CME PROJECT Math with a Twist! - … PROJECT. Math with a Twist! Math That’s Focused ... If you add more than two numbers, the order in which you group them does not matter. 3

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CME PROJECT

Integrated 1 • Integrated 1I • Integrated 1II

C O M M O N C O R E

Math with a

Twist!

CME PROJECT

FYI on CME, EDC, and NSF

CME Project, or the Center for Mathematics Education Project, was developed at Education Development Center, Inc.

(or EDC). Led by the renowned mathematician and scholar Dr. Al Cuoco, CME Project is supported by the National Science

Foundation (NSF) and informed by extensive mathematics research, decades of classroom studies, and ongoing field tests.

Pearson, the largest educational publisher in the world, is the exclusive publisher of CME Project.

Somewhere between an instructional approach that is traditional and one

that is progressive lies another way to teach math—CME Project ©2013.

This four-year, NSF-funded, comprehensive program offers you a Common

Core curriculum organized around the structure of Integrated I, Integrated II,

and Integrated III. The program meets the dual goals of mathematical rigor

and accessibility for all students through innovative, research-based instruction

and a curriculum that is designed around problem-based, student-centered

tasks. It’s math with a twist!

CME PROJECT

Math with a Twist!

Math That’s Focused . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4CME Project follows a traditional course structure

with a progressive, student centered approach.

Math That’s Balanced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4CME Project blends investigation with methods, skills, and calculation.

Math That’s Habit-Forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6CME Project develops mathematical habits of mind

and Standards for Mathematical Practices

Math That’s Thoughtful and Rigorous . . . . . . . . . . . . . . . . . . . 8CME Project promotes deep understanding of math concepts

by focusing on connected ideas.

2

8

5

4

1

1 Arithmetic to Algebra

2 Expressions and Equations

3 Graphs

4 Lines

5 Exponents and Functions

6 Statistics and Fitting Lines

7 Introduction to Geometry

8 Congruence and Transformations

1 Real Numbers

2 Polynomials

3 Quadratics and Complex Numbers

4 Functions

5 Applications of Probability

6 Congruence and Proof

7 Similarity

8 Circles

9 Using Similarity

10 Analytic Geometry

1 Functions and Polynomials

2 Sequence and Series

3 Statistical Inference

4 Trigonometry

5 Analyzing Trigonometric Functions

6 Complex Numbers and Polynomials

7 Polynomial and Rational Functions

8 Exponential and Logarithmic Functions

9 Optimization and Geometric Modeling

Most teachers choose between traditional math programs that follow an accepted course

structure and progressive, student-centered approaches. The twist is that CME Project does

both. This NSF-funded program takes a balanced approach to teaching mathematics and is built

for the Integrated Pathway of the Common Core State Standards.

Math That’sFocused

2

Each course is organized by chapters, with each chapter providing focused, in-depth instruction on a core mathematical topic. Each chapter includes three or four investigations that open with exploration, progress to formalization, and close with reflection.

Investigation A Investigation B Investigation CChapter Project, Review, and Test

Getting Started Lessons Mathematical Reflection

Chapter

CME Project Structure

3

Getting Started

When you understand how a number trick works, you can have fun writing and performing your own. In this lesson, you will learn from Spiro the Spectacular and Maya the Magnifi cent, who specialize in number tricks.

1. Here is one of Spiro the Spectacular’s favorite number tricks.

• Choose a number.

• Add 6.

• Multiply by 3.

• Subtract 10.

• Multiply by 2.

• Add 50.

• Divide by 6.

Spiro says, “Now, tell me the result.”Georgia replies, “17.”Spiro exclaims, “Your starting number was 6!”Georgia replies, “You’re right! How did you know that?”a. How did Spiro fi nd Georgia’s number?

b. If Georgia’s ending number is 13, what was her starting number?

c. If Georgia’s ending number is 6, what was her starting number?

2. Maya the Magnifi cent also does number tricks. Here is one of her favorites.

• Choose a number.

• Multiply by 3.

• Subtract 4.

• Multiply by 2.

• Add 20.

• Divide by 6.

• Subtract your starting number.

a. What is the trick?

b. Explain why the trick always works.

3. a. Make up your own number trick.

b. Find a partner. Perform your number tricks for each other. Try different starting numbers until you fi nd how your partner’s trick works.

2.1

Habits of Mind Habits of Mind Look for a pattern.Try it with numbers! Pick a number and see what you get. Do this a few times.

2.1 Getting Started 91

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Math That’sBalanced

You don’t have to choose between a student-centered program or a traditional program.

The twist is that CME Project utilizes the best parts of each type of program and presents a

uniquely balanced math program. Students begin by experimenting and previewing the math

before they formalize it through traditional instructional elements.

Time to ExploreEach Investigation begins with a

problem set that activates prior

knowledge, gives access to the concept,

and lets students explore ideas before

instruction.

In-Class Experiment

110 Chapter 2 Expressions and Equations

2.5 Rephrasing the Basic Rules

You have applied the basic rules of arithmetic to expressions. Now you can use these expressions to write the basic rules concisely.

Match each statement in List 1 with a statement in List 2 that has the same meaning.

List 1 Basic Rules of Arithmetic Using Words1. The order in which you add numbers in a sum does not affect the result.

2. If you add more than two numbers, the order in which you group them does not matter.

3. The order in which you multiply two numbers in a product does not affect the result.

4. If you multiply more than two numbers, the order in which you group them does not matter.

5. Multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results.

6. When you add 0 to any number, the result is the number itself.

7. When you multiply 1 by any number, the result is the number itself.

8. When you add any number to its opposite, the result is 0. When the sum of two numbers is 0, each number is the opposite of the other.

9. When you multiply a nonzero number by its reciprocal, the result is 1. When the product of two numbers is 1, each number is the reciprocal of the other number.

List 2 Basic Rules of Arithmetic Using Symbols A. For any three numbers a, b, and c, a 1 (b 1 c) = (a 1 b) 1 c.

B. For any two numbers a and b, ab = ba.

C. For any three numbers a, b, and c, a(b 1 c) = ab 1 ac.

D. For any number a, a 1 0 = a.

E. For any three numbers a, b, and c, a(bc) = (ab)c.

F. For any two nonzero numbers a and b, a ? 1a = 1, and if ab = 1, b = 1

a .

G. For any two numbers a and b, a 1 b = b 1 a.

H. For any number a, a ? 1 = a = 1 ? a.

I. For any two numbers a and b, a 1 (2a) = 0, and if a 1 b = 0, b = 2a.

0088_cme09a1_se_02a.indd 110 4/24/08 12:15:32 PM

Experience the MathIn-Class Experiments engage students

and encourage in-depth exploration.

These activities also provide an ideal

informal assessment opportunity.

Example


In Lesson 1.5, you learned the basic rules of arithmetic. You can apply the rules to expressions and numbers. For instance, you can change the order of numbers and variables in a sum.

x 1 7 = 7 1 xYou can regroup the numbers and variables in a sum.

(a 1 8) 1 z = a 1 (8 1 z)

You can use the Distributive Property.

2(x 1 3) = 2 ? (x 1 3) = 2 ? x 1 2 ? 3 = 2x 1 6

The identities are still true.

x ? 1 = x and x 1 0 = x

You can also use the Distributive Property backward. For instance, you can simplify 2x 1 3x using the Distributive Property.

2x 1 3x = 2 ? x 1 3 ? x = (2 1 3)x = 5x

The expression 2x 1 3x has two terms connected by the plus (1) sign. A term is an expression that only uses multiplication or division. When the variables are the same in both terms, you call them like terms. Grouping

parts of an expression such as 2 1 3 is called combining like terms.

Problem Find a simpler way to write 3x 1 7y 1 8 1 4x 1 2y 2 10.

Solution Rewrite the expression. Group the x terms together and the y terms together. Then group the numbers together.

3x 1 4x 1 7y 1 2y 1 8 2 10

Combine the like terms. Group the 3x and the 4x together to get 7x by using the Distributive Property backward.

3x 1 4x = (3 1 4)x = x ? 7 = 7x

You can combine the y terms the same way. There are two terms with y, 7y and 2y, that you can combine.

7y 1 2y = (7 1 2) ? y = 9y

You can transform the expression this way.

3x 1 7y 1 8 1 4x 1 2y 2 10 = 3x 1 4x 1 7y 1 2y 1 8 2 10 = 7x 1 9y 1 (22) = 7x 1 9y 2 2

You can simplify this expression using the any-order, any-grouping properties, but be careful of subtraction!

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Work It OutWorked-out examples, definitions,

and theorems formalize concepts, so

students can apply their skills and

knowledge to solve new math problems.

4

Math That’s Habit-Forming

Problem solving is an essential part of any math curriculum. The twist is that CME Project

fosters good Habits of Mind so students can solve problems that don’t always appear in

textbooks. The emphasis on mathematical habits of mind, the core organizing principle of the

program, is aimed at helping students develop precisely the kind of mathematical practices

described in the Common Core State Standards.

MATHEMATICAL PRACTICES MATHEMATICAL HABITS OF MIND

MP1 Make sense of problems andpersevere in solving them

• Performing thought experiments

• Expecting math to make sense

MP2 Reason abstractly and quantitativelyFinding and explaining patterns

• Creating and using representations

• Generalizing from examples

• “Delayed evaluation” – Seeking form in calculations

• Purposefully transforming and interpreting expressions

• Seeking and specifying structural similarities

MP3 Construct viable argumentsand critique the reasoning of others

• Expecting math to make sense

• Extending operations to preserve rules for calculating

MP4 Model with mathematics Creatingand using representations

• “Delayed evaluation” – Seeking form in calculations

MP5 Use appropriate tools strategicallySeeking and specifying structural similarities


MP6 Attend to precision Expectingmathematics to make sense

• Seeking and expressing regularity in repeated calculations

MP7 Look for and make use of structure • “Delayed evaluation” – Seeking form in calculations

• “Chunking” (changing variables in order to hide complexity)

• Reasoning about and picturing calculations and operations

• Extending operations to preserve rules for calculating


• Seeking and specifying structural similarities

MP8 Look for and express regularityin repeated reasoning

• Seeking and expressing regularity in repeated calculations

• Generalizing from examples

• Finding and explaining patterns


5

Developing Habits of Mind


Step 2 Make a list that reverses the order of the first list and shows how to undo each operation.

• Add 14.

• Divide by 3.

Here is a machine diagram showing these steps.

x 37

Step 3 Start with the output. Perform each step on the list of reverse steps to find the value of the input variable x. Start with output 37.

37 1 14 = 51 Add 14 to the output 37.

51 4 3 = 17 Divide by 3 to find the value of the input variable, x.

x = 17

Establish a process. Here is a method for performing good backtracking steps.

Step 1 Make a list of steps, in order, that show how to get from the input variable to the output. You can build a machine diagram or a fl owchart to show your steps.

Step 2 Make a list that reverses the order of the steps in the fi rst list and shows how to undo each operation.

Step 3 Start with the output. Perform each step on the list of reverse steps to fi nd the value of the input variable.

2. Derman solves an equation such as 3x 2 14 = 37 by making a guess, checking it, and then making a better guess until he fi nds the solution. Compare Derman’s method with the backtracking method. What advantages does backtracking have? Are there any disadvantages to backtracking?

Why is it important to keep track of the steps?

This process is the same as following 37 through the machine diagram above.

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Example 2

Example 1

Problem Why is the value 3 a solution to the equation x 1 4 = 7?

Solution The value 3 is a solution to the equation x 1 4 = 7, since 3 makes the equation true.

x 1 4 = 7

3 1 4 = 7 ytrue

Any other value of x makes the equation false, so 3 is the only solution.

Some equations have more than one solution. For instance, x2 = 9 has two solutions, 3 and 23, since both numbers make it true. You use the term solution set for the collection of all solutions of an equation. The expression x2 = 9 has the solution set 523, 36.When an equation is always false, it has no solutions. For instance, the equation x = x 1 1 has no solutions, so its solution set is the empty set, or the null set.

To fi nd out if a number is a solution to an equation, just test it out! A variable such as x represents a number, so every time you see an x in an equation, replace it with the same number. If you get a true statement, that number is a solution.

Problem Is the number 7 a solution to the equation 3x 2 28 = 46?

Solution No. Replace x with 7 and find whether the result is true.

3x 2 28 = 46

3 ? 7 2 28 0 46

27 2 46 X false

4. Suppose you want to find the solution to 3x 2 28 = 46 by guessing. How can you do it?

5. Can you solve the equation 3x 2 28 = 46 by backtracking? Explain.

6. Suppose you want to find both solutions to x2 2 x 2 2 = 0. How can you do this?

You can write the empty set as two braces with nothing inside { } or the null symbol Ø.

Habits of Mind Habits of Mind Represent x with a number. Try replacing x with a number different from 3. What is your result?

2.8 Solving Equations by Backtracking 127

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Math That’s Habit-Forming

See What DevelopsVisual reminders throughout the program emphasize

good habits related to process, visualization,

representation, patterns, and relationships.

Habits of MindMathematical habits of mind appear in every lesson

and emphasize the processes and proficiencies of the

Standards for Mathematical Practices.

(CONTINUED)

6

Minds in Action

In this lesson, you will solve a one-variable equation using two basic moves for solving equations.

episode 6

Tony and Sasha solve the equation 7x 2 8 = x 1 16.

Tony To solve this problem, I’d start by drawing a number line, and and then . . .

Sasha Don’t bother with all of that, Tony. I’ve got a shortcut.

Tony Show me.

Sasha Well, whenever I solve an equation, the solution ends up being x = some number. So, I make the equation look like that.

Tony How?

Sasha First I get rid of the x term on one side of the equation. To do that, I subtract x from each side of the equation.

7x 2 8 = x 1 162x 2x6x 2 8 = 16

See, no x term on the right. I’m almost done.

Tony This equation is like the ones we’ve solved before.

Sasha Exactly. Then, add 8 to each side.

6x 2 8 = 1 161 8 1 8

6x = 24

Now we have 6x = 24. Finally, I divide each side by 6 to get the answer.

6x6 =

246

x = 4

2.11 The Basic Moves for Solving Equations

2.11 The Basic Moves for Solving Equations 143

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Check Your UnderstandingCheck Your Understanding

1. Getting into a car involves these steps.

• Open the car door.

• Sit down.

• Close the car door.

• Buckle the seat belt.

Describe the steps you take in getting out of a car. How are they related to the steps involved in getting into a car?

2. Find a partner. Each person thinks of a number. Take your number and follow these steps.

• Add 6.

• Divide by 4.

• Multiply by 8.

• Add 7.

• Multiply by 10.

Take your partner’s result and fi nd the starting number. Describe your process.

3. Write each algebraic expression as a statement of one or more operations. For each operation that is reversible, describe the operation that reverses it.

a. n 1 13

b. b22

c. 3(5m 2 12)

d. 15m 2 36

4. Dana says, “I take a number, multiply it by 2, add 7, and then subtract 5. My fi nal result is 22.” What is Dana’s starting number?

5. Hideki says, “I take a number, multiply it by 12, and then subtract 9. My fi nal result is 25.” What is Hideki’s starting number?

Remember...Remember...You perform each step starting with the result that you got from the step before it.

Describe, in words, what each of these expressions tells you to do with the number.

2.7 Reversing Operations 123

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Minds in ActionSample dialogs promote conversations about the

math students are learning. Students who can talk

about the math are more likely to understand it.

Practice Makes PermanentStudents are given daily opportunities to practice and

use the habits of mind. This consistent format keeps

the habits in sight and always in mind.

" Behind the CME Project is the belief that every course or academic experience in high school should be used as an opportunity to help students develop good general habits of mind. . .. Students should be Pattern Sniffers, Experimenters, Describers, Tinkerers, Inventors, Visualizers, and Conjecturers."

— Al Cuoco CME Project Lead Author

7

Getting Started

You know the directions from your home to school. To go from school to your home, it may be possible to simply reverse the directions. Such a “backtracking” skill will be useful for solving equations.

Kelly gives directions for walking from Cambridge, Massachusetts, to the Thomas P. O’Neill Federal Building in Boston.

• Walk across the Longfellow Bridge from Cambridge to Boston on Cambridge Street. Stay on the right side of Cambridge Street to avoid the construction.

• When you reach Staniford Street, turn left. Walk down the hill. Staniford Street becomes Causeway Street. You should see the O’Neill Federal Building on your left—it’s gigantic! You can’t miss it.

When you arrive at the O’Neill Federal Building, you see Justin. He asks you for directions to return to Cambridge.

1. Work in a group. Write directions for Justin.

2. Compare the directions you write to Kelly’s directions. How do your directions differ from Kelly’s? How are your directions the same as Kelly’s?

3. Spiro the Spectacular asks you to choose a number, multiply it by 5, and then subtract 10. When you tell Spiro the ending number, which of the following methods can he use to fi nd your starting number?

a. Multiply the ending number by 5 and then subtract 10.

b. Divide the ending number by 5 and then subtract 10.

c. Divide the ending number by 5 and then add 10.

d. Add 10 to the ending number and then divide by 5.

e. Add 10 to the ending number, double it, and then divide by 10.

f. Drop the last digit of the ending number and then add 10.

g. Divide the ending number by 5 and then add 2.

4. Maya wants to be absolutely sure that she can undo any step, so that she can fi nd the starting number without guessing. For each step, describe how to undo it, or explain why you cannot undo it.

a. Add 5. b. Divide by 10. c. Multiply by 0.

d. Multiply by 3 and then subtract 28.

e. Find the sum of the digits of a number.

f. Subtract 11 from a number six times in a row.

5. Spiro tells you to start with the number 3 and then add 5 as many times as you want. You tell him your ending number. Spiro tells you how many times you added 5. Explain.

2.6

More than one of these methods will work. Find them all.


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On Your OwnOn Your Own

10. Solve each equation using backtracking.

a. 3a 1 11 = 29 b. 22(p 2 15) 1 5 = 215

11. Write About It You cannot solve the equation 3t 1 12 = 5t 1 6 by using backtracking. Explain why.

12. Take It Further Solve the equation 3t 1 12 = 5t 1 6. Explain your steps.

13. For each equation, determine whether r = 22 is a solution.

a. 6r 1 2 = 12 1 r b. 3r 1 2 1 10r = 7 1 7r 1 (217)

c. r 1 11 2 3r = 15 1 2r d. 7(r 1 2) 1 8 = 4r 1 16

14. For each equation, determine whether s = 43 is a solution.

a. 4s = s 1 4 b. 9s 2 2 = 5s 1 103

c. 5(s 2 1) 2 1 = 2s 2 23 d. 2(s 1 1) 1 5 = 7s 1 1

3

15. Colleen works on a number game. She says, “I’m thinking of a number. I do some things to it, and I end up with 27. The last step in my game is to add 27.”

What is Colleen’s ending number if she changes the last step of her game to each of the following?

a. add 8 b. multiply by 2 c. subtract 7

16. Here is an arrangement of two small squares and two rectangles that form a large square. Find an expression for the area of each of the four smaller regions. Find two expressions for the area of the large square.

Maintain Your SkillsMaintain Your Skills

17. For each equation, fi nd a value of x that makes the equation true.

a. 8 ? x = 1 b. 219 ? x = 1 c. 1113 ? x = 1

d. 1011 ? 11

13 ? x = 1 e. 57 ? 11

12 ? x = 1

ba

ba

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b

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b

a

b

ba

ba

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a

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Web Code: bde-0775

PHSchool.com

Go nlineVideo Tutor

0134_cme09a1_se_02c.indd 137 4/24/08 7:40:28 AM

Math That’sThoughtful and

RigorousDeep understanding of math helps students see underlying themes and connections.

The twist is that CME Project focuses students’ thinking on a smaller number of connected

ideas. Recurring themes, contexts, and methods give students solid grounding in mathematics,

so they become “power users” of math.

On Your OwnAmple practice blends conceptual mathematical

thinking with technical skills, so students develop

habits of mind and computational fluency.

For You to ExploreStudents learn math in a context that allows them to

think in non-mathematical terms first, building from

the concrete to the numerical.

8

Developing Habits of Mind

Focus on the Distributive Property

Learning to use the Distributive Property is especially important when solving equations. It helps you avoid losing a negative sign somewhere and fi nding an incorrect result.

1. What’s Wrong Here? Rebecca, Anna, and Jenna tried to solve the equation 40 2 4(x 1 3) = 7x 2 5. They got three different results.

Rebecca 40 2 4(x 1 3) = 7x 2 5

40 2 4x 1 12 = 7x 2 5 52 2 4x = 7x 2 5

52 2 4x 1 5 = 7x 2 5 1 5 57 2 4x = 7x

57 2 4x 1 4x = 7x 1 4x 57 = 11x5711 = x

Anna 40 2 4(x 1 3) = 7x 2 5

40 2 4x 1 3 = 7x 2 5 43 2 4x = 7x 2 5

39x = 7x 2 5 39x 2 7x = 7x 2 5 2 7x

32x = 25

x = 25

32

Jenna 40 2 4(x 1 3) = 7x 2 5 40 2 4x 2 12 = 7x 2 5

28 2 4x = 7x 2 5 28 2 4x 1 4x = 7x 2 5 1 4x

28 = 11x 2 5 28 1 5 = 11x 2 5 1 5

33 = 11x 3 = x

Who has the correct result? What mistakes did each of the others make?

Repeat a familiar process. In Investigation 1C, you used an expansion box for multiplying numbers. Recall that to multiply 327 ? 6, you made an expansion box similar to the one below.

6

300

1800

20

120

7

42

Then you added all the numbers inside the box to get the product.

2.13

2.13 Focus on the Distributive Property 153

0134_cme09a1_se_02c.indd 153 4/24/08 7:41:23 AM

Minds in Action

518 Chapter 6 Exponents and Radicals

Sasha We want Theorem 6.1 to hold true, right? So, we want A20B A25B = 2015.

2015 is just 25. So, we want A20B A25B = A25B.Tony We have no choice. Divide each side of this equation by 25, and

you have 20 5

25

25

5 1 .

Sasha So, 20 has to be 1. Otherwise, the rules we already know won’t keep working.

1. In the dialog, Sasha and Tony use the basic rule of multiplying exponents to fi nd a defi nition of 20. Another way to fi nd a defi nition of 20 is to use the basic rule for dividing exponents.

ab

ac

= a b 2c

If you substitute a = 2, b = 7, and c = 7, you get the following equation.

27

27

= 2727

Explain why this approach produces the same defi nition that Sasha and Tony found, 20 = 1.

episode 24

Tony and Sasha discuss possible defi nitions for 223.

Tony Let’s try to think this through instead of just guessing what 223 should be.

Sasha Alright. Well, we want our favorite rule to keep working.

A2b B A2c B = 2b 1 c

Tony Well, what happens if we say b = 23 and c = 3?

Sasha I see where you’re going. That’s genius! Now we can say thatA223B A23B = 223 1 3 = 20 since 23 1 3 = 0.

Tony Also, 20 = 1, so we have A223B A23B = 1.

Sasha We can do what we did for 20. Solve for 223 as if it were an unknown.

A223B A23B = 1

223 =

123

So, 223 =

123

.

Remember...Remember...Theorem 6.1 says that if b and c are positive integers, then ab ? ac = ab1c.

0500_cme09a1_se_06a.indd 518 4/28/08 3:14:02 PM

What’s Wrong Here?Examples of worked-out solutions help students

to recognize and avoid common mistakes. The

emphasis is on ways to think about math problems.

More Minds in ActionMinds in Action doesn’t just help students

communicate mathematically, it helps them

reason through mathematical concepts.

" The basic results and methods of high school math—the Pythagorean Theorem, solving equations, graphing lines, and so on—are the products of mathematics. The actual mathematics lies in the thinking that is used to discover and develop these results."

— Al Cuoco CME Project Lead Author

9

CME PROJECT

Teacher’s EditionThis comprehensive teaching and planning tool supports all you do. Each chapter includes mathematics background, pacing suggestions, lesson plans, error prevention, assignment guides, and more. Wrap-around teaching notes put the information right where you need it.

Implementing and Teaching Guide

This valuable professional guide helps you implement the CME Project curriculum based on research and effective practices.

Practice WorkbookMore problem-solving and procedural practice enhance achievement.

Teaching ResourcesBlackline masters support lessons. Includes answers to the Practice Workbook.

Assessment ResourcesLesson quizzes, chapter tests, and cumulative tests simplify preparation time and help you monitor students’ progress.

Solutions ManualWant to check an answer? Here are worked-out solutions for all Student Edition exercises. Use this manual to prepare for class and deliver rigorous and relevant instruction.

Student EditionA balance of traditional and student-centered instructional elements develop both problem-solving skills and procedural fluency. Developing students’ Habits of Mind, or ways of mathematical thinking, is a hallmark.

Components

Online

Print

10

The TI-Nspire logo is a trademark of Texas Instruments.

Technology HandbookThe Student Edition includes a Technology

Handbook that explains in clear, step-by-step terms how to use TI-Nspire functions with the

explorations in CME Project.

Technology is a big part of everyday life. The

twist is that CME Project collaborated with

Texas Instruments to integrate the newest

handheld and computer software, TI-Nspire™.

This handheld graphing calculator lets students

explore multiple representations of a math

concept on a single screen.

Math That’s Inspiring

TI-Nspire™ Technology Handbook 771

Generating a Scatter Plot, Lesson 3.9

1. Use existing data in a spreadsheet.Choose the Scatter Plot option in the Graph Type menu.

2. Select the desired variable from the x-value box. Press enter . Press tab . Do the samefor the y-value box.

Using the Fill-Down Feature in a Spreadsheet, Lesson 5.12

1. Navigate to the cell you wish to fi ll down. Choose Fill Down from the Data menu.

2. Press to highlight the desired range of cells. Press enter .

3. Choose Zoom—Data from the Windowmenu.

0764_cme09a1_se_emti.indd 771 5/9/08 7:11:08 AM

11

12

Math That’sRemarkable

“ One of the strengths of the CME Project curricula is the rich mathematical contexts in which

students learn important concepts and practice important skills. The investigation on Lagrange

Interpolation is a perfect example. One of the problems in this investigation requires students to

demonstrate that many questions given on standardized tests are flawed in that any of the answer

choices given to extend a number pattern could be correct. Completing this investigation laid the

groundwork for a conceptual understanding of the factor and remainder theorems, and my students

enjoyed it! Being able to outsmart the standardized test authors was an added bonus. ”Kent Werst, Arlington, Virginia

“ The expansion tables were a great organizational tool for the students. It helped many of them ‘see’

things much more clearly than before. Real-life examples (like positioning the ladder in Chapter 4)

piqued the students’ interest and answered the age old question, ‘When am I ever going to use this?’

I had one student tell me that, thanks to me, he would never fall off a ladder! ”Jayne Abbas, Hookset, New Hampshire

“ I teach in an inclusion classroom, with both regular education and Special Education students, in an

inner city public high school. I had placed the students in small groups so that I could listen to the

conversations they were having about the mathematics when I heard one of my Special Education

students enthusiastically explaining the pattern that he had found on a particular task. This student

had not had a positive experience in mathematics class in a long while. These materials had him

excited to come to math class, excited about the mathematics we were doing, and excited to share

with the class. Needless to say, I was excited to teach with these materials..”

James Stallworth, Cincinnati, Ohio

“ I learned more about algebra and mathematics concepts than ever before by using the

CME materials to do my lesson studies and presentations. ”Arnell Crayton, Houston, Texas

Want to know more?Visit PearsonSchool.com/integratedcme or scan the QR code below.

Research Behind the CME Project Approach

CME Project Core TeamAnna Baccaglini-Frank, Al Cuoco, Kevin Waterman, Doreen Kilday,

Nancy Antonellis D’Amato, Ryota Matsuura, Jean Benson, Bowen Kerins,

Sarah Sword, and Wayne Harvey

Absent from photo: Daniel Erman, Brian Harvey, Stephen Maurer, and Audrey Ting

The Center for Mathematics Education brings together an eclectic

staff of mathematicians, educators, and scientists internationally

known for leadership in mathematics education.

Current work in the field of

education led to four research-

based goals of CME Project.

1. To ensure that students who

complete the CME Project

demonstrate a high level of

mathematical proficiency

2. To provide a coherent and rigorous

curriculum, based on current

learning research and world-class

best practices, with a focus on the

central themes in mathematics, for

teachers who desire the traditional

sequence of high school courses

3. To provide a curriculum that will

help more students succeed in four

years of rigorous yet accessible

mathematics in high school

4. To give students the experience of

working as mathematicians and

scientists to highlight the profound

utility of modern mathematical

methods in mathematics, fields

related to mathematics, and

everyday life

1

2

3

4

t

How Many of Each?Addition, Subtraction, and the Number System 1

Making Shapes and Designing Quilts2D Geometry

Solving Story ProblemsAddition, Subtraction, and the Number System 2

What Would You Rather Be? Data Analysis

Fish Lengths and Animal JumpsMeasurement

Number Games and Crayon PuzzlesAddition, Subtraction, and the Number System 3

Color, Shape, and Number PatternsPatterns and Functions

Twos, Fives, and TensAddition, Subtraction, and the Number System 4

Blocks and Boxes3D Geometry

7

How M

any of Each?Addition, Subtraction, and the Num

ber System 1

UNiT1

Curriculum Units

8

9

6

5

4

3

2

1

GRADE

1

investigationsin number, Data, anD Space®

Counting, Coins, and Combinations

Addition, Subtraction, and the Number System

1Unit

1

GRADE

2


Trading Stickers, Combining Coins

Addition, Subtraction, and the Number System

1UniT

1

GRADE

3


Factors, Multiples, and Arrays

Multiplication and Division 1

Unit1

GRADE

4


Who Is in School Today?

Classroom Routines and M

aterialsUnIT

1

GRADE

K

Investigationsin number, Data, anD Space®

Investigations in Number, Data, and Space®

Kindergarten Grade 1 Grade 2 Grade 3 Grade 4

Color, Shape, and Number Patterns

Patterns and Functions SystemUnit

7Num

ber Puzzles and Multiple Tow

ersM

ultiplication and Division 1UNiT

1

GRADE

5


Grade 5

Connected Mathematics 3

CME Project

Algebra 1 Geometry Algebra 2 Precalculus

Integrated CME Project

Integrated I Integrated II Integrated III

Pearson NSF-Funded Programs

800-848-9500Copyright Pearson Education, Inc., or its affiliates. All rights reserved.

SAM: 000-0-000-00000-0 Mat

Bro

1400

00

Grade 6 Grade 7 Grade 8 Grade 8 Algebra 1

Experience Student Place atmymathuniverse.com/cmp3

ACTIVe-book Math Tools VideosStudentActivities

Lappan, Phillips, Fey, Friel

ISBN-13:ISBN-10:

978-0-13-327449-30-13-327449-7

9 7 8 0 1 3 3 2 7 4 4 9 3

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CME PROJECT Math with a Twist! - … PROJECT. Math with a Twist! Math That’s Focused ... If you add more than two numbers, the order in which you group them does not matter. 3