whole thing could go like that. That would be one. But that wouldn't be the only one, of course. So in other words, we have a two dimensional space of mechanisms and you could give me two different, and there are not just two guys, all their combinations are there. So this would have two mechanisms. Two mechanisms. And I could put in bars, of course, that would try to save it. Well, how many bars, what's the minimum number of bars I absolutely need to make this thing stable again? Two. Well, now suppose I put in these two bars. Right? I've got enough bars, I've got an eight by eight matrix, but I haven't saved it. Right? Because it still has that mechanism. So you can't assume that because the count is right you've avoided mechanisms because in that example you haven't.
OK, so that would be a case of square eight by eight, but not good. So as soon as I say there's a solution to Au=0, I know that A transpose A will be singular. And unstable. OK, before I go to the framework let's just do one more thing. Suppose I take away the supports. All right, let me put in some bars, though. I'll put in some bars. OK, plenty of bars. Want another one? OK, how many bars have I got? Lots, right? OK, now the matrix A, what do you think about this? Are there solutions? You haven't even seen the matrix A, of course, but you've seen the truss, that's what matters. How many solutions, are there solutions to Au=0? Are there ways that this truss could move without stretching? Are there ways that this truss could move without stretching? And what are they, and how many are there? And what name should we use? OK, what are they? How could that move without stretching? Well, it's got no supports at all. It's just free out there in space. So it could move. How many ways could it move? Three. It could move, everybody could move this way. All ones on the horizontal guys. Everybody could move this way, all six ones on the vertical guys, or be 12 unknowns here. And it could also rotate, what would be the rotation? I'm not talking about this rotation. This could not happen. What could happen? What rotation could happen here? For this, there's a third rigid motion. Translation, translation, and rotation around, well take this one as an example. The whole thing could swing around this. That would be a motion.
Well now you're going to say well, why didn't I swing it around that one? And of course it could. But what would be the deal? It would have to be, there are only three rigid motions, right, up and around. So if you give me another one, like, around this one, then somehow it had to be a combination of those. I don't even want to think what combination it is. But there are three rigid motions. So I sort of distinguish mechanisms, this word mechanism. So that's where the truss deforms. In these and rigid motions, so I'll say plus, possibly. Plus rigid motions, and rigid motions would be, you know, it doesn't deform internally, the whole thing moves. And this is of course what we get in the case of not enough supports. And this is what we get in the case of not enough bars. Yeah. So maybe it's worth separating those two. In the examples we do, we'll usually put in enough supports to kill the rigid motions. And then the question would be are there some mechanisms.
OK. Now, I have to start on what this is. Well it'll be just a very quick start. So what I'll do at the beginning of Friday, so Friday's the other lecture on this topic. And then the homework will ask you to do some trusses in this section. It's probably Section 2. something. 2.7, maybe. What's the matrix C? Last second question, what's the matrix C, what size is it? What size is the matrix C for our original problem? Or no. What size is C, is C involving, if I know these numbers, what size is C? Five by five. m by m, right? C is the diagonal matrix, one entry for each bar, C is just C. It has a c_1, c_2, c_3, and this w=Ce, it's just Hooke's Law on each bar. So, simple. It gets there in the middle, just the way that C in the first exam problem popped in, and other C's. That gets there in the middle. But it's very, extremely, simple. OK, so the real attention is on A, as usual. And that will come Friday morning |
College Algebra and Trigon Dugopolski Precalculus series for 1999 is technology optional. With this approach, teachers will be able to choose to offer either a strong technology-oriented course, or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility. College Algebra and Trigonometry is designed for students who are pursuing further study in mathematics, but is equally appropriate for those who are not. For those students who will study additional mathematics, this text will provide the... MORE skills, understanding, and insights necessary for success in future courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Additionally, the focus on problem solving that is a hallmark of this text provides numerous opportunities for students to reason and think their way through problem situations. The mathematics presented here is interesting, useful, and worth studying. One of the author's principal goals in writing this text was to get students to feel the same way. This text provides numerous strategies for success for both students and instructors. Instructors will find the book easier to use with such additions as an Annotated Instructor' s Edition, instructor notes within the exercise sets, and an Insider' s Guide. Students will find success through features that include highlights, exercise hints, art annotations, critical thinking exercises, and pop quizzes, as well as procedures, strategies, and summaries. |
More About
This Textbook
Overview
This Handbook fills the gaps of Open Geometry by explaining new methods, techniques and various examples.One its main strengths is that it enables the reader to learn about Open Geometry by working through examples. In addition, it includes a complete compendium of all the Open Geometry classes and their methods. Open Geometry will be of great attraction to those who want to start graphics |
books.google.co.jp - Now... One-variable calculus, with an introduction to linear algebra
Calculus: One-variable calculus, with an introduction to linear algebraユーザーの評価
This book offers a beautiful foundation - starting in the introduction with some basic axioms of real numbers (not quite starting from Peano's axioms). It is not necessary to get this in depth but for ...レビュー全文を読む
Calculus Book Text - Physics Forums Library [Archive] Calculus Book General Math. ... Can anyone recommend an introductory Calculus book for a Grade 11 student? I know this may sound dumb, ... archive/ index.php/ t-53600.html
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著者について (1967)
TOM M. APOSTOL, Emeritus Professor at the California Institute of Technology, is the author of several highly regarded texts on calculus, analysis, and number theory, and is Director of Project MATHEMATICS!, a series of computer-animated mathematics videotapes. |
Algebra 2
Student Expectations
Coach Ford Conference 5rd Period: 11:30am -12:54pm
Room 1711 – donald.ford@desotoisd.org Phone: (972) 230-0726 ext. 1711
Welcome to Algebra 2. I'm here to help you succeed in Algebra 2.All I ask from
each of you is to have a positive attitude and the willingness to work and study.
Course Description: This is a second course in algebra for the college bound student. Algebra II
includes the study of more advanced algebraic concepts and techniques such as matrices, complex
numbers, andlogarithms as well as reinforcement of the basic skills introduced in Algebra I.
I. Daily Work 40% (Class assignments, notes, homework, quizzes, vocabulary, etc…)
A. You must show your work.
B. Assignments must be at least 95% complete to be mandatory. 100% is expected!!!
C. Quizzes will be given regularly throughout a unit. (Be prepared at all times.)
D. Homework is due the next day unless otherwise indicated.
E. Late assignments will be penalized according to the District Grading Policies. Assignments
turned in after 2 days will receive a zero.
II. Tests / Project – 60%
A. 2-4 written tests will be given a six weeks.
B. Projects count as a test grade. Guidelines and a grading rubric for each project will be given at
least two weeks prior to due date. Projects are long-term assignments to be completed outside
of class.
C. Students will keep an organized notebook of all assignments which is worth one test
grade each six weeks.Binder may be used for other subjects also.
III. Procedures:
1. All papers turned in to be graded must have a title and heading which includes:
Name, date, and period.
2. Pencil will be used on all papers with exceptions of projects.
3. In case of absence, it is the student's responsibility to schedule make-up tests and
quizzes outside of class time. Homework assignments are to be picked up the first day
you return to school, or you may e-mail me to get the assignment early.
Parents:
I'M LOOKING FORWARD TO A GREAT YEAR!
Coach Ford
*Keep this page. It will be the
first page of your notebook*
Class Rules
(Stay out of the doghouse.)
1. To avoid being tardy, be in your seat ready for class when the bell
rings.(Homework and notesout on desk , pencil sharpened, etc.)
2. Bring all supplies to class everyday.(Binder, pencil, paper, etc…)
3. Turn work in on time – legible.(Be responsible for make-up work.)
4. Participate actively and properly in class.
5. RESPECT the teacher, classmates, and yourself at all times.
(No rudeness or profanity. Keep hands to yourself, etc…)
6. NO CELL PHONE USE DURING CLASS. Personal use of a cell
phone for any reason (texting, calculator, phone calls, charging, etc…)
will result in the phone being picked up and turned into the front
office.
NO EXCEPTIONS!!!
7. LEAVE THE ROOM NEAT .(Calculator must be returned. No food or drink in
room) Students who follow the rules and perform well in class will have the opportunity to
earn bonus points, homework passes, and of course great knowledge.
Consequences for not following rules will follow the guidelines in the student code of conduct.
ALGEBRA 2 SUPPLIES
The following supplies should be brought with you to class each day:
1. 3 ring binder notebook 1.5" or2"
This will be your math notebook. The notebook is a graded assignment and counts as a
TEST grade EACH six weeks. (may be used for other classes also)
2. Notebook Paper – LOTS!!! Will be used for assignments, notes, vocab, etc…
3. 1 subject 70 page spiral
4. 4 dividers
5. Pencils – several packages, you'll need them all year
6. Personal pencil sharpener
7. 2 GB flash drive
8. Pencil Bag with holes (to be put in notebook) unless already included on binder
The following supplies will be left in the classroom for daily use by student.
9. 2 Red Pens
10. 2-4 Dry erase markers
11. 4 – AAA batteries (student will be provided a Ti-84 calculator for use in class)
12. Box of Kleenexoptional, but definitely needed
13. Ti-84 plus graphing calculator is recommended, but not required. Ti-83, Ti-83plus also
work great as do the older Ti-82 and Ti-81. It is a good investment since students will use
this calculator in all of their high school math classes. This calculator is also WIDELY used in
college classes.
Coach Ford – Algebra 2
Coach Ford Algebra 2
Student/Parent Information Sheet
Student Name: ____________________________________ ID #___________ Period __________
Home Phone # _________________________ Birthday: ___________________
Geometry Teacher: _______________________________
Extra-Curricular Activities: ___________________________________________________________
(sports, band, journalism,etc…)
Hobbies/Talents: ____________________________________________________________________
Who has been your favorite math teacher so far? _______________________________________
Why? _______________________________________________________________________________
_____________________________________________________________________________________
Parent Information:
Mother's Name _____________________________ Father's Name ____________________________
Mother's Daytime Phone # ____________________ Father's Daytime Phone # ___________________
Parent e-mail _________________________________________________________________________
Please print clearly with correct casing.
I have read and agree to follow the expectations and procedures for Coach Ford's classroom.
Parent Signature ________________________Date _______________
Student Signature ________________________ Date ______________
What is your child's dream for his/her future?
_____________________________________________________________________________________ |
QuantumMechanicsDemystified
Friday, February 12, 2010
Learn about a new book called "calculus without limits" that's going to revolutionize your understanding of calculus. This book uses a plain-English writing style combined with detailed step-by-step problem solutions to show you how to do calculus problems. It might be the only study guide you'll ever need, ending frustration saving time and helping you pass calculus. It's great as a textbook supplement, for college or AP courses, or for self-study.
Let's face it-calculus sucks for a lot of people. Its hard and confusing, and its frustrating. But what if someone would just show you the exact steps required to solve any problem?
Calculus without limits teaches in plain-English. Its an easy to understand problem solving based review of all topics in first year calculus.
Each section features complete step by step solutions of the same problems you'll see on homework and exams. Here's a chapter by chapter breakdown. Each chapter is written in plain-English, with a get-in, get-out approach to explanations, and a focus on showing you solved problems.
Chapter 1 reviews functions and graphing chapter 2 covers computing limits The next two chapters cover differentiation The next chapters are packed with solved integration problems covers definite and indefinite integration integration by u-substitution integration by parts integration using partial fractions trig substitution integration of trig function and powers of trig functions integrating exponentials, natural log, and inverse trig functions then its on to sequences and series learn the basics about sequences and series see how to do convergence tests learn about power and taylor series the final chapter covers ordinary differential equations
So whats it cost? Calculus without limits is $27.Compared to your average calculus book-that can cost more than a hundred dollars, that's dirt cheap.And calculus without limits is available for instant download-you can have it in 30 seconds, read it online or print it out. calculus without limits
Monday, August 31, 2009
Calculus Test is a new app for the iphone that drills you on calculus problem. Test your knowledge of limits, derivatives, indefinite integrals, definite integrals, the chain rule, integration by parts, u-substitution, and more using this handy iphone app.
Tap limit, derivative, or integral and a problem is randomly selected and displayed for you to solve. Solve it, then tap "Answer" and in flash card format, the screen view flips to reveal the answer.
This simple drill program is great to help you get ready for your calculus exams, whether its college calculus or the dreaded AP Calculus exam. Also great for those who want to learn calculus through self-study.
Friday, December 19, 2008
Tuesday, December 16, 2008
Randy Mills with his company "Blacklight Power" has been claiming for years he can generate power by putting hydrogen atoms in a "state below the ground state". As anyone who has studied quantum physics knows, you can't put a hydrogen atom in any energy state lower than the ground state. Its not physically possible and would violate the laws of quantum physics as we know it. Those laws have been repeatedly tested and verified to higher and higher precision over the past hundred+ years, and the theory of quantum mechanics is completely solid, so why should anyone believe this nonsense?
Apparently the goons at CNN don't care about the details of quantum theory. They'd rather get happy about Blacklight power's claim to no CO2 emissions, cheap power, 200 times more powerful than burning gasoline or coal. All based on a pseudo-scientific claim. CNN is supposed to be a news organization so they should have consulted some leading scientists in this report.
Blog Archive
About Me
I'm a physicist that happens to own 3 horses and 5 dogs. I do horse training in my spare time and follow expert horse trainer Eric Bravo around when I get a chance, sometimes with a video camera. Email me at dmmcmah@gmail.com with questions. |
Curriculum for Excellence (C.F.E)
This book forms the 2nd half of the Level 2 CfE Course and should
follow on from Book 2a. Together, these 2 books cover the entire
contents of the CfE Level 2 course.
Along with Book 2a, this will prepare pupils to attempt our Level 2 Assessments and our end of Level Diagnostic Assessment.
There are no A and B exercises. The books basically cover the entire Level 2 course without the teacher having to pick and choose which questions to leave out and which exercises are important. They all are!
Unlike Book 2a, it does NOT contain a "Chapter Zero". Instead, every new Chapter is preceded by a Consolidation Exercise, which basically revises all of the previous work covered for the topic in our Book 2a. This means Each Chaper of new work is sandwiched between a Consolidation of former work Exercise and a Revisit-Review-Revise Exercise which consolidates all the work covered.
Non-calculator skills will be emphasised and encouraged throughout the book. |
Math-a-Logic
If you thought math was all numbers, you're in for a surprise. The ability to reason logically is both a prerequisite for learning mathematics and a desired outcome of mathematics instruction. Mathematics provides an excellent context in which to make students aware of the logical structures they need to function successfully in any setting.
Math-A-Logic is an award-winning text that successfully merges logical thinking with mathematical concepts and calculations. Eight areas of logic are introduced:
patterns and sequences,
analogies,
deduction,
inference,
sets and Venn diagram,
propositions and logical notation,
syllogisms, and
logical problem solving.
Attractive, reproducible worksheets lead students through each topic, providing explanations, examples, and exercises to test their understanding. With mathematics as the vehicle for presenting and practicing the logical concept, students get practice in mathematical concepts and computations while building thinking skills. The end result is clearer thinking and enhanced problem-solving abilities. This unique approach is sure to be a favorite supplement to your regular math program. The attractive illustrations, clear instructions, solid content, and ease of use make this book a winner. |
This key introductory Level 1 course provides a gentle start to the study of mathematics. It will help you to integrate mathematical ideas into your everyday thinking and build your confidence in using and learning mathematics. You'll cover statistical, graphical, algebraic, trigonometric and numerical concepts and techniques, and be introduced to mathematical modelling. Formal calculus is not included and you are not expected to have any previous knowledge of algebra. The skills introduced will be ideal if you plan to study more mathematics courses, such as Essential mathematics 1 (MST124). It is also suitable for users of mathematics in other areas, such as computing, science, technology, social science, humanities, business and educationIn order to study this course successfully you should expect to be actively doing mathematics, rather than just reading it. You will also be encouraged to develop skills in interpreting and explaining mathematics, and this aspect will be assessed in some of the assignment questions.
Samples of the study materials, including example assessment questions, are available from our Maths Choices website.
Providing you have the appropriate background knowledge (see Entry), you should expect to study for about eight hours a week. Many of the topics covered in the course depend on your understanding of topics in earlier units. So, if you have not fully understood earlier material, you may find later material more difficult and time consuming. This is particularly true of graphs, formulas and algebra. Naturally, the study time required for the course tends to increase before an assignment deadline.
You will learn
Successful study of this course should begin to develop your skills in working with mathematical concepts and using them to solve problems.
You will learn about:
key ideas in mathematics, including some statistics, algebra, geometry and trigonometry
mathematical vocabulary and notation introduced and developed in the course
selection and use of mathematical techniques for solving problems
interpretation of results in the context of real life situations
simple mathematical arguments
how to explain mathematical ideas from the course in writing
development of skills in learning mathematics
use of relevant ICT tools for learning and for working on mathematical problems
describing problems mathematically
analysing mathematical reasoning.
The course contains many real world contexts such as journey planning, glaciers, supply and demand, depreciation, poverty levels, chance events, and medical conditions (such as cancer), to help illustrate mathematical topics.
Entry
This is a key introductory Level 1 course. Level 1 courses provide core subject knowledge and study skills needed for both higher education and distance learning, to help you progress to courses at Level 2.
You are advised to have previous experience in mathematics, before commencing this course. In particular, you should be confident with the following topics:
arithmetic of numbers, including negative numbers and fractions
scientific notation for numbers (sometimes known as standard form)
powers of numbers including square roots
using your scientific calculator effectively for the above topics, and for working with brackets and π
using simple word formulas
drawing and interpreting simple charts and graphs.
You are not expected to have any skills in algebra before the course starts.
It is essential that you establish whether or not your background and experience give you a sound basis on which to tackle this course, since students who are appropriately prepared have the best chance of completing their studies successfully and get the most enjoyment out of it. You are strongly advised to follow the recommendations given in the Preparatory work section below.
There are two mathematics entry level courses, this one and Essential mathematics 1 (MST124). Your choice of which one to start with depends on your mathematical knowledge, experience and on the qualification you have in mind.
For advice about where to begin your Level 1 study in maths please look at our Maths Choices website. The website also contains a self-assessment quiz to help you decide if MU123 is the right course for you.
Preparatory work
It is recommended that you work through some of the free and open educational resources from the Maths Help website, where there is a module to help you to refresh your knowledge of each of the following topics:
Numbers, units and arithmetic
Rounding and estimation
Ratio, proportion and percentages
Squares, roots and powers
Diagrams, charts and graphs
Language, notation and formulas
Geometry.
Alternatively, you could study any textbook that covers the same topics.
Regulations
As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are
available on our Essential documents website.
If you have a disability
By its nature mathematics is a visual subject, and this course contains considerable amounts of mathematical notation and graphs, and other forms of diagram. If you have a visual impairment or limited manual dexterity you may experience difficulties with some of the activities and assessment questions which involve the interactive use of ICT or which have a high graphical content.
It is important to note that use of the online activities and resources, which include on-screen dynamically-changing graphs and mathematical notation, will be an integral part of your study. You will need to spend considerable amounts of time using a personal computer, and some of your assignments will be interactive and online.
Written transcripts of any audio and video components and Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader and mathematicalYou will need
A scientific calculator. We recommend any Casio scientific calculator with 'natural display', as these enable you to key in calculations in the same order as they usually appear in written text, and have a two-line display so that you can see both your calculation and the answer. Some instructions for using the Casio fx-83ES, and compatible models, are provided in the study materials. Any other scientific calculator is also acceptable provided that you know how to use it before the course starts, and you have access to the appropriate calculator manual (these are often available to download from the manufacturer's website). Please note that you do not need to have a graphics or programmable calculator to study this course If you are new to the OU, you will find that your tutor is particularly concerned to help you with your study methods. We may also be able to offer local group tutorials or day schools that you are strongly encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking MU123. Some tutors may offer online group tutorials in addition to or instead of face-to-face tutorials.
Assessment
The assessment details for this course can be found in the facts box above.
Please note that TMAs for all undergraduate mathematics and statistics courses must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.
The first iCMA, covering Unit 1, is to be submitted about two weeks after the start of the course. The first TMA is to be submitted about a month after the start.
TMA questions typically involve calculating, creating and/or interpreting a graph or diagram, using algebra, and explaining your work and conclusions. The latter is one factor that makes this a university-level course and it is a new approach for some students, who may find it challenging initially. Some TMAs may also include a short question covering a wider aspect of studying maths.
As there is no examination, the EMA aims to consolidate your learning across different aspects of the course. It covers the whole of the course, and is compulsory if you wish to pass the course.
Professional recognition
This course is sometimes accepted as an acceptable equivalent qualification to GCSE grade C in mathematics by teacher training institutions, but always at the discretion of each institution. So, if you hope to use it for this purpose, you are advised to check as early as possible with your chosen teacher training institution(s).
Future availability
The details given here are for the course that starts in October 2013 and February 2014. We expect it to be available twice a year.
How to register
To register a place on this course return to the top of the page and use the Click to register button.
Student Reviews
"Very good course. No matter how good you think you are at maths, this course shows how you can still ..."
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"I would highly recomend this course to any forty something "mature" students like myself. I really had a strong aversion |
Algebra 1a Pathway –
mat116p
(3 credits)
This course introduces basic algebra concepts and assists in building skills for performing specific mathematical operations and problem solving. Students will solve equations, evaluate algebraic expressions, solve and graph linear equations and linear inequalities, graph lines, and solve systems of linear equations and linear inequalities. These concepts and skills will serve as a foundation for subsequent business coursework. Applications to real-world problems are also explored throughout the course. This course is the first half of the college algebra sequence, which is completed in MAT 117P, Algebra 1B |
Algebra 1b SYLLABUS
Winter 2011
INSTRUCTOR INFORMATION
Instructor: Dan Jenkins
Telephone: 503-518-5925 x16
Email: jenkinsd@nclack.k12.or.us
Office Hours: 7:45-9:15am/2:45-3:45pm or by arrangement
CLASS INFORMATION:
Course Description: This course is the second trimester in a two trimester course in first year
algebra topics. Major topics include linear equations and inequalities, exponential properties
and functions, and polynomials, factoring and quadratics. At the high school level, Algebra 1 is
the foundation math course required for more advanced study and is the first math class that
requires students scored work samples at the state level.
Credits: 0.5 Credits per term
Class Schedule: Monday-Friday
Location: CMC main campus
Pre-requisites: Algebra 1a
Textbook: Elementary and Intermediate Algebra (3rd ed.) by Baratto and Bergman
Resources:
Students have access to resources posted on the CMC website under the instructor's page
(
Supplies: Students are to bring a writing utensil every day along with a binder, notebook paper,
and completed work from the previous day, handouts given out in class, and a calculator.
TOPICS and STANDARDS:
Linear Equations and Inequalities
H.2A.1 Identify, construct, extend, and analyze linear patterns and functional
relationships that are expressed contextually, numerically, algebraically, graphically, in
tables, or using geometric figures.
H.2A.2 Given a rule, a context, two points, a table of values, a graph, or a linear
equation in either slope intercept or standard form, identify the slope, determine the x
and/or y intercept(s), and interpret the meaning of each.
H.2A.3 Determine the equation of a line given any of the following information: two
points on the line, its slope and one point on the line, or its graph. Also, determine an
equation of a new line parallel or perpendicular to a given line, through a given point.
H.2A.4 Fluently convert among representations of linear relationships given in the form
of a graph of a line, a table of values, or an equation of a line in slope-intercept and
standard form.
H.2A.5 Given a linear function, interpret and analyze the relationship between the
independent and dependent variables. Solve for x given f(x) or solve for f(x) given x.
H.2A.6 Analyze how changing the parameters transforms the graph of
f (x) = mx + b.
H.2A.7 Write, use, and solve linear equations and inequalities using graphical and
symbolic methods with one or two variables. Represent solutions on a coordinate graph
or number line.
Exponential Properties and Functions
H.3A.1 Given an quadratic or exponential function, identify or determine a corresponding table
or graph.
H.3A.2 Given a table or graph that represents an quadratic or exponential function, extend the
pattern to make predictions.
H.3A.4 Given an quadratic or exponential function, interpret and analyze the relationship
between the independent and dependent variables, and evaluate the function for specific
values of the domain.
Polynomials, Factoring and Quadratics
H.1A.5 Factor quadratic expressions limited to factoring common monomial terms, perfect-
square trinomials, differences of squares, and quadratics of the form x2 + bx + c that
factor over the integers.
H.3A.1 Given a quadratic or exponential function, identify or determine a corresponding table or
graph.
H.3A.2 Given a table or graph that represents a quadratic or exponential function, extend the
pattern to make predictions.
H.3A.4 Given a quadratic or exponential function, interpret and analyze the relationship
between the independent and dependent variables, and evaluate the function for
specific values of the domain.
H.3A.5 Given a quadratic function of the form f (x) = x2 + bx + c (or equation of the form
y = x2 + bx + c) with integer roots, determine and interpret the roots, the vertex of the
parabola, and the equation for the axis of symmetry of the parabola graphically and
algebraically.
Comparison of Functions (Linear, Quadratic and Exponential)
H.3A.3 Compare the characteristics of and distinguish among linear, quadratic, and exponential
functions that are expressed in a table of values, a sequence, a context, algebraically,
and/or graphically, and interpret the domain and range of each as it applies to a given
context.
RESPONSIBILITIES and POLICIES:
Student Responsibilities: As a student of CMC, I expect you to adhere to the policies of the
school, as outlined by the Student Handbook (located on the website). You are responsible for
the assignments in this class and to communicate any questions, comments or concerns you
have to me. Acceptable means of communication include an appointment, e-mail, voicemail or
through online discussion forums/blogs. Use of correct grammar and punctuation is required in
all written communications.
Plagiarism, cheating, and collusion are prohibited at CMC. Students who fail to observe these
standards are subject to disciplinary action. Please refer to the CMC Student Handbook for
further definitions and consequences of these behaviors, available at:
Attendance: Attending class daily will affect a student's opportunity to learn in a positive
manner and should result in mastery of skills, benchmarks, and standards mentioned above.
Class participation: Class participation will result in a greater understanding of the subject
matter and will help in skill development. This includes classroom or online discussions, group
work, project or other participation requirements that influence student's opportunity to learn.
Use of Electronic Devices: Cell phones, iPods, and other relevant or irrelevant electronic
devices are not to interfere with the learning environment unless these electronic devices are
being used for a class assignment. The instructor reserves the right to take any devices that
pose a problem. If a device is taken, then it will be returned in a timely fashion with a discussion
about classroom expectations. If problem persists then disciplinary action may be taken.
Other Policies: Refer to the CMC Student Handbook
Instructor Responsibilities: As your instructor, I commit to communicating openly and
frequently with you about this class. I will maintain a professional, safe learning environment
adhering to the policies of CMC. You can expect a reply to communication, be it via e-mail,
voicemail or in person, within 24-48 business hours.
Syllabus Changes: As your instructor, I retain the right to make changes based on the timeline
of the class, feedback from learners and/or logistical issues and will inform you as soon as a
change is made.
Grading rubric: For each topic, the mastery of standards noted above will be the basis for
grading. Opportunities to master these standards will be in the form of daily work (individually
or in groups), concept checks (quizzes), and unit tests and projects.
Grading Scale:
Percentage Grade
90-100 A
80-89 B
70-79 C
60-69 D
0-59 |
More About
This Textbook
Overview
College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an often surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.
Editorial Reviews
Booknews
An introductory text for students majoring in mathematics or for education majors seeking teacher certification in secondary school mathematics. For students who are education majors, material develops mathematical concepts along traditional lines and includes problems and examples from current secondary school texts. This second edition incorporates experiments with the software , adds new problems and a high school geometry review, and adds treatment of three-dimensional geometry. Kay is affiliated with the University of North Carolina-Asheville 1, 2013
Highly Recommended
I needed this book for a course while at school and it is very useful and easy to understand!
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Anonymous
Posted February 10, 2010
Falling apart
This books content is very useful and easy to understand. However, the book itself is falling apart on me and I have only opened it to do homework 3 times. There are already more then ten pages that have just fallen out because I simply had to open the book to look inside. Not happy with books condition and I bought it brand new...
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
INTEGRATED MATH
COURSE DESCRIPTION:
This course helps students develop mathematical skills that enable them to solve problems and use reason and logic in math courses. Integrated Math gives them an overview of the many mathematical disciplines; topics include number sense, operations, algebraic sense, introduction to probability, geometric figures, geometric movement, measurement, and a more in-depth look at probability (including permutations and combination). Content is expressed in everyday mathematical language and notations to help students learn to apply the skills in a variety of applications. Instruction is supplemented with self-check quizzes, audio tutorials, Web quests, and interactive games that engage students in the content they are learning.
COURSE OBJECTIVES:
Students will:
Perform computation by applying concepts of various number types, and check for reasonable results.
Evaluate and write algebraic expressions, single and multi-step equations, and inequalities
Graph lines and inequalities
Demonstrate an understanding of theoretical and experimental probability
Calculate permutations using the multiplication principle
Identify geometric fundamentals like lines, polygons and types of triangles as well as solve complex problems using geometric concepts
Demonstrate understanding of the metric and customary systems of measurement and conversion within the system. |
Mathematics
Mathematics is the foundation for many of the natural sciences and, as knowledge is expanded in these sciences, new demands are made on mathematics to provide ideas to be used in advancing the sciences. Older sciences such as physics, chemistry, and engineering depend on mathematics, as do a large number of new and sophisticated subjects. The student's career in mathematics might include college teaching and research, computers, statistics, and many others. |
Hi, can anyone please help me with my math homework? I am not quite good at math and would be grateful if you could explain how to solve integration by parts calculator problems. I also would like to find out if there is a good website which can help me prepare well for my upcoming math exam. Thank you!
I really don't know why God made algebra, but you will be happy to know that someone also came up with Algebrator! Yes, Algebrator is a software that can help you crack math problems which you never thought you would be able to. Not only does it provide a solution the problem, but it also gives a detailed description of how it got to that solution. All the Best!
I remember I faced similar problems with graphing circles, cramer's rule and rational inequalities. This Algebrator is rightly a great piece of math software program. This would simply give step by step solution to any algebra problem that I copied from workbook on clicking on Solve. I have been able to use the program through several Algebra 2, Algebra 1 and Remedial Algebra. I seriously recommend the program.
I remember having often faced difficulties with graphing function, adding numerators and factoring. A really great piece of algebra program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Algebra 2, Basic Math and Algebra 1. I greatly recommend the program. |
books.google.com - Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Third Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered... Concise Introduction to Pure Mathematics, Third Edition |
Courses
MAC 1105H - Honors College Algebra
This course is a study of the fundamental topics in advanced algebra with an emphasis on applications, the understanding of the function concept and manipulative skills. Major topics include operations on algebraic expressions and complex numbers; solving polynomial equations and inequalities, absolute value equations and inequalities and rational equations and inequalities, applications; functions; exponents and logarithms; graphs of polynomial, exponential and logarithmic functions and systems of equations and inequalities. The use of graphing calculators will be incorporated throughout the course. Honors level content including enhanced use of technology and critical thinking skills in application problems will be essential components of this course. This course partially satisfies the mathematics requirement of S.B.E. 6A-10.030.
Prerequisites: acceptance into Honors program and MAT 1033 with a grade of "C" or higher or sufficient score on placement test. Terms Offered: Fall, Spring, Summer |
nbsp Scientific calculators are used in secondary and higher education institutions in the United States and around the world, in addition to the workplace. The top calculators fulfill the user's needs and are..... Read more
About Scientific Calculator
A scientific calculator is like a glorified version of a basic one: It does everything and then some. If you need a calculator to do more than add, subtract, multiply, or divide, then you're going to need the next step up. Whereas mathematicians had to once use slide rules and tables for their calculations, a scientific calculator cuts down on work and time. These are often used in higher level math classes and used to solve complex scientific, engineering, or mathematic problems. Another advantage of scientific calculators is that they have the means to compute in fraction and decimal form. It can compute in scientific notation, floating point arithmetic, and logarithmic and exponential functions, and it also has designated keys for "pi" and "e." There are even scientific calculators available that can perform even more complex tasks including but not limited to Boolean math, complex numbers, fractions, statistics, probability, and equation solving. While scientific calculators are generally limited to one-line displays, they allow more digits to be displayed, and they often have abilities to express exponentials and roots. Scientific calculators are a requirement for most middle and lower high-school math classes; many students graduate to a graphing calculator as they progress. One main advantage of having a scientific calculator over a graphing one is that scientific calculators are allowed on standardized tests. Graphing calculators are just bought off the shelves or online anymore. There are smartphone and tablet applications that convert your device into a scientific calculator. So no matter where you buy yours, a scientific calculator is a good thing to have around. |
Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in scenes from popular movies and television. By incorporating John Hornsby's "Math Goes to Hollywood" approach into chapter openers, margin notes, examples, exercises, and resources, this text makes it easy to weave this engaging theme into your course.
The Twelfth Edition continues to deliver the superlative writing style, carefully developed examples, and extensive exercise sets that instructors have come to expect. MyMathLab continues to evolve with each new edition, offering expanded online exercise sets, improved instructor resources, and new section-level videos.
MyMathLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online.
About the Author
Charles Miller has taught at America River College for many years.
Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.
John Hornsby: When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across |
COURSE OBJECTIVES AND METHOD OF PRESENTATION: In this class, student will be able to perform arithmetic operations with real numbers, polynomials, rational expressions, and radicals; factoring polynomials; linear equations and inequalities in one and two variables; Systems of linear equations and inequalities in two unknowns; Application problems; Equations with rational expressions; Equations with radicals; Introduction to quadratic equations in one variable. Calculators are allowed in the classroom. To receive credit for this course, the student must PASS EACH TEST AND THE FINAL EXAM. Homework will be assigned and is due at the end of each chapter. Questions arising on the homework should be discussed at the beginning of the class. New material should be presented in a lecture format that contains a larger number of examples. In-class assignments can be given to allow the students to work in groups. Students should be highly encouraged to continue these groups outside of class lecture. For students in need of additional assistance outside of class lecture, they should go to the Math Lab where Math Assistants and Math tutors are available at no charge. Students should be highly encouraged to form the habit of using the Lab. EXAMS: There will be 6 in class exams worth 100 points each, and in class Final Exam with 150 points, and 50 points* for the homework and class participation. I will throw out the lowest in class exam score except the final exam in determing your course grade. The total point count will be 700 points. There will be absolutely no makeup exams given. If you miss an exam, you will receive a zero score. Also note that there will be a common final exam for all Math 31 students. Students caught cheating will be given a grade of zero for the exam and the incident reported to the Department Chairman's Office. GRADING CURVE: 90-100% A OOOO 80-89% B OOO 68-79% C OO 60-67% D O 0-59% F
RULES AND ATTENDANCE: Failure to turn in homework will result in lowering your grade. For the final grade homework and class participation will be deterministic for borderline cases. My exams are entirely based upon the lectures and materials presented in class. I regularly give out hints on exam questions and solve sample problems during my lectures. Therefore missing my lectures will put you at a disadvantage when it is time to take exams.
IMPORTANT NOTES: Please let me know if you decide to stop attending class. Do not automatically assume that I will drop you if you decide not to show up anymore. I may not drop a student especially if it is passed the midpoint of the course. It is better to get a "W" rather than to fail the class. It is your responsibility to be aware of college drop deadlines and regulations.
A SUGGESTED GUIDE TO STUDY FOR THIS CLASS: 1. Read your notes. Do the problems in your notes over and over again. Make sure you understand the content of your notes completely. 2. Study the corresponding sections in the text, by first; a) Carefully reading the sections, b) Creating a formula sheet, that includes all the theorems and formulas covered in the specific section, c) Doing the examples, and after all of the above, d) Do the exercises. 3. Randomly select problems from each section and solve them without your notes/text. 4. Put together a study group and regularly get together to do problems. (This step may be your ticket out of this class)
* The distribution of the 50 points will be completely based upon my judgment call. It will be directly related to the amount of participation, homework, group work, quizzes, and effort a student has put in this class may be part of the evaluation process. |
The Aftermath of Calculator Use in College Classrooms
13.11.2012
Students may rely on calculators to bypass a more holistic understanding of mathematics, says Pitt researcher
Anzeige
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center.
King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics |
With students beginning to attend classes across the nation, I wanted to focus the site towards some of the things they're going to be addressing. This latest page publicize some scripts that I wrote to help with polynomial arithmetic. Originally I wrote these as homework exercises for a class in programming, but I have found them useful ever since – both in teaching mathematics classes like college algebra, which spends a lot of attention on polynomials, and in my research life. Its funny (and sad) the number of simple errors that a person (mathematician or not) can make when performing simple arithmetic, so I found it very useful to have a calculator more advanced than the simple scientific calculators that are so easily available.
I'm not going to spend a lot of time discussing the importance of polynomials, or trying to justify their need. I will bring up some problems that I'd like to address in the future, that deal with polynomials. The first is finding the roots of the characteristic polynomial of a matrix. This is useful in research because these roots are the eigenvalues of the matrix and can give many properties of the matrix. There are also some data analysis tools like Singular Value Decomposition and Principal Component Analysis where I will probably build out from this initial set of instances.
The user interface for the scripts I've written generate two polynomials and ask the user what is to be done with those polynomials. The options are to add the two, subtract polynomial 2 from polynomial 1, multiply the two, divide polynomial 1 by polynomial 2, and divide polynomial 2 by polynomial 1. There is also the option to make the calculations more of a tutorial by showing the steps along the way. Users who want new problems can generate a new first or second polynomial and clear work.
For addition and subtraction, the program works by first ensuring that both polynomials have the same degree. This can be achieved by adding terms with zero coefficient to the lower degree polynomial. Once this has been accomplished, we simply add the terms that have the same exponent.
For multiplication, the program first builds a matrix A, where the element ai, i+j on row i and column i+j of the matrix A is achieved by multiplying the ith term of the first polynomial by the jth term of the second polynomial. If an was not given a value in the matrix, then we put a value of zero in that cell. Once this matrix is formed, we can sum the columns of the matrix to arrive at the final answer.
The division of two polynomials works first by dividing the first term of the numerator by the first term of the denominator. This answer is then multiplied by the denominator and subtracted from the numerator. Now, the first term in the numerator should cancel and we use the result as the numerator going froward. This process is repeated as long as the numerator's degree is still equal to or greater than the denominator's degree (hidden) Numbers Are Randomly Learning Problem, which asks the question "How can I improve a HMM so that it would be more likely to have generated the sequence O = o1, o2, …, oT?
The Baum-Welch algorithm answers this question using an Expectation-Maximization approach. It creates two auxiliary variables t(i) and t(i, j). The variable t(i) represents the probability of being in state i at time t, given the entire observation sequence. Likewise t(i, j) represents the joint probability of being in state i at time t and of being in state j at time t+1, given the entire observation sequence. They can be calculated by Decoding Problem, which asks the question "What is the most likely sequence of states that the HMM would go through to generate the sequence O = o1, o2, …, oT?
The Viterbi algorithm finds answers this question using Dynamic Programming. It creates an auxiliary variable t(i) which has the highest probability that the partial observation sequence o1, …, ot can have, given that the current state is i. This variable can be calculated by the following formula:
t(i) = maxq1, …, qt-1 p{q1, …, qt-1, qt = i, o1, …, ot | }.
1(j) = jbj(o1), for 1 j N.
Once we have calculated t(j) we also keep a pointer to the max state. We can then find the optimal path by looking at arg max 1 j NT(j) and then backtrack the sequence of states using the pointerM Randomly Likely
2) Smaller Numbers Are More Likely
How often does the casino change dice?
Which sides on
the loaded dice
are backwards algorithm is one such method (as is the forward algorithm). It creates an auxiliary variable t(i) which is the probability that the model has generated the partially observed sequence ot+1, …, oT, where 1 t T. This variable can be calculated by the following formula:
t(i) = j = 1 to N(t+1(j) * aij * bj(ot+1))
We also need that T(i) = 1, for 1 i N.
Once we have calculated the t(j) variables, we can solve the evaluation problem by p{O | } i = 1 to N1(i) forward algorithm is one such method. It creates an auxiliary variable t(i) which is the probability that the model has generated the partially observed sequence o1, …, ot, where 1 t T. This variable can be calculated by the following formula:
t+1(j) = bj(ot+1)i = 1 to N(t(i)aij), where 1 j N, 1 t T-1.
1(j) = jbj(o1), for 1 j N.
Once we have calculated the t(j) variables, we can solve the evaluation problem by p{O | } = i = 1 to NT(i)
Suppose I gave you some red fingerpaint and asked you to make all the colors you could from this paint. You'd probably come up with a diverse collection of pinks, reds and burgendys – going through the range of reds – but you would be unable to produce a color that does not depend solely on red, like purple.
If I were to ask you to produce purple, your reply may be something like "well, give me blue and I'll be able to color in purple". When we think in terms of colors, it is easy to understand the concept of the span of a set of colors. In this context, span refers to the set of colors we can create from our original colors.
Now, lets think in terms of numbers (actually vectors) instead of colors. If I gave you a similar task as above, but instead of the color red, I gave you the vector (1, 0, 0) and told you to see what other numbers you could get from this (by scalar multiplication and the addition of any two vectors already produced) then you would probably come back to me and show me how you could use the vector (1, 0, 0) to produce the entire real number line in that first dimension, but leaving the other coordinates at 0.
If (similar to the color example) I asked you to use the vector (1, 0, 0) to produce the vector (1, 1, 0), then you may reply with a similar statement as above: "you give me the vector (0, 1, 0) and I'll produce (1, 1, 0)". That's because the vectors (1, 0, 0) and (1, 1, 0) are linearly independent. This is a mathematical way of saying what we've already stated, that you cannot get one vector as a scalar multiple of the other vector for any real number scalar.
If two vectors are linearly independent then neither one belongs to the span of the other. Just as you cannot create blue from red, you cannot create red from blue. So this means that if I were to give you the colors red and blue, then the set of colors that you can create has increased from what you could create from either only red or only blue. Similarly, the vector sets {(1, 0, 0), (0, 1, 0)} spans more vectors than just {(1, 0, 0)} or {(0, 1, 0)}.
Lets to back to colors and think of the set {red, purple}. Here we can think of purple as a simple combination of red and blue (i.e. purple = red + blue). What happens if we mix red and purple? If we think of it in terms of an axis, the fact that purple contains red in it means that as we walk along the purple axis, we are walking along the red axis as well. If we considered the set {red, blue}, we see that this is not happening. As we change the amount of red in our color, the amount of blue is unaffected. Likewise, if we change the amount of blue, the amount of red is not affected. If we were to draw these axes, we could see that this happens because the colors red and blue are perpendicular (or orthogonal) to one another, while red and purple are not.
Replacing these colors with vectors again, we get the same thing. We have the option of using the vector set {(1, 0, 0), (1, 1, 0)} or {(1, 0, 0), (0, 1, 0)} as our axis and it is better to use the second set because the two vectors are not just independent of one another, but also are at a 90[degree] angle, or are orthogonal to one another.
When given a set of vectors (or a set of colors), an important problem is to determine the span of those vectors and to be able to produce an orthogonal set of vectors that spans that same space. The Gram-Schmidt process provides a procedure for producing these orthogonal vectors.
The way the procedure works is to build an orthogonal set of vectors from the original set by computing the projection of the current vector being worked on in terms of the previous vectors in the orthogonal set. This projection procedure is defined as proju(v) = (u, v / u, u)u. The formula for the ith vector of the Gram-Schmidt process is
I love to play with puzzles. When I was in grade school I would spend hours at a time figuring out ways to solve from things like Tetris, Mindsweeper, Solitare, and Freecell. Later I was introduced to puzzles involving numbers like Sudoku and Nonograms.
These puzzles are often interesting in part because there is generally a very large way that things can be arranged, but only a few of these arrangements are correct. Generally a person solving a puzzle will figure out certain things that must be true or cannot be true, which helps in solving the puzzle and reducing the number of possible cases. Initially, though, we are often left with a situation where we have a new puzzle and our only method is to keep trying every possible solution until we start to notice a pattern (or reach a solution).
For example, consider a Sudoku puzzle. We are given a partially filled in grid and our job is to fill in the remaining cells with the rules that every row, column and marked subgrid must have the numbers 1 – 9 exactly once. One initial attempt at solving such a puzzle could be to attempt to permute the string 1, 2, 3, 4, 5, 6, 7, 8, 9 until we find a solution that fits the first row, then do the same with the second row, and so on and so forth.
One immediate question is how many ways are there to permute the numbers 1, …, 9? We can answer this by realizing that each permutation is a new string. So for each string that we construct, we have 9 choices for the first element in the string. Then once that element has been chosen, we are not allowed for that element to appear anywhere else. So there are only 8 possible choices for what can go in the second string. Continuing this process, we see that the number of possible permutations we can construct from the string 1, …, 9 is
9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362880
This is a large number of possible strings to generate just to get one row of a Sudoku, so hopefully you'll be able to notice the pattern before going through this whole set (because once you've generated the first row you still have to do the other 8 rows).
Nonetheless because there is often great value that can be gained by knowing how to permute through all possible solutions, I have written three functions that help with this process: Next_Permutation, Previous_Permutation, and Random_Permutation.
Before I give these algorithms, I want to highlight two notations on ordering string. A string (a1, a2, …, an) is said to be in lexicographical order (or alphabetical order) if for each i [in] 1, …, n-1, ai [<=] ai+1. Likewise, a string is said to be in reverse lexicographical order if for each i [in] 1, …, n-1, ai [>=] ai+1.
Next Permutation
If the given string is not in reverse lexicographic order, then there exists two elements j1 and j2 such that j1 [<] j2 and aj1 [<] aj2.
1. The Next_Permutation algorithm first searches for the largest element j1 such that aj1 [<] aj1 + 1. Since we said the string is not in reverse lexicographic order, this j1 must exist.
2. Once this j1 is found, we search for the smallest element aj2 such that aj2 [>] aj1 lexicographic order (i.e. in order such that ai [>=] ai+1
If the given string is in reverse lexicographic order, then we simply reverse the string.
Previous Permutation
If the given string is not in lexicographic order, then there exists two elements j1 and j2 such that j1 [<] j2 and aj1 [>] aj2.
1. The Previous_Permutation algorithm first searches for the largest element j1 such that aj1 [>] aj1 + 1. Since we said the string is not in reverse lexicographic order, this j1 must exist.
2. Once this j1 is found, we search for the smallest element aj2 such that aj1 [>] aj2 reverse lexicographic order (i.e. in order such that ai [<=] ai+1
If the given string is in lexicographic order, then we simply reverse the string. |
ForBasic Properties and Definitions
Fundamental Definitions and Notation
Sets and Venn Diagrams
The Real Numbers
Simple and Compound Inequalities
Arithmetic with Real Numbers
Properties of Real Numbers
Recognizing Patterns
Equations and Inequalities in One Variable
Linear Equations in One Variable
Formulas
Applications
Linear Inequalities in One Variable
Equations with Absolute Value
Inequalities Involving Absolute Value
Equations and Inequalities in Two Variables
Paired Data and the Rectangular Coordinate System
The Slope of a Line
The Equation of a Line
Linear Inequalities in Two Variables
Introduction to Functions
Function Notation
Algebra and Composition
Variation
Systems of Linear Equations and Inequalities
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Applications of Linear Systems
Matrix Solutions to Linear Systems
Systems of Linear Inequalities
Exponents and Polynomials
Properties of Exponents
Polynomials, Sums, and Differences
Multiplication of Polynomials
The Greatest Common Factor and Factoring by Grouping
Factoring Trinomials
Special Factoring
Factoring: a General Review
Solving Equations by Factoring
Rational Expressions and Rational Functions
Basic Properties and Reducing to Lowest Terms
Division of Polynomials and Difference Quotients
Multiplication and Division of Rational Expressions
Addition and Subtraction of Rational Expressions
Complex Fractions
Equations and Graphs with Rational Expressions
Applications
Rational Exponents and Roots
Rational Exponents
More Expressions Involving Rational Exponents
Simplified Form for Radicals
Addition and Subtraction of Radical Expressions
Multiplication and Division of Radical Expressions
Equations with Radicals
Complex Numbers
Quadratic Functions
Completing the Square
The Quadratic Formula
Additional Items Involving Solutions to Equations
Equations Quadratic in Form
Graphing Parabolas
Quadratic Inequalities
Exponential and Logarithmic Functions
Exponential Functions
The Inverse of a Function
Logarithms are Exponents
Properties of Logarithms
Common Logarithms and Natural Logarithms
Exponential Equations and Change of Base
Conic Sections
The Circle
Ellipses and Hyperbolas
Second-Degree Inequalities and Nonlinear Systems |
Science Books
Algebra Workbook For Dummies
Problem topics can include improper numbers, grouping symbols, using proportions, rationalizing fractions, multiplying and factoring expressions, solving linear and quadratic equations, working with inequalities, and using formulas in story problemsThe Mathematics Of A Lampshade(June 7, 2001) — Try to solve the following maths problem: does x^3+y^2+1 produce the same form as x^3+3y^2+xy^2? For cubic equations, it's possible to solve this problem, but mathematicians found things more ... > read more |
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
Reviews:
"Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids."--MAA Online
"This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly."--J.T. Zerger, Choice
"Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant."--Mathematics Teacher
Endorsements:
"I used Adrian Banner's The Calculus Lifesaver as the sole textbook for an intensive, three-week summer Calculus I course for high-school students. I chose this book for several reasons, among them its conversational expository style, its wealth of worked-out examples, and its price. This book is designed to supplement any standard calculus textbook, thus my students will be able to use it again when they take later calculus courses. The students in my class came from diverse backgrounds, ranging from those who had already seen much of the material to others who were struggling with basic algebra. They all uniformly praised the book for being one of the clearest mathematics texts they have ever read, and because it reviews the required prerequisite material. The numerous worked-out examples are an ideal supplement to the lectures. The only difficulty in using this book as a primary text is the lack of additional exercises in the text. However, there are so many sites and sources for calculus problems that this was not a problem. I would definitely use this book again."--Steven J. Miller, Brown University |
ince polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.
Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another--without even realizing it |
0205795854
9780205795857
Elementary and Middle School Mathematics:Elementary and Middle School Mathematicsguides both new and experienced teachers through a basic understanding of mathematics and problem solving, and encourages them to think about their own perceptions and misconceptions about mathematics.
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Rent Elementary and Middle School Mathematics 3rd edition today, or search our site for John A. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson Education Canada. |
9780534948ane Trigonometry
This time-tested book develops students' problem-solving skills using a unique and accessible approach to trigonometry. Appropriate for a one-term course in trigonometry, this book introduces trigonometric functions early (in Chapter 2) with an emphasis on modern applications, including the graphing calculator. By providing a solid foundation in triangle trigonometry from the beginning, the authors help students make the natural transition to analytic trigonometry |
Announcements
The algebra 1/2 has online practice quiz and test questions and online video guides for helping with homework problems. To access either, start by going to
On the bottom right your will enter a web code that corresponds to a section of the book and either quiz & test practice questions or video guides.
To access quiz practice questions In the first box for the web code, type ata In the second box you will type a 4 digit number that matches a chapter and section of the book. The first 2 digits are the chapter number and the last 2 digits are the section number. For example; chapter 1, section 3 is 0103. You will see 5 questions that are multiple choice. After you select your answers, click on the "score my test" button. You will know which answers were correct and which ones were incorrect. You can try a new version of the quiz over and over again by clicking on the "try again" button.
To access test practice questions The web codes are similar, except the last 2 digits are always 52 For example, a test on chapter two is ata 0252. A test for chapter 6 is ata 0652. You will see 20 questions that are multiple choice. Click on "score my test" to see correct and incorrect answers. You can also try a new version of the test by clicking "try again"
To access video guides The format is the same as for quizzes, except that the first box needs to be age instead of ate. The second box is 4 digits just like for quizzes. The video guide for chapter 1 sections 5 is age 0105, the video guide for chapter 3 section 2 is age 0302. Some sections have more than one video. Once you select the video you want, a viewing window will open and the video will begin. |
Calculus with analytic geometry by Ron Larson(
Book
) 50
editions published
between
1979
and
2007
in
3
languages
and held by
1,131
libraries
worldwide
A textbook on analytic geometry and calculus.
Precalculus by Ron Larson(
Book
) 40
editions published
between
1985
and
2011
in
English
and held by
633
libraries
worldwide
Elementary statistics : picturing the world by Ron Larson(
Book
) 18
editions published
between
1999
and
2012
in
English
and held by
471
libraries
worldwide
[This text shows] how statistics is used to picture and describe the world has helped students learn about statistics and make informed decisions.-Pref.
College algebra by Ron Larson(
Book
) 24
editions published
between
1985
and
2011
in
English and Undetermined
and held by
466
libraries
worldwide
[This text focuses] on making the mathematics accessible, supporting student success, and offering instructors flexible teaching options.-A word from the authors.
Elementary linear algebra by Ron Larson(
Book
) 22
editions published
between
1988
and
2010
in
English and Spanish
and held by
373
libraries
worldwide
[This text] is designed for the introductory linear algebra course generally taken by sophomores and juniors majoring in engineering, computer science, mathematics, economics, statistics, science, or operations research. The primary prerequisite for this course is algebra.-Pref.
Algebra and trigonometry by Ron Larson(
Book
) 30
editions published
between
1985
and
2011
in
English and Undetermined
and held by
364
libraries
worldwide
A firm foundation in algebra is necessary for success in college-level mathematics courses. [The book] is designed to help students develop their proficiency in algebra, and so strength their understanding of the underlying concepts. Although the basic concepts of algebra are reviewed in the text, it is assumed that most students taking this course have completed two years of high school algebra. The text takes every opportunity to show how algebra is a modern modeling language for real-life problems -Pref.
Trigonometry by Ron Larson(
Book
) 23
editions published
between
1985
and
2011
in
English and Undetermined
and held by
330
libraries
worldwide
College algebra : concepts and models by Ron Larson(
Book
) 12
editions published
between
1992
and
2008
in
English
and held by
316
libraries
worldwide
[This text] provides a solid understanding of algebra, using modeling techniques and real-world data applications. [The text] enhances students' problem-solving skills and makes college algebra concepts more meaningful to students.-Back cover.
Calculus of a single variable by Ron Larson(
Book
) 20
editions published
between
1990
and
2010
in
English and Spanish
and held by
288
libraries
worldwide
This [text] provides a range of conceptual, technological, and creative tools that make it easier for instructors to teach and provide student with resources that help them more fully understand the rigors of Calculus.-Back cover.
Intermediate algebra by Ron Larson(
Book
) 17
editions published
between
1992
and
2010
in
English
and held by
262
libraries
worldwide
[In this text, the authors] provide students with a firm understanding of algebra and how it functions as a modern modeling language through applications, real data, and visualization. In [the text], emphasis is placed on helping students learn a variety of techniques - symbolic, numeric, and visual- for solving problems. Through the use of real-world applications nad real data, students are shown the relevance of algebra to the world around them.-Back cover.
Algebra 1(
Book
) 31
editions published
between
2001
and
2011
in
English
and held by
248
libraries
worldwide
The content of Algebra 1 is organized around families of functions, with special emphasis on linear and quadratic functions.
Elementary algebra by Ron Larson(
Book
) 13
editions published
between
1992
and
2011
in
English
and held by
241
libraries
worldwide
[This book] provides students with [an] understanding of algebra and how it functions as a modern modeling language. In this [book], emphasis is placed on helping students learn a variety of techniques - symbolic, numeric, and visual - for solving problems. Through the use of real-world applications and real data, students are shown the relevance of algebra to the world around them.-Back cover.
Algebra 2(
Book
) 27
editions published
between
2001
and
2011
in
English
and held by
209
libraries
worldwide
The content of [this book] is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical, and rational functions ... In addition to its algebra content, [it] includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry and trigonometry.-unp.
Precalculus with limits : a graphing approach by Ron Larson(
Book
) 17
editions published
between
1995
and
2012
in
English
and held by
198
libraries
worldwide
Throughout [this] text, [the authors] present solutions to many examples from multiple perspectives - algebraic, graphic, and numeric.-A word from the authors.
Intermediate algebra : graphs and functions by Ron Larson(
Book
) 14
editions published
between
1994
and
2003
in
English
and held by
179
libraries
worldwide
[The authors'] approach ... includes presenting solutions in selected examples from multiple perspectives - algebraic, graphical, and numerical. The side-by-side format allows students to see that a problem can be solved in more than one way and to compare the accuracy of the solution methods.-A word from the authors.
Calculus : early transcendental functions by Ron Larson(
Book
) 15
editions published
between
1995
and
2011
in
English
and held by
174
libraries
worldwide
This three-semester calculus textbook presents the principles and applications of calculus. Topics include: continuity and limits, differentiation and integration of algebraic and trigonometric functions, fundamental theorem of the calculus, applications of the derivative to curve sketching, rectilinear motion, maximum/minimum problems, and related rates, applications to the integral to problems of area, volume, arc length, and work. In addition to the beginning concepts of calculus this text also provides instruction in the differentiation and integration of transcendental functions, standard techniques of integration, curves in polar coordinates, and sequences and series, multivariable calculus, partial differentiation, two- and three dimensional vectors, Stokes and divergence theorems, and differential equations. |
This is the guide for students taking a first course in combinatorics at degree level. There are exercises at the end of each chapter, and the explanations are easy to follow. Offers both enumerative and mathematical proofs. A textbook to aid your course and very easy to comprehend idea's concerned with the subject of combinatorics. |
Course: Photography
Submitted by: Rob Wakeley, CATE Photography, Tulsa Public Schools
Project Name: Photography Company Startup
Project Description and Purpose: This project is geared toward providing the
student a basic understanding of both the photographic processes necessary to run a
photography firm, but also to better understand and maintain professional business
practices. This project will help the student realize the stringent demands of running a
financially successful photography firm.
Situation or Problem: Students will use mathematical skills in completing the tasks for
this assignment.
Performance Specifications:
Tulsa Public Schools Photography
Standard 2 Identify, plan, and prepare for a future career
2.3 Develop good work ethics and the skills necessary to become a viable
part of the community at large.
Standard 4 Demonstrate knowledge of skills in chosen area
4.4 Practice business and industrial team leader skills
Standard 5 Demonstrate appropriate workplace attitudes, ethics, and etiquette
5.1 Demonstrate how respect and positive attitude in classroom will
prepare students for workplace attitudes, ethics and etiquette.
Tulsa Public Schools Algebra
Standard 2 Relations and Functions
Instructions and Parameters: Students will divide into groups of two or three and will
become a theoretical photography company. Each group may create a company name
and logo (Warm up activity). In addition to a company name and logo, the teacher may
ask each group to have a small portfolio of images and resumes ready for the final
interview. Each photographic company will create a schedule of fees and pricing for the
various services that they provide. This schedule will contain a flat rate fee, as well as
several variable fees. These variable fees (such as costs for each photographers' time,
transportation, film, processing, printing, etc.) will be added to the flat rate to become an
algebraic equation. Each group will need to be able to explain their billing method or
equation to me, the customer. They will be expected to justify the hourly rates as well as
fees for lab and chemical use etc. The culmination of this project will be an interview
with each of the groups. Each group will be expected to have an industry standard
professional billing schedule.
Length of project (time allotted): Two class periods to a week.
Project Based Activity – Photography – Photography Company Startup - 1
GRADING RUBRIC:
100-90(A) = This group has a very professional looking billing schedule and each member of
the group is able to explain what each of the variables represents and how this operation is
carried out in the most professional and cost effective manner.
89-80(B) = This group has a billing schedule that is not industry standard professional, may
not be able to fully explain what each of their fees is and how it is necessary. (ex. A
customer might say, " Why do I have to pay for film development at a color lab? You're the
photographer?!")
79-70(C) = This group did not type the necessary billing schedule, does not seem prepared
to speak to a possible client, and is not able or willing to explain the billing process to said
client.
69-60(D) = This group did a minimal amount of presentation for this meeting, does not have
a written billing schedule, but is creating it "on the fly" for the customer, or may just be
disrespectful to the customer in some way.
59-0(F) = This group is not in any way prepared for the interview with potential client. They
seem unable to manage a small photography firm and would not be hired by the average
public.
Project Based Activity – Photography – Photography Company Startup |
The math wars of the 1990′s have quieted down and are almost a thing of the past.
With the release of their 2006 guidelines, the National Council for Teachers of Mathematics (NCTM) effectively ended 17 years of promoting 'reform math' programs and acknowledged the need for schools to return to more traditional math programs.
Teachers and Homeschool parents can now move on to the next question. Which traditional math curriculum is best? The correct answer depends largely on the needs and preferences of each teacher and student.
There are many traditional math programs to choose from. This provides a brief review of two of the most popular programs, Singapore Math and Saxon Math. These two curriculums have some things in common:
• Both are used in public schools, private schools and homeschools
• Both have clear track records of improving standardized test scores
• Both share the traditional math emphasis on math facts as the building blocks of all math concepts
• Both have proven to be effective with a wide range of students
They also have some important differences:
Cost Comparison -Saxon Math books are more expensive than Singapore Math books because Saxon has a lot more pages. Saxon student books are hard cover from 8th grade and up.
Saxon Emphasizes Practice – Saxon Math puts more emphasis on doing practice exercises while Singapore Math puts more emphasis on critically thinking through concepts. After concepts are introduced, Saxon moves immediately into practice exercises to help cement the concept in the student's mind. Saxon requires students to memorize formulas, achieve fluent recall of math facts and apply algorithms to solve problems.
Singapore Emphasizes Thinking – Singapore teachers spend more time helping students to think through and verbally discuss each component of the concept. Singapore Math avoids reliance on memorized formulas and algorithms so there is not as much emphasis on repetitive practice exercises. Instead, Singapore strives to give students an understanding of math concepts by walking students through each component of a problem, and then presenting them with the whole problem to solve. This way, students are trained to think actively as they work through each step of a problem instead of plugging the problem into a formula.
Saxon is More Structured – Saxon Math is more structured, making it easier for teachers and students to follow the road map. Each new concept is followed by practice exercises. Review questions are provided after every 10 lessons.
Singapore Requires More Teaching – Singapore Math is less structured, using an approach which is less familiar to anyone who learned math in the U.S. As a result, Singapore Math can be more challenging for U.S. teachers and students, especially older students who are already familiar with U.S. math programs. Singapore's approach puts more burden on teachers to:
• spend more time teaching new concepts, breaking the concepts into components to ensure students are understanding
• continually assess how well students are grasping concepts then provide additional assistance as needed
Singapore is More Focused – Saxon Math practice exercises blend previously covered concepts together with new concepts, forcing students to continually review previous concepts. The rationale is repetitive practice over time is necessary to grasp the concepts and to achieve quick and effortless recall of math facts. Singapore focuses on one concept at a time, seeking mastery of each concept before moving on to the next one. One of the reasons why the NCTM liked the Singapore curriculum is because it focuses only on a few key concepts for each school year. The NCTM recognized a key weakness with some U.S. programs is having too many objectives, making them incoherent and difficult for students to master anything.
Recommendations – For school teachers who are willing to try something new and put more effort into teaching, my recommendation is Singapore Math. Singapore students lead the world in math test scores and your students can do the same. For Homeschool parents who are pressed for time and need a program that allows students to work more independently, my recommendation is Saxon Math. Saxon also offers CD ROM teaching videos to enable students to work even more independently. Saxon is also a great choice for U.S. school teachers looking for a program with a more familiar approach. Saxon Math has proven success with a wide range of students, even turning struggling math students into math lovers!
You have some gaps in your understanding of Singapore Primary Math (SPM) , or you have not really explained it: 1. The SPM curriculum assumes that you drill your math facts elsewhere. You mentioned flash cards, but a combination of recitation, workbooks, and worksheets may be used. You can use any drugstore workbook. A "math facts" worksheet should be given at least 3 times a week. 2. In addition to the SPM textbook and workbook, you should be using *at least one* of the following: Extra Practice, Intensive Practice, Challenging Word Problems" (CWP). The average student should use Extra Practice. If he/she can just whip right through them, you switch to Intensive Practice. CWP is a wonderful supplement. 3. Unless the teacher is willing to learn in order to achieve a "profound understanding of fundamental mathematics" (See Liping Ma), Singapore Math might not help much. |
About the Course
MA101 is a new way for students to learn the algebra concepts they need to be successful in logical systems courses and other courses that require algebra as a skill for success. This course is structured but individually tailored. Students receive instruction from computer software called ALEKS and have access to one-on-one assistance during class. This is not an on-line course. Through an attendance policy, students will be required to attend class as scheduled. Success in this course is dependent upon students committing to attending every class meeting and spending at least 3 hours every week outside of class working on the material. Students must have access to a computer with internet access to fulfill the 'outside of class' requirements of the course. This can be done at home or in any of the University's open labs.
Costs and Materials
There is no paper textbook for this course, although an e-textbook is available. As part of the course fee, students will have an 18-week (for a fall or spring semester) subscription to ALEKS which they will use in class. Students will access ALEKS through the class website. Students will also be expected to keep a notebook of their work as they are guided through the topics by the software. This notebook will be graded.
How Students will be Assessed and Given Grades
Students enrolled in MA101 will work to master approximately 150 objectives. This material is divided into 10 units and there are deadlines for finishing each unit. Students may choose to work ahead, but the deadlines help to insure students stay on schedule to finish the course in the allotted time. The grade in the course is determined by the following: 30% Final exam (instructor generated test). 20% Midterm exam (instructor generated test). 10% Pencil and paper quizzes over 8 units (8 quizzes). 10% Notebooks (collected twice). 20% Two unit exams. 10% Completion of the ALEKS objectives.
Course grade is CR, F or X.
CR grade will be awarded for an overall percentage of 70% or above.
F grade will be awarded for an overall percentage less than 70%.
X grade will be awarded for students not taking the final exam.
NOTE: A grade of CR in MA101 does not get computed into the GPA, but a grade of F or X does.
Students enrolled in MA101 may and are encouraged to work ahead to complete the course early. When a student has notified the instructor that the course objectives have been completed, the instructor and student will work together to schedule the remaining quizzes in the course and a date for an early final exam. If the student passes all of the quizzes and gets at least a 70% on the final exam, the student's ALEKS subscription will be transferred to the MA102 course. No transfer in the Southeast enrollment will occur until the end of the semester. Students who 'transition' to MA102 will merge into the course at its current unit and not be required to start over from the beginning (since the first part of MA102 is a fast-paced review of MA101 content). The student must work on the MA102 course content, take the remaining MA102 exams and quizzes, and complete the MA102 final exam with a 70%. If the student meets these requirements, then the student's Southeast enrollment will be transferred from MA101 to MA102 and the student will receive a letter grade for MA102 on the transcript.
Students in MA102 will work to master approximately 265 objectives. The first part of the course content is a quick review of the MA101 material which prepares the students for more advanced objectives that are covered the second half of the semester. Mastery of course objectives will be determined by written quizzes, notebooks, a midterm exam, two unit exams, completion of ALEKS objectives, and a final exam as indicated below. MA102 students have the option to work ahead to finish the course early.
Overall percentage will be determined as follows:
30% Final exam (instructor generated test).
20% Unit exams
20% Midterm exam (instructor generated test).
10% Completion of ALEKS objectives
10% Pencil and paper quizzes over Intermediate Objectives (8 quizzes)
10% Notebooks (collected twice)
Final letter grade will be determined as follows:
A = overall percentage of 90.0% or above.
B = overall percentage above 80.0% but less than 90%.
C = overall percentage above 70.0% but less than 80%.
D = overall percentage above 60.0% but less than 70%.
F = overall percentage less than 60%.
X grade will be awarded for students not taking the final exam.
How to Determine the Pre-Requisite for Logical Systems
Students who pass MA102 – Intermediate Algebra with a grade of 'C' or higher have the prerequisite for any logical systems course. Students who are currently enrolled in MA101 and are on track to complete both MA101 and MA102 by the end of a semester may have difficulty enrolling in a logical systems course. Students should contact the Department of Mathematics Administrative Assistant at (573) 651-2164 for enrollment assistance.
Frequently Asked Questions About MA101/102
Does this course count for credit? Both MA101 and MA102 count as three hours of elective credit. Students who complete MA101 early and transition to MA102 will only receive 3 hours of credit for MA102.
What about GPA? The grade for MA101 will be either CR or F. A grade of CR does not impact the student's GPA, but a grade of F does. MA102 receives a letter grade and it will be computed into the student's GPA.
Will all students need both MA101 and MA102? All students start with MA101. Those students who have a good grasp on the content will be able to finish the MA101 content by the middle of the semester and transition to MA102, completing all of the content in one semester. The content was divided into two courses to allow students, who need extra time to master the content, two semesters to accomplish this.
What if the student doesn't master all of the objectives in MA102? Students enrolled in MA102 must receive a grade of C (70% - 79.9%) or higher to progress to a Logical Systems course. If the student receives a D or F, they will need to repeat the course.
I'm still not sure whether to recommend to my advisees enrolled in MA101, who indicate they plan to finish both courses in one semester, which course to take next: MA102 or a logical systems course. Is there any other information I can use to make a good recommendation? Students will receive a midterm grade for MA101 and MA102. Advisors will be forwarded a midterm report from the MA101/102 instructors.
A CR grade at midterm in MA101 means the student is on track to receive a CR grade in the course. A grade of F typically means the student is not putting in enough time with the program to be making adequate progress.
Students in MA102 will receive a letter grade on the midterm report. A student with a grade of D or F needs to work to increase the amount of time and effort spent working on the ALEKS program.
The ALEKS program tells the student how many objectives she has mastered, how many hours have been logged in and which topics still need to be covered.
You may contact the instructor of the course and ask for his best judgment about placement for the next mathematics course.
You may contact the Department of Mathematics at (573) 651-2164 or Cheryl McAllister at (573) 651-2778 (cjmcallister@semo.edu) if you still have questions about MA101 and MA102. |
On the Shoulders of Giants : New Approaches to Numeracy - 90 edition
ISBN13:978-0309084499 ISBN10: 0309084490 This edition has also been released as: ISBN13: 978-0309042345 ISBN10: 0309042348
Summary: What mathematics should be learned by today's young people as well as tomorrow's workforce? On the Shoulders of Giants is a vision of richness of mathematics expressed in essays on change, dimension, quantity, shape, and uncertainty, each of which illustrate fundamental strands for school mathematics. These essays expand on the idea of mathematics as the language and science of patterns, allowing us to realize the importance of providing hands-on experience and the d...show moreevelopment of a curriculum that will enable students to apply their knowledge to diverse numerical |
PRECALCULUS HONORS SENIOR PROJECT DUE DATE: APRIL 27 / 28, 2009 Group Project (Each group may have three members or less.) You may choose one of these topics for your project.
a. Designing and Constructing a vending machine
This project must have the following components to complete the tasks for it.
- State the name of the vending machine and the functions of the machine.
- Design of the machine - blue print of the machine ; it doesn't have
to be in blue ink. You may draw with pencil or use computer graphic
tools. If you use computer graphic, you will gain more points for the
project.
- You should specify how the machine dispenses items.
- The size of the machine shouldn't exceed 2ft X 2ft X 2ft.
- Explain why your machine is so special and unique.
- Write ideas, formula, geometric facts and principles, and any Mathematical components if any.
- you may choose your creative way to present the machine, for example, video clip, powerpoint slides, presentation board, etc.
- the machine should work as you designed.
- important: you may use battery power to make it work, but you are not allowed to use electricity for safety reasons.
- the project will be graded based on the rubrics in the Preston student handbook.
b. Designing and Constructing a cryptogram system (Making the codes and breaking the codes)
- you may use various resources and methods to make and to break code.
- your cryper machine or cryptogram should work. It means that it
should create codes and interpret the codes that are created by the
system into plain language that everybody can understand.
- you may create a cryptogram machine like German Enigma
As long as one finds where one stands,p90x cheap, one knows how to package oneself,p90x for sale, just as a commodity establishes its brand by the right packaging,ghd,Toy Companies Push High-Tech Robotic ToysThe 2006 holiday season is filled with robo-toys,ghd australia, in hopes to woo young consumers NEW YORK (AP) — If children didn't get their fill of high-tech toys during the 2005 holiday season,ghd hair straightener. |
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Usage ideas: Watch math skills improve as students work through activities that involve everyday activities such as comparison shopping, using coupons, buying in quantity, learning about budgets, withholding tax and so much more
Usage ideas: A variety of rules, theorems, and processes are presented with easy to understand examples, students will use the rules and theories in a variety of activities to instill a solid foundation of algebra |
BUS500A Intermediate Algebra
Course Description
An introduction to quantitative methods for business graduate students with no previous exposure to the subject, it covers topics including algebraic operations, equations, graphs and functions, exponential and logarithmic functions, and an introduction to linear programming. No credit is awarded.
Learning Outcomes
Perform basic operations on rational expressions.
Perform the basic operations on roots and radicals.
Solve quadratic equations by factoring, completing the square and by formula.
Plot the graph of a given equation.
Recognize the particular and special characteristics of linear, quadratic, logarithmic, exponential. |
Pages
November 5, 2012
Memorizing Rules
I don't like the idea of memorizing rules but Glenn Stevens of the PROMYS program talks about learning things by heart. The difference being if you learn something by heart you've tried so many examples that you learned the pattern, whereas memorizing is just being able to recite something without necessarily understanding. I thought my precalculus students had learned to shift and stretch functions by heart. Many of them probably have, it's certainly a topic they study in Algebra 1 and 2 plus they had to do a big summer project for me that involved 8 parent functions. But, two things happened today that made me wonder if there's a better way than learning "outside the function is vertical, inside is horizontal, multiplying stretches, adding shifts."
The first thing was a comment from a student after I gave back a test (which, by the way, no one studied for! They admit it at least, but apparently the juniors need to read the article on how to study math too.) There was a question asking students to compare y=sec(x) and y=sec(2x)-3. One student said to me "I feel like I just have to memorize all these parts that don't make sense." At which point I thought "Um, yes, but also no" We have done a lot of examples, made connections and they had use of a graphing calculator to answer that question so it wasn't just about memorizing. But it was also concerning that this student hadn't figured the role of each piece out yet since we've been talking about them ad nauseum.
Then I went to a class this evening at the EDC and the awesome Bowen Kerins shared an insight about shifting and stretching functions. First: the whole "inside the function is backwards" doesn't sit well with him or with students (or with me) and, all of these rules are null when you get to something like a circle where there is no "inside the function." Instead, he suggests using a change of variable to get back to the parent function. The strategy of chunking is useful all over the place, and by the time students get to calculus, u substitution will seem obvious. So here's how it works:
y=(x-5)2 - 7
y+7=(x-5)2
N=M2
Make a table for M, N (so much easier since the vertex is at 0,0).
Then, use these linear transformations to get back to x, y.
M=x-5 x=M+5 (Shift right 5)
N=y+7 y=N-7 (Shift down 7)
To find the point you plot, use a fancy tool some call a pointer finger: cover the M and N, plot the x and y. The shifts are right there in the linear transformations you did, and they always work, no inside, outside, intuitive, counterintuitive or solving to find the vertex. It makes sense! Now if only I'd known this before all this work on shifting and stretching.
And, it works for any type of function, let's try a sine wave:
y=sin(πx+π)+4
y - 4=sin(πx+π)
N=sin(M)
Even though the period of this function is 2 and the usual suspects for x values will give ugly y values, the usual suspects work perfectly for M and N.
M=πx+π x=(M-π)/π (Shift left π, shrink/change the period by dividing by π)
N=y - 4 y=N+4 (Shift up 4)
My students always struggle with picking the "right" x and y values to get the real shape of the graph, including the maximum and minimum. With this method there's no need to figure out good x values to choose, they just need to know the parent function well enough and learn that one set of "good x values."
P.S. I left for school at 7 am, ran a club from 2-3 and was in class from 4-8, 45 minutes away. Over twelve hours out of the house and I still blogged! I didn't proofread, but I shared an idea. I will fill in the table and maybe another example tomorrow.
1 comment:
First, congrats on the still blogging! As far as the method goes, it looks very similar to the I/O diagrams that I use in my teaching... for instance, let's say we have y=2sin(4x+8)-3. (Um, I'm going to work in degrees because I don't have a pi key.)
Now simply grab a lot of key points on the original function (in this case sine, but could be a parabola or root or whatever), and follow the arrows to figure out where it maps. If you're tracking an arrow backward, use the inverse operation. So...
Period of 90 comes right out. Nice thing about it is you don't need to worry about factoring out the "4" first, it kind of takes care of itself in the order you're doing the operations. (If you do factor it, divide first, then subtract 2.)
The main difference I see is that with the M, N you're isolating for the function on one side first, and thus in both cases using inverse operations. Which may make more sense when you have the circle or something, I'd have to think about it. |
Part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, PRECALCULUS: A GRAPHING APPROACH, 5/e, is an ideal student and instructor resource for courses that require the ...
Now in its eighth edition, this book masterfully integrates skills, concepts, and activities to motivate learning. It emphasizes the relevance of mathematics to help readers learn the importance of ... |
Course in Combinatorics
9780521422604
ISBN:
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Publisher: Cambridge University Press
Summary: This major textbook, a product of many years' teaching, will appeal to all teachers of combinatorics who appreciate the breadth and depth of the subject. The authors exploit the fact that combinatorics requires comparatively little technical background to provide not only a standard introduction but also a view of some contemporary problems. All of the 36 chapters are in bite-size portions; they cover a given topic i...n reasonable depth and are supplemented by exercises, some with solutions, and references. To avoid an ad hoc appearance, the authors have concentrated on the central themes of designs, graphs and codes.
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Resources
Maple T.A. is an easy-to-use web-based system for creating tests and assignments, and automatically assessing student responses and performance. Maple T.A. provides everything you would expect in an assessment system plus features designed specifically for technical courses involving mathematics, making it ideal for science, technology, engineering, mathematics (STEM), or any course that requires mathematics.
During this webinar, you will have the opportunity to see how Maple T.A. works from both the instructor and student view point, and see how features such as conventional mathematical notation in questions and responses, intelligent evaluation of responses for mathematical equivalence, and extensive mathematical and visualization tools provide instructors the ideal testing and assessment environment for technical courses. Along the way, you will have the opportunity to see the new features in Maple T.A. 8, including the new highly secure Proctored Browser to discourage cheating and adaptive questions to deepen student understanding within the testing environment.
Presenter:
Carl Hickman, Maple T.A. Developer Dr. Hickman received a Ph.D. degree in Mathematics from Dalhousie University in Halifax, Canada. He has taught at the university level and his research has focused on the interplay between graph theory and algebra. Carl is currently a developer on the Maple T.A. team.
View Recording Fill out the form below to view the webinar "Introduction to Maple T.A. 8".
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Algebra
The Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of ...Show synopsisThe Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do.Hide synopsis
Description:New. 0131467662 Purchased as new and in great condition. We...New. 0131467662Reviews of Elementary Algebra
Received the book in a timely manner. It was in good condition. I don't think this will happen every time, so don't expect this, but it turned out to be an instructor's manual, which I didn't ask for, but I'm glad I got - the answers are right next to the problems; no flipping to the back to check |
Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as driving a car, climbing a mountain, and growing to full adult height |
Science at St. Andrews - Mathematics
Our
objective is to develop rigorous mathematical reasoning and critical thinking
skills, which enable students to solve real-life problems. Our students
learn by doing, and they, not the teacher, are the center of the classroom.
Through
our curriculum, we'll guide you through a degree program filled
with mathematical problem solving of increasing difficulty, thus
developing rigorous mathematical reasoning which will enable you
to move from the concrete to the abstract to the theoretical.
We
have made learning mathematics an active process, so our computer
classroom
may often look chaotic to an outsider. Most of our classes employ computer-interactive
texts through which you can explore and "discover" mathematics.
You will write to learn mathematics and learn to write mathematics. By
working often in small groups and giving both oral and written presentations,
you will learn to communicate mathematics. Through this process you will
internalize mathematics and develop rigorous thinking skills. |
MATH FOR WELDERS (P)
by MARION
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Description
Math for Welders is a combination text and workbook that provides numerous practical exercises designed to allow welding students to apply basic math skills. Major areas of instructional content include whole numbers, common fractions, decimal fractions, measurement, and percentage. Provides answers to odd-numbered practice problems in the back of the text. |
INTEGRATED ALGEBRA
COURSE SYLLABUS 2012-2013
Miss Prendergast
Course Objectives
This class is the first course in the iSchool Math Curriculum. It is intended for any student who has not
yet passed the Integrated Algebra Regents Exam with an 85. It covers a variety of algebra topics and prepares
students for the Integrated Algebra Regents Exam in June 2013 and to continue onto Geometry. Integrated
Algebra is a year-long course, and earns students two mathematics credits.
The math that is covered in this Algebra course is the foundation to upper mathematics studied in high
school and college. Algebra is also a very large part of the math that is tested on the PSAT and SAT as well as the
math that can be used in science classes and in everyday life. Algebra is often nicknamed 'The gateway to
success' referring to success in high school and beyond. Every student can be successful in this class with the
right amount of work and effort. So be prepared to be challenged, work hard, and have a little fun with math
along the way.
Mastery Requirements
Each quarter between 3 and 5 topics will be covered. Each topic will have a mini- quiz (covering the
basics of that skill) and a test (covering more advanced, abstract, or combined skills). A student can earn 1
Mastery Point (MP) on a mini quiz and up to 2 Mastery Points on a test for each skill being tested. The total
number of Mastery Points earned in a topic shows how well the student truly understood the material.
Mastery Points are the most important part of this Algebra class and it is necessary that every child and parent
to be aware of the student's mastery points in order to be successful and pass the course.
If a student does not earn a mastery point they have the opportunity to make it up by retaking the
assessment:
If a student misses a mastery point on a mini quiz they should review the skill on their
own, or come to office hours to review with Ms. P. When they are ready they should
attend office hours or make an appointment during lunch to re-take the mini quiz.
If a student misses a mastery point on a test they first should look through their test and
read any comments that Ms. P made while grading it. They should then re-work the
problems on a separate piece of paper and check their answers with the answer key
that will be posted on the class website. After they turn in their corrections to Ms. P.
they can set up a time to take a retake of the appropriate sections during office hours or
during a lunch appointment.
Students must earn at least 2/3 of the mastery points possible each quarter to pass the quarter and 2/3 of the
total points throughout the year to pass the course.
Expectations for Students:
Entering the classroom: Enter only when the door is open and a teacher is present.
Seating: Sit in your assigned seat, get out your out-of-class work, and begin the Get Ready.
Beginning of class: The Get Ready will only be 3-5 minutes with the timer on SMARTboard; you are
expected to complete the Get Ready within the time allowed.
Class Notes: You are expected to take class notes, as they help you process and learn new information.
In addition, class notes will be provided by the teacher and posted on the class website.
Out of Class Work: you should expect to have homework 4 times a week. All homework assignments
will be posted on the class website and must either be printed out or completed on loose leaf paper (if
you do HW on loose leaf, you must copy down the problems). Some homework assignments will
contain an online video portion. You are expected to watch the video and complete the assignment that
goes along with it before class.
Supplies: You must be prepared with the following materials. Random 'supply checks' will be done to
ensure that students have the appropriate materials.
o PENCIL and a PEN to Algebra class every day.
o Algebra Binder-This binder should be at least a 1.5 inch binder with loose leaf lined paper and
loose leaf graph paper. It is recommended that the binder also have pockets, or students insert
a 3 whole-punched folder into the binder.
o Laptops and calculators will be supplied to you for in-class work when needed.
Dismissal: Before dismissal, you will need to pickup and discard any trash, help return laptops,
calculators, and other materials. Remain at your desk until dismissed by your teacher and push in your
chair before you leave.
Class Website: you should be checking the class website daily. The class site has all HW assignments,
Review materials, Answer Keys, Links to videos, Course Calendar and video links. The site is
ischoolalgebra.wordpress.com
Respect/Behavior: You are young adults and will be treated as such. That means we expect you to be
respectful of your teacher and your fellow classmates, just as we will be respectful of you. We expect
you to come to class prepared to learn and put in your best effort.
Specific Classroom Guidelines
o Do not talk while another person in the room is speaking.
o Raise your hand in the air if you have something to share.
o No hats on your head- I will take them from you.
o Drinks with lids are okay- please don't leave your garbage in my room.
o You may chew gum but not chomp, blow bubbles, or snap it.
o If you don't do your homework- I will be disappointed in you.
o If you're nice, study, and do your homework you will get treats!
o Office hours are meant for YOU- please use them!!!
Grading
** All grades will be posted in Jupitergrades**
it is the student's and families responsibility to check jupitergrades at least once a week
Each student's grade is comprised of the following components:
Homework Assignments: Each quarter you Grade Percentages:
can expect to complete around 0 HW assignments.
Most HW assignments are worth 10 points. Late Mastery 60%
homework assignments can be turned in up to one Quizzes and Unit Tests 30%
week late for half credit. Exams 20%
Project 10%
Online Assignments: There will be Mastery Points Extra Credit
approximately 10-20 online assignments for
students to complete each quarter. These Work Habits 30%
assignments are comprised of a video and a short Home Work 20%
assignment. Each online assignment will have a code Online assignments 10%
that the students must write on their assignments.
This is put in place to show if the students have Contributing Factors 10%
watched the video or not. If a student does not Attendance/Lateness 5%
complete an online assignment they will be required Behavior/Participation 5%
to attend a detention that day to make it up.
Quizzes and Unit Tests: There will be short, mini quizzes that cover a single skill or topic. Unit tests
cover a set of connected topics. Expect questions on the mini quizzes to be straight forward computation while
the unit tests have higher level thinking questions that require students to connect many ideas or skills.
Mastery Points: As a student masters a topic they will earn 'Mastery Points'. Students can earn 1
Mastery Point by answering 2/3 of questions correctly on a mini quiz. Students can earn 2 mastery points on a
unit test by answering ¾ of questions correctly or 1 point by answering 2/3 of questions correctly. Therefore
one point equates to basic understanding, two points to sufficient understanding and three points to mastery.
Mastery points are the best way to tell if a student is understanding the material in class. A student must earn
at least 2/3 of the mastery points per quarter to pass the class.
Exams: At the end of each quarter there will be a cumulative exam. The exam consists of two parts; part
1 is a teacher made test covering all of the material from the trimester, part 2 is a Regents Exam. The exam is
used to assess students retention of knowledge and serve as a progress tracker towards passing the Regents
Exam in June.
Incomplete Grades
If a student does not pass a quarter they will receive a 55 on their report card. The student must then
see Miss P. to set up a plan to make up the missed work and mastery points from that quarter to raise their
grade. At the end of the school year, students who receive below a 65% will receive an incomplete. The student
will then have the opportunity to recover this credit through an optional summer program.
Student Absences
If a student is absent is their responsibility to come to office hours as soon as they return to school
to determine what must be done to catch up. A student will have 1 week to complete missing assignments due
to absences without penalty. After 1 week, the student will have 1 additional week to complete the work for
Late credit. After two weeks no assignments will be accepted.
Completion of the Course
This course is meant to prepare students for the Integrated Algebra Regents in June 2013. All
New York State students must pass (earn a 65 or higher) this test to graduate high school. In order for students
to pass this class they must pass the Algebra Regents with at least a 75 and earn at least 2/3 of the mastery
points possible throughout the year. After a student successfully completes Integrated Algebra at the iSchool
they will be promoted to Geometry the next school year.
Resources
Students should be checking the class website daily: ischoolalgebra.wordpress.com
Students should get in the habit of checking iSchool email DAILY.
Students should check the course website daily, as assignments and resources will be posted.
Additional help is available during Office Hours (Monday, Tuesday, Thursday from 3:20 – 4pm) or by
appointment in room 404.
If you have additional concerns please e-mail me at sprendergast@mail.nycischool.org
I have read this document, understand the course I am I have read this document, understand the course my
taking and what is expected of me. student is enrolled in and what is expected of them.
(student signature) (parent signature)
Together, as a family, we went to the class website, looked around and watched today's assigned video.
Video Code:__________________________ Student's Initials:_______ Parent Initials: |
This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a...
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This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a theorem of geometry. There are 9 chapters, each 13 minutes long. The book contains a total of 117 minutes of video, but can also be read as an ordinary textbook.The film can be enjoyed by anyone, provided the chapters are well-chosen. There are 9 chapters, each 13 minutes long. Chapters 3-4, 5-6 and 7-8 are double chapters, but apart from that, they are more or less independent of each other.
Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino,...
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Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two and four year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.
Book description: This is a text on elementary multivariable calculus, designed for students who have completed courses in...
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Book description: This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.
This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to...
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This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to read on their own to refresh or clarify what they learned in class. This text is designed for use with the "Advanced Algebra II: Homework and Activities" ( and the "Advanced Algebra II: Teacher's Guide" ( collections to make up the entire course.
OCW is pleased to make this textbook available online. Published in 1991 and still in print from Wellesley-Cambridge Press,...
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OCW is pleased to make this textbook available online. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.
Elementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is...
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Elementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
The materials here form a textbook for a course in mathematical probability and statistics for computer science students.״Why...
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The materials here form a textbook for a course in mathematical probability and statistics for computer science students.״Why is this course different from all other courses?״ * Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc. * The R statistical/data manipulation language is used throughout. Since this is a computer science audience, a greater sophitication in programming can be assumed. It is recommended that my R tutorial, R for Programmers, be used as a supplement. * Throughout the units, mathematical theory and applications are interwoven, with a strong emphasis on modeling: What do probabilistic models really mean, in real-life terms? How does one choose a model? How do we assess the practical usefulness of models? * There is considerable discussion of the intuition involving probabilistic concepts. However, all models and so on are described precisely in terms of random variables and distributions.For topical coverage, see the book's detailed table of contents. |
Algebra and Trigonometry - 01 edition
ISBN13:978-0534434120 ISBN10: 0534434126 This edition has also been released as: ISBN13: 978-0534380298 ISBN10: 0534380298
Summary: James Stewart, the author of the worldwide best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. Algebra and Trigonometry was designed specifically to help readers learn to think mathematically an...show mored to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, College Algebra, Third Edition, and Precalculus, Third EditionNo comments from the seller
$2.95 +$3.99 s/h
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Savannah Goodwill Savannah, GA
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Functions, Data, and Models by Sheldon P. Gordon & Florence S. Gordon
This is a college algebra-level textbook that is written to provide the kind of mathematical knowledge and experience that students will need for courses in other fields such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The book focuses on fundamental mathematical concepts and realistic problem-solving via mathematical modeling rather than the development of algebraic skills. Functions, Data and Models presents college algebra in a way that differs from almost all college algebra books available today. The authors teach something new rather than covering the same ground as high school courses. By changing the content of the course, the authors are able to give students an introduction to data analysis and mathematical modeling that even students with limited algebraic skills can handle. The book contains rich exercises, many of which use real data. Also included are thought experiments or what if questions that are meant to stretch the student's mathematical thinking. Contents: 1. Data Everywhere; 2. Functions Everywhere; ;3. Linear Functions; 4. More About Linear Functions; 5. Families of Nonlinear functions; 6. Polynomial Functions; 7. Extended Families of Functions; 8. Modeling Periodic Phenomena. Appendics: Absolute Values; Factorial Notation n!; Summation Notation; Statistical Calculations on TI Calulators; Statistical Calculations using Excel; Algebra of Linear Functions; Solving Equations Graphically; Zoom-and-Trace; Linear Regression on TI Calculators; Linear Regression in Excel; Solving Systems of Linear Equations Algebraically; Curve Fitting in Excel; Symmetry; Arithmetic of Complex Numbers; 2009 World Population Data. |
Deped Fourth Year High School Course Syllabus Math
Anchor Bay High School Course Syllabus. educators and technical experts. The academy's curriculum meets national standards and provides classroom materials that ensure students master the fundamentals of the
Course Curriculum Map Mendota High School Course Syllabus. geometry. Euclidean geometry is the structuring of a mathematical system involving the physical world in which we live. Students All student handbook policies will be followed. You need to be in class practicing and strengthening your skills. Prentice Hall Mathematics. Geometry. Copyright 2007. Online Resources:
HIGH SCHOOL COURSE SYLLABUS PSYCHOLOGY 260110. Course Description Psychology is a half credit course where students satisfy the half credit requirement for Students will gain an understanding of individual development as it pertains to mental Glencoe/McGraw-Hill, 2001 (Tremper HS)
Mendota High School Course Syllabus Algebra II Standards. Extra help availability a. I am available You must practice it and practice it well, just as if you Quarter: 1. Text: Prentice Hall: Algebra 2. Topic/Timeline. Chapter and. Sections 5-6 Determine types of solutions of quadratic equations by
HIGH SCHOOL COURSE SYLLABUS WORLD HISTORY 230111. This course is a study of modern world history, including the foundation of Spielvogel, World History: Modern Times Glencoe, 2010. importance of learning about the development of human societies and connecting current events to topics of study. the final exam represent 20 percent of the final grade, but this single |
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Mathematics
This subject enables pupils to develop their understanding of Mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment. Pupils will strengthen their ability to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs. As part of the A Level course they will develop an understanding of progression and cohesion in Mathematics and how different areas of Mathematics may be connected.
Pupils are encouraged to recognise how a situation may be represented mathematically and understand the relationship between 'real world' problems and standard and other mathematical models. They will read and comprehend mathematical arguments concerning applications of Mathematics and acquire the skills needed to use technology such as calculators and computers effectively. The course will foster an awareness of the relevance of Mathematics to other fields of study, to the world of work and society in general.
Future directions
As well as being an essential prerequisite for a mathematics (or mathematics-related) degree, mathematics is of significant value in a huge number of careers such as: medicine, dentistry and veterinary science; engineering and science; business administration; computing and applications of ICT; architecture and design; accountancy, financial services and banking; economics; interpretation of statistics in politics and journalism; education and research. |
* Immediate and easy access to high-quality interactive content by integrating it seamlessly with the Student Book. * Multi-lingual glossary gives audio translations for common maths terms in five languages. * Allows you to personalise content by interacting directly with the text and saving your own annotations, enabling you to reapply your thinking the next time your deliver the lesson. * Facilitates classroom management by allowing the whole class to view items in the textbook together. * Prepares your students for exam success through integrated grade improvement tools. * Make Assessment for Learning an achievable reality by tracking the progress of your whole class and then planning the most effective intervention and remediation strategies |
Mathematics
Main Contents of the course:
This course is designed to take you from level 0 to level 2 and include the following topics:
► Counting
► Plus and Minus
► Working with numbers
► Times and Divide
► Shapes
► Measurement
► Handling Data
Course Requirements:
There are no requirements to start this course. You can start this course now. It is designed for absolute beginners. |
More About
This Textbook
Overview
Designed to enhance math skills of the reader in the field of drafting, this completely updated fourth edition of Practical Problems in Mathematics For Drafting and CAD presents a comprehensive overview of contemporary drafting problems, CAD drawings, and industry applications and practices. This text provides a variety of integrated math problems and CAD operations in order to facilitate critical thinking, problem solving, and basic mathematics literacy. Filled with real-world applications and designed to cover a range of skills and levels of difficulty, the fourth edition includes updated figures, illustrations, problem sets, examples, and solutions in order to give you the skills you need to succeed in the field of drafting.
Related Subjects
Meet the Author
Dr. John Larkin recently retired as Professor Emeritus of Technology Education from Central Connecticut State University, where he was an experienced drafting and CAD instructor. He is still active in numerous professional organizations. Dr. Larkin earned his doctorate from the University of Maryland.
Dr. Concetta Duval earned her doctorate from the University of Rochester, majoring in mathematics and mathematics education. She is currently a consultant, specializing in creating mathematics and science materials for K - 12 students and teachers and published by a variety of textbook and computer education companies. Before working as a consultant, Dr. Duval was employed as a chemical engineer, public high school math and science teacher, school administrator, and Director of Mathematics at four private companies. She is an active member of several professional |
Trigonometry
Course #: MA 133
Credits: 3
Class/Lab Hours: 3, 0
The purpose of this course is to introduce and study the properties of the trigonometric functions. This course is designed to persue many skills necessary for success in calculus and other advanced mathematics and science courses. Emphasis will be placed on understanding trigonometric functions in a unit circle and a right triangle, their graphs and inverses along with applications. Identities, solving equations, as well as spherical trigonometric form of a complex number will be taught. The course concludes with polar equations and their graphs. Prerequisite: MA 130 or high school equivalent. |
Saxon Advanced Math Homeschool Kit with Solutions Manual, 2nd Ed.
Prepare your students for future success in calculus, chemistry,
physics, and social sciences! The 125 incremental lessons provide
in-depth coverage of trigonometry, logarithms, analytic geometry, and
upper-level algebraic concepts. Includes continued practice of
intermediate algebraic concepts and trigonometry introduced in Algebra 2
and features new lessons on functions, matrices, statistics, and the
graphing calculator.
This kit includes the solution manual, which
features solutions to all textbook problem sets. Early solutions
contain every step, while later solutions omit the obvious steps. Final
answers are in bold type for accurate, efficient grading.
Saxon Advanced Mathematics Kit & DIVE CD-Rom, 2nd Edition
Get everything you need for a successful and pain-free year of learning
math! This kit includes Saxon's 2nd Edition Advanced Mathematics
textbook and tests/worksheets book & answer key, as well as the
DIVE Advanced Math CD-ROM. A balanced, integrated mathematics program
that has proven itself a leader in the math teaching field, Advanced
Math covers algebraic concepts, trigonometry, functions, matrices,
statistics, and the graphing calculatorSaxon Advanced Math, Solutions Manual
This solutions manual accompanies Saxon Math's Advanced Math Curriculum.
Make grading easy with solutions to all textbook problem sets. Early
solutions contain every step, and later solutions omit obvious steps;
final answers are given in bold type for accurate, efficient grading.
Paperback.
Switched-On Schoolhouse 2012 Grade 12 Math
Provide your students with a comprehensive mathematical education in an
engaging format. Mastery is developed through step-by-step instruction
on grade-appropriate concepts, helping to prepare students for
upper-level studies and further problem-solving development.
SOS 2012 System Requirements: Note: XP users MUST have Service Pack 3 Installed. Vista users MUST have Service Pack 1 installed prior to installation. Vista & Windows 7 Aero users are strongly recommended to meet the optimal performance requirements. Only English Language versions of Microsoft, Windows XP, Vista, and 7 are supported. Windows 8 is not supported at this time.
Switched-On Schoolhouse 2012 Trigonometry
Follow your child's interests, supplement your standard program, and dig
deeper into a specific area of study with Switched-On Schoolhouse
Electives! With a variety of subjects and grades available, SOS 2012
elective students will enjoy the change of pace and the chance to learn
more about topics they're interested in.
Get your student ready for
college-level math with Switched-On Schoolhouse Trigonometry. A prep
course designed for advanced math courses, this computer-based course
will cover trigonometry in clear, step-by-step lessons. Meant for
students who have passed Algebra II, topics taught include like-right
angle trigonometry, trigonometric identities, graphing, the laws of
sines and cosines, and polar coordinates through video clips, learning
games, and engaging animation. Quizzes and tests are included for
progress assessment. Easy for both parents and students to use, SOS
features automatic grading and lesson planning, a built-in calendar, and
message center! Algebra II is a prerequisite. 5 Units with Review and
Final Exam.
Home Study Kit--Calculus, Second Edition
Understanding the abstractions of calculus requires far more than
limited exposure. Through the 148 sequential lessons in this
comprehensive text, future mathematicians, scientists, and engineers
will incrementally build and reinforce their knowledge through
continual practice and review. Following a condensed summary of key
algebra, trigonometry, and analytic geometry topics, students explore
limits, functions, and the differentiation and integration of
variables. Includes test and answer key booklets. 758 pages, hardcover.
Saxon Calculus Kit & DIVE CD-ROM, 2nd Edition
Boost your students understanding of Saxon Calculus Kit with DIVE's
easy-to-understand lectures! Each lesson in Saxon Math's textbook is
taught step-by-step on a digital whiteboard, averaging about 10-15
minutes in length; and because each lesson is stored separately, you
can easily move about from lesson-to-lesson as well as maneuver within
the lesson you're watching. Taught from a Christian worldview, Dr.
David Shormann also provides a weekly syllabus to help students stay on
track with the lessons.
Saxon Physics Home Study Kit
Saxon
Physics home study kit contains the complete hardcover teacher text and
one paperback homeschool packet. Offering 100 physics lessons, tests,
answers, periodic table, charts, and more: all you need to teach a
complete physics course. Students starting this course will do well to
have completed Saxon Algebra II course, and will benefit even more if
they have completed at least half of Saxon Advanced Math course.
Saxon Physics, Solutions Manual
This manual contains solutions to every problem in the Physics textbook
by John Saxon. Early solutions of a problem of a particular type
contain every step. Later solutions omit steps considered unnecessary.
Key Curriculum
These workbooks can satisfy a variety of
needs for math. They can be used for remedial purposes, review or
challenging younger students. Instructions are clear, direct and
self-explanatory. Grades 4-12
Mathematical Quilts, Grades 7-11
Written by teachers with a love for quilting, this innovative
curriculum features 50 math activities based on beautiful, eye-catching
quilt designs. Your 12- to 18-year-olds will learn the Pythagorean
theorem, Fibonacci sequences, tessellations, tiling, and general
problem-solving techniques as they re-create quilts using colored
paper, computer drawing, or even needle and thread! Each section
includes math concepts, research projects, and Internet-based
activities. 184 pages, softcover.
Functional Melodies: Finding Mathematical Relationships in Music
Capitalize on your students' interest in music to deepen their
understanding of algebra and geometry. Engaging activities and an
easy-to-use music CD help pupils hear, visualize, perform, think,
graph, and write about musical relationships and the mathematics they
illustrate. Includes thorough teacher notes, black-line masters,
resource pages, and work sheets. Musical training not required! Grades
8 to 12. 170 perforated reproducible 3-hole punched pages, softcover.
Real-Life Math: Statistics
22
intriguing activities cover the basics of statistics, ways statistics
are used, how to determine when data changes are statistically
significant, and even how statistics are misused. Concepts are built
around a wide variety of real-life contexts - including sports,
nutrition, consumer science, television, and more, thereby adding
interest and relevance. Reproducible teachers book- Grades 9 - Adult. This may not cover 1 year evil'. |
Site Services
Introduction to the Math Readiness Course
Welcome to the electronic version of the Math Readiness
Course, MRC for short.
My name is Keith Taylor, a professor in the Department of Mathematics
and Statistics at the
University of Saskatchewan. I am the director of the MRC project, but many
others have contributed in a variety of ways, see
Credits and Awards.
In this course, we have collected together those topics from arithmetic,
algebra, geometry, and trigonometry that seem to be most frequently used in
university courses which have a high degree of mathematical content. Examples
of such quantitative programs are engineering, physics, chemistry, biology,
economics, business, computer science, statistics, and mathematics.
With mathematics, maybe more than any other subject,
the knowledge is
cumulative. For example, a
skill that was covered in grade 10 algebra may be exactly what
is needed to carry out an interest rate calculation in a
business course at university. Those students who retain the particular skill
and who are able to call on it whenever necessary may find the calculation,
and the whole course, "a snap". Those who cannot rely on the skill when the
need arises will be lost and confused. This same story is repeated in many
different classes.
Our Math Readiness Course is designed to help you refresh those skills. You
cannot expect miracles; mathematics is like gymnastics or playing the piano
in that doing it well requires serious
work and practice. To encourage you, we have provided interactive
tutorials for you to work through after each lesson and you will
occasionally be directed to enter a Virtual Mathematics Laboratory to carry
out experiments with important concepts. Moreover, your learning progress
will be monitored by quizzes.
We urge you to keep in touch with us. Please e-mail us (readin@math.usask.ca) with
your most perplexing questions, those which you cannot answer yourself after
a reasonable period of thought. You might like to check our FAQ (Frequently
Asked Questions) page; we will post answers to the most common questions
there. As well, you can and should consult with other students via our
discussion board.
We encourage your comments regarding this course. We hope you share
in our excitement about the possibilities for an electronic math course.
Did you know that the MRC is one of the very first internet mathematics
courses to be
offered by any university? We'd like to know what works, what doesn't, and
how you think we can improve the course. You can help us by taking a minute to fill out our survey form.
We wish you every success in your studies.
For those who are in Saskatoon, a "live" version of this course is offered
as a two week camp each summer. For more information,
you can e-mail me at
taylor@math.usask.ca or call me
at (306) 966-6092. |
Websites
Wolfram|Alpha Step-by-Step Math Problem Help
First check out this blog post for directions, then click on the link to Wolfram|...more 2/01/step-by-step-math/ How Stuff Works
Everything from auto, communication, computer, electronics to animals, geography, health and more! Online Calculators on Math.com
Basic and scientific calculators allow you to do basic as well as trigonometry, probability, and finance equations. ators/calculators.html What's That Stuff?
What's really in hair coloring, Silly Putty, Cheese Wiz, artificial snow, or self-tanners? C&EN presents a collection of articles that gives you a look at the chemistry behind a wide variety of everyday products. tuff.html Multimedia Tour of the Solar System
Easy to understand information about our solar system and beyond. Show all websites |
A First Course in Mathematical Model an introduction to the entire modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem solving process to enhance a student's problem solving capabilities. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving stude... MOREnts in the mathematical process as early as possible, beginning with short projects, the book facilitates their progressive development and confidence in mathematics and modeling. |
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overview - Mathematics For Class - IX
Mathematics is one of the most important subject which not only decides the careers of many a young students but also enhances their ability of analytical and rational thinking. It is a common belief that Mathematics is a difficult and dry subject, on the contrary, if it is presented in a systematic and illustrative manner it becomes very easy to understand, even for a beginner.
This edition has been revised as per the CCE guidelines based on the latest syllabus prescribed by the CBSE. The entire syllabus has been divided into two terms. Term-1 consists of Chapters 1 to 12 and Term-2 consists of Chapters 13 to 25. Formative Assessments are given at the end of each chapter and Summative Assessments have been given at the end of each term. |
This book, 'Finding out', from the Shell centre offers a range of materials designed to support students as they pursue extended tasks relating to statistical investigations. The analysis of real data which is of some personal significance can be much more rewarding for students than the completion of exercises containing…
The teacher's guide from the Shell Centre which accompanies the series of modules to support school-based assessment is the main guide to the materials. It makes some suggestions as to how the materials might best be used. It was not intended that this guide should be read from cover to cover at the first attempt but was designed…
These two books from the Shell centre focus on the pure investigations. The pure investigation tasks are, perhaps, rather different from the other two main types of extended task, those of a practical nature and those of an applied nature, in the sense that they allow students to seek out the pattern and beauty of mathematics without…
These two books from the Shell Centre focus on applications. The tasks are intended to stimulate students' interest in, and understanding of, the world in which they live. As they pursue these tasks students will be involved in selecting materials and mathematics to use for their chosen task, checking they have sufficient information,…
These two books from the Shell Centre are part of the Extended Tasks for GCSE Mathematics support material produced for students as they pursued practical geometry tasks within any mathematics scheme. The practical geometry tasks were intended to stimulate students' interest in, and understanding of, the three-dimensional world…
Volume oneThis resource, published at a time when teachers had become aware of the tremendous need for motivational topics in mathematics, gives students an appreciation of, and insight into, mathematics and helps adopt an experimental attitude to the teaching and learning of the subject. The book contains ten units.
A Hint of Magic: explores…
This book followed the introduction of the Century Maths Scheme. It was published to give teachers and students the opportunity to choose an interesting context in which to use mathematics for GCSE coursework.
Students may have had a special interest in, say, photography, boats or farming, in which case they could choose accordingly.
There
Scheduling jobs in a fashion workshop is the context for this Nuffield exploration. There are six people in the workshop and a series of jobs to be completed in one day.
The key processes which developed include:
• Representing - identifying factors that affect decisions, producing a clear plan for the six people who contribute…
This Nuffield exploration is a simulation of a booking system for a small guesthouse. Students have to manage the bookings and, as far as possible, arrange to give people the accommodation they request.
The key processes in this exploration are :
• Representing - finding and using alternative ways to handle a large amount…
This Nuffield investigation involves determining the number of text messages sent if four people send texts to each other, and then extending this for different numbers of people.
• Key processes applicable to this activity are:
• Representing - choosing method of representation to show the texts sent and
choice…
In this Nuffield investigation students study paper sizes in the A and B international series, exploring relationships within each series and between the series.
The key processes are:
• Representing - identifying the mathematics involved in the task and developing appropriate representations.
• Analysing - working…
This Nuffield activity is set in the context of a park. Students determine where spies should sit in the park that has a square grid of benches, interspersed by bushes, so that they cannot see each other. Students also investigate how many different arrangements of spies are possible.
The key processes involved in this activity…
This Nuffield activity asks students to experiment with the placing and number of fire hydrants required in a city with square blocks that form a rectangular grid.
Key processes developed in this investigation are:
• Representing - diagrammatic representation and moving to more abstract mathematical methodology.
•…
In this Nuffield activity students investigate how different numbers of squares can be joined corner to corner and the effect their arrangement has on the area of the rectangle that encloses the squares.
The key processes developed in this activity are:
• Representing - determining which aspects to investigate and record,…
In this Nuffield investigation students explore limiting values of an iterative process, using arithmetic, algebra or spreadsheets. Students can move from identifying patterns to forming, verifying and proving conjectures.
The key processes developed in this activity include:
• Representing - moving from generation of…
This Cre8ate maths activity allows the opportunity to discuss the modelling function of mathematics. The tasks allow students to develop their own strategies and to consider the idea of an 'efficient' algorithm.
In addition, 'First fit and full bins' activity involves work on ratio and pie charts.
.
The…
Based on information and guides provided by the Department of Transport, this Cre8ate maths activity introduces the cost benefits of improving the aerodynamics of the cab section of a truck.
Mathematical connections involve using calculators and spreadsheets to work on conversions and percentages in the context of a complex multi-step…
…
…
This activity from Cre8ate maths investigates the lines of horizontal and vertical weakness in walls. Initially students are shown four walls and have to identify the lines of weakness in them, before finding the smallest rectangular solution which has no lines of weakness. Students should record their designs as they work and use…
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GAIM Activities are open-ended tasks where achievements in using and applying mathematics can be assessed alongside content. In the practical problems students apply mathematics to real-life situations.
GAIM provides teachers with 80 Activities (40 Investigations and 40 Practical Problems) as a resource for teaching and assessment.…
GAIM Activities are open-ended tasks where achievements in using and applying mathematics can be assessed alongside content. In the investigations students explore pure mathematics.
GAIM provides teachers with 80 Activities (40 Investigations and 40 Practical Problems) as a resource for teaching and assessment. These are open-ended… |
Elementary Algebra - 3rd edition
Summary: Elementary Algebra is a book for the student. The authors' goal is to help build students' confidence, their understanding and appreciation of math, and their basic skills by presenting an extremely user-friendly text that models a framework in which students can succeed. Unfortunately, students who place into developmental math courses often struggle with math anxiety due to bad experiences in past math courses. Developmental students often have never developed nor ...show moreapplied a study system in mathematics. To address these needs, the authors have framed three goals for Elementary Algebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm.The authors' writing style is extremely student-friendly. They talk to students in their own language and walk them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the "monkey-see, monkey-do" approach that some books take6.0792 +$3.99 s/h
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Introduction to Problem Solving Grades 3-5
9780325009704
ISBN:
0325009708
Edition: 2 Pub Date: 2007 Publisher: Heinemann
Summary: Susan O'Connell is the editor of Heinemann's Math Process Standards series, as well as the author its volumes Introduction to Problem Solving (grades PreK - 2, 3 - 5, and 6 - 8) and Introduction to Communication (grades PreK - 2, 3 - 5, and 6 - 8). She also wrote the popular Now I Get It (Heinemann, 2005). Sue has a varied background, including years as a classroom teacher, a school-based instructional specialist, a ...testing coordinator, a talented-and-gifted teacher, a district school-improvement specialist, and a university professional-development schools coordinator. Currently she is a project consultant for a federal teacher-quality grant in the College of Education at the University of Maryland. Additionally, she is an educational consultant, conducts mathematics seminars for teachers throughout the country, and a Heinemann Professional Development Provider.
O'Connell, Susan is the author of Introduction to Problem Solving Grades 3-5, published 2007 under ISBN 9780325009704 and 0325009708. Sixteen Introduction to Problem Solving Grades 3-5 textbooks are available for sale on ValoreBooks.com, six used from the cheapest price of $44.55, or buy new starting at $35.09.[read more]
Ships From:Secaucus, NJShipping:StandardComments: NCTM's Process Standards were designed to support teaching that helps children develop independe... [more] NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore eac... [less]
NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process S [more]
NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore eac...[less] |
MTH102 Linear Mathematics 1
Duration :1 semester
39 lectures
Aim:
This course, which is mostly about algebraic ideas and complements the
material in Calculus 1, introduces and
develops concepts (including complex numbers and the algebra
of polynomials) necessary for a first course in linear algebra. Linear
algebra is a subject that grew out of the business of solving
systems of linear equations, and then found many other applications in all
branches of mathematics and in every science. As this is a first course in
linear algebra, our goal is the elementary theory of matrices and
determinants, and their application to solving
systems of equations, leaving the abstract theory of linear spaces to Linear
Mathematics 2. Along the way we include some of the mathematical areas where
linear structure emerges as the common feature, to give motivation and
illustration for
the theory.
Course Outline:
COMPLEX NUMBERS AND POLYNOMIALS. Definition and manipulation of complex
numbers; statement of the fundamental theorem of algebra and complete
factorization over $\Bbb C$; complex conjugate roots of real polynomials;
solution of quadratic and cubic polynomials by radicals.
VECTORS. Real and complex vectors in $n$ dimensions, addition and scalar
multiplication, linear independence, bases for $\Bbb R^n$ and
$\Bbb C^n$, the
scalar
product of two vectors; geometrical representation of real vectors and the
scalar product in $\Bbb R^2$ and
$\Bbb R^3$, the vector product and
triple
products in $\Bbb R^3$ , simple applications to geometry and
mechanics.
9
THEORY OF MATRICES, DETERMINANTS AND LINEAR ALGEBRA. Matrices and systems of
linear equations: formulation of systems of linear equations (over
$\Bbb R$ and
$\Bbb C$) in terms of matrices and vectors; matrix algebra, row
and column operations, applications to linear equations, the rank of a
matrix, the inverse of a matrix. Determinants and properties of
determinants. |
Yes, the Mathematics Department operates a Math Study Area which is open to students wanting extra help in mathematics. This extra help opportunity is available to students on a drop in basis whenever they have a free in their schedule. A mathematics teacher will be there to provide this help.
For students without frees, there is one Mathematics teacher available to give extra help at lunch in the library on days 1, 2, and 6 in our 8 day cycle (as of 1st semester in 2009-2010). These days may change in 2nd semester.
Should extra help be needed beyond these times, the student should see their teacher to arrange a mutually convenient time.
All students have been advised of this above information!
Some may need occasional reminding!
How much homework is assigned in Math?
All students in Academic Math courses are expected to complete approximately 30 minutes of homework between classes. Assignments will also be given and are to be completed by the assigned dates.
All students in advanced or IB courses will be expected to complete more than 30 minutes of homework between classes. Assignments will also be given and are to be completed by the assigned dates.
Homework is an important component of these courses so that students have the opportunity to independently practice and develop their skills and understanding in Mathematics. In class students are usually working with other students. By doing homework, students will find out what they can do on their own and identify any areas which need further explanation. This independent study should allow students to build confidence in their abilities!
Not Taking Math 10 Academic Until Second Semester?
The Park View Mathematics Department has put together a unit with grade nine material to help you review some basic concepts. Copies can be picked up during Parent Teacher interviews or from any math teacher. |
If you are an instructor and looking for solutions, please email me, d.barber@cs.ucl.ac.uk (you will need to provide me with evidence of your academic appointment and that you're using the book on a course). I'll then email you the password to the solutions which also contains the matlab solution files and Latex slides for presentations. |
Finding the Missing Link: Building an Integrated System in Mathematica (Spanish)
Frank ScherbaumChannels: Spanish
See how Diego Oviedo-Salcedo, a PhD candidate at the University of Illinois at Urbana-Champaign, uses Mathematica to investigate river-aquifer interactions as part of his civil engineering research. Includes Spanish audio
This video features Dana Vazzana, an associate professor of mathematics at Truman State University, who explains why integrating Mathematica into her university-level math classes helps students gain deeper understanding of concepts and insights into real-world applications. Includes Spanish audio. Includes Spanish audio.
Mathematica integrates important high-performance computing (HPC) technologies in a single seamless system, so you don't have to choose between speed and accuracy. This screencast gives an overview of how to access Mathematica's HPC capabilities. Includes Spanish audio.
Research analyst Joel Drouillard uses Mathematica's data handling for an accurate picture and deeper understanding of how clients search for fixed income securities. He explains the advantages in this video. Includes Spanish audio.
Mathematica's graphical and visualization capabilities play a crucial role in developing models to analyze and test the safety of new flight operations. Mike Ulrey, a member of the advanced air traffic management team at Boeing, explains why in this video. Includes Spanish audio.
This video features George Woodrow, a research specialist at Quest Diagnostics, who shares how he uses Mathematica for developing process-control algorithms in a clinical laboratory, exploring their performance, and communicating functionality. Includes Spanish audio.
Seth Chandler of the University of Houston Law Center analyzes catastrophe models and other data in Mathematica to show how the insurance market can better handle paying for hurricane damages. Includes Spanish audio.
The mathematics department at Roanoke College makes a firm commitment to incorporating Mathematica throughout its curriculum. Associate professor Chris Lee explains the advantages. Includes Spanish audio.
This tutorial screencast encourages users to work along in Mathematica 7 as they learn the basics to create their first notebook, calculations, visualizations, and interactive examples. Includes Spanish audio.This screencast helps you get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions. Includes Spanish audio.
Mathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom. Includes Spanish audio. |
Learners follow step-by-step instructions for dividing algebraic fractions. They begin by reducing the fractions to their...
see more
Learners follow step-by-step instructions for dividing algebraic fractions. They begin by reducing the fractions to their simplest form. Immediate feedback is provided. This activity has audio content.
This site contains tutorial lessons for College Algebra, Intermediate Algebra, Beginning Algebra, and Math for the Sciences....
see more
This site contains tutorial lessons for College Algebra, Intermediate Algebra, Beginning Algebra, and Math for the Sciences. Each lesson contains explanations, examples, and videos. There are also practice problems with complete solutions.
ClassZone is a place to log into McDougal Littell's Mathematics, World Languages, Science, Social Studies, and Language Arts...
see more
ClassZone is a place to log into McDougal Littell's Mathematics, World Languages, Science, Social Studies, and Language Arts textbooks and more. There are video lectures, powerpoint presentations, self assessments, vocabulary flashcards, games, & more. |
1996 Paperback A few creases to the spine end of the book. A few small marks to the page edges. Slight Shelfwear. Good condition book. Good condition is defined as: a copy that ...has Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a clear, straightforward approach, the book develops ideas in a logical, coherent way, allowing you progressively to build a thorough working understanding of the subject.
Topics are organized into three parts: algebra, calculus, differential equations, and expansions in series; vectors, determinants, and matrices; and numerical analysis and statistics. The extensive use of examples illustrates every important concept and method in the text, and demonstrates the application of mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter are an essential element of the development of the subject, and have been designed to give you a full understanding of the material in the text.
Students often feel unprepared and ill-equipped to cope with the mathematical content of their chemistry courses. The Chemistry Maths Book is the perfect guide through this challenging, yet essential, |
Customers who bought this book also bought:
Our Editors also recommend:
Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Point Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.
Introduction to Knot Theory by Richard H. Crowell, Ralph H. Fox Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition.
Undergraduate Topology by Robert H. Kasriel This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 |
b. Rearrangement of jumbled words and expressions in meaningful sentences
MATHS
1. Trigonometrical Identities
2. Similar Triangles
3. Quadratic Equations
4. Circle [Tangent]
5. Heights and Distance
6. Area and Perimeter of Circle
7. Volume and Surface Area of 3D Solids
8. Statistics
9. Probability
10. Application of Algebraic Identity
11. Test of Reasoning
SCIENCE
BIOLOGY
1. Heredity and Evolution
2. Reproduction
3. Management of Natural Resources
4. Our Environment
5. Life Processes
6. Control and Co-ordination in Plants and Animals
CHEMISTRY
1. Periodic Table and Properties
2. Types of Chemical Reactions
3. Acids, Bases and Salts
4. Carbon and Compounds
5. Metals, Non-metals and their Compounds
6. Mole Concept
PHYSICS
Electric Current:
Potential Difference, Ohm's Law, Resistance, Resistivity, Factors on which the resistance of a conductor depends, Parallel and Series Combination of resistance and its application in daily life. Heating effects of electric current and its applications in daily life, Electric Power, Relation between P, V, I and R.
Magnetic Effects Current:
Magnetic fields, field lines, field due to current carrying conductor, current carrying coil or solenoid. Force on current carrying conductor, Fleming, left hand rule. Electromagnetic induction. Induced potential difference, Induced current, Fleming right hand rule, direct current, Alterning current frequency of A.C, Advantages of A.C over D.C. Domestic electric circuits.
Law of refraction, refractive index, spherical lens, Images formed by lens, lens formula, magnification. Power of a lens, human eye, defects of vision and their corrections, applications of mirrors and lenses.
Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life. |
Developmental Mathematics/TASP its reputation for accurate content and a unified system of instruction, the Seventh Edition of Bittinger/Beecher's Developmental Mathematics paperback integrates success-building study tools, innovative pedagogy, and a comprehensive instructional support package with time-tested teaching techniques. Whole Numbers, Fraction Notation, Decimal Notation, Percent Notation, Data, Graphs, and Statistics, Geometry, Introduction to Real Numbers and Algebraic Expressions, Solving Equations and Inequalities, Graphs of Linear Equations, Polyno... MOREmials: Operations, Polynomials: Factoring, Rational Expressions and Equations, Systems of Equations, Radical Expressions and Equations, Quadratic Equations For all readers interested in Developmental Mathematics. Developmental Mathematics, Fifth Edition, is a comprehensive text intended for use by students needing a review in arithmetic skills before covering introductory algebra topics. The text begins with a review of arithmetic concepts, and then develops statistics, geometry, and introductory algebra. It is designed for use in combined (two-semester) courses and to prepare students for statewide or local mathematics proficiency exams. All the math objectives on the Texas Academic Skills Program test (TASP) are incorporated in this edition, as are the majority of topics on other state tests. The TASP version of the text will have a sample of the TASP test. As part of MathMax: The Bittinger System of Instruction, it is accompanied by a comprehensive and well-integrated supplements package to provide maximum support for both instructor and student. MathMax: The Bittinger System of Instruction offers a completely integrated package of four-color text, interactive tutorial software, multimedia CD-ROM, and videos that guide students successfully through developmental math with learning objectives keyed to the exposition, exercises, and examples, a hallmark five-step problem-solving process, and modern, interesting applications and problems. |
Find a Sea Cliff GeometryThinking of finite functions in infinite terms might feel counterintuitive, but it is the way we can find exact instantaneous figures for a constantly changing world. The first time a student sees a derivative, it generally either makes perfect sense, or none at all. Let Michal work through the process to reach that "aha" moment with your child |
ALEX Lesson Plans
Title: Systems of Equations: What Method Do You Prefer?
Description:
TheStandard(s): [MA2010] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE82 (9-12) 27 ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama) (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The
Thinkfinity Lesson Plans
Title: Escape from the Tomb
Description:
In ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama)
Subject: Mathematics Title: Escape from the Tomb Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Supply and Demand
Description:
This
Standard(s): [T1] ECN (12) 3: Analyze graphs to determine changes in supply and demand and their effect on equilibrium price and quality. Supply and Demand Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Pick's Theorem as a System of Equations
Description:
In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem.
Standard(s): Title: Pick's Theorem as a System of Equations Description: In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: There Has to Be a System for This Sweet Problem
Description:
In this Illuminations lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution1 (9-12) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [A-REI7]
Subject: Mathematics Title: There Has to Be a System for This Sweet Problem Description: In this Illuminations lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Investigating Pick's Theorem
Description:
In
Standard(s): Investigating Pick's Theorem Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
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