11-4a multiplication as scaling · 2 develop the concept: interactive 10–15 min problem-based...

Objective Essential Understanding Vocabulary Materials

Students will compare the size of the product to the size of one factor without multiplying as they begin to consider multiplication as scaling.

The relative size of the factors can be used to determine the relative size of the product.

resizingscaling

Lesson Overview

Multiplication as Scaling

1 Daily Common Core Review

Daily Common Core Review not available for this lesson. Consider using additional practice found in the Student Edition as review.

PROFESSIONAL DEVELOPMENT

Math Background

One of the major difficulties for students in multiplying fractions is overcoming the mistaken notion that “multiplication makes bigger.” Students need to understand that multiplication is an operation by which one factor scales the second up or down. If the first factor is greater than 1, then the product is greater than the second factor; this enlargement scales up the second factor. If the first factor is less than 1, then the product is less than the second factor; this shrinking

scales down the second factor. If the first factor is equal to 1, then the number remains unchanged. Understanding multiplication as a scalar is fundamental for later developing understanding of ratio and proportion, where scaling is used to relate one number in each ratio to the other. It is also fundamental to understanding dilations in geometry, where geometric figures are enlarged or shrunk using mathematics.

Common Core

DomainNumber and Operations—Fractions

ClusterApply and extend previous understandings of multiplication and division to multiply and divide fractions.

Standards5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number... explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a _ 

b  5 (n  a)

_____ (n  b)

to the effect of multiplying a _ 

b  by 1. Also

5.NF.5, 5.NF.5.a

Mathematical Practices

✔ Make sense of problems and persevere in solving them.

✔ Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

✔ Use appropriate tools strategically.

Attend to precision.

✔ Look for and make use of structure.

✔ Look for and express regularity in repeated reasoning.

Lesson

11-4A

40A

MTH12_TE05_CCTK_TPC11_4A.indd 1 7/23/11 1:14 AM

2 Develop the Concept: Interactive

10–15 min Problem-Based Interactive LearningOverview Students will compare the size of the product to the size of one factor without multiplying as they begin to consider multiplication as scaling.

Focus How does multiplying by a fraction change the second factor?

Vocabulary scaling

Set the Purpose You have learned to multiply fractions and mixed numbers. Today, you will learn how to use multiplication to scale or resize something.

Connect Why might you need to resize something? [Sample responses: Making a scale model, enlarging a drawing, using a copy machine]

Pose the Problem Write the following sets of problems on the board and ask students to find which problem will give the greatest product and which the least product in each set without multiplying. Give students a few minutes to work individually and then have them compare their answers with a partner. Have students share their work with the class.

Expand Student Responses When we multiply a number by another number, we can think about one factor as a scaling number that changes the size of the other factor. Look at Set 1. Which problem(s) will give us an answer greater than 2? [c] less than 2? [a] equal to 2? [b] Repeat this process with each set. How can you tell when multiplication will make a number greater? [When the other factor is greater than 1] When will multiplying reduce the value of a number? [When the other factor is less than 1] How can you multiply and leave a number unchanged? [Multiply by 1.]

Give examples of numbers that you would multiply by 3 to get an answer that is greater than 3, equal to 3, or less than 3.

Set 1 Set 2a. 1 __ 2 × 2 a. 3 3 _ 4 × 2 1 __ 2 b. 3 __ 3 × 2 b. 3 _ 4 × 2 1 __ 2 c. 2 2 _ 3 × 2 c. 4 _ 4 × 2 1 __ 2

Set 3a. 3 _ 4 × 6 _ 6 b. 3 _ 4 × 1 5 _ 6 c. 3 _ 4 × 5 _ 6

MATHEMATICAL PRACTICES


Use StructureEncourage students to predict whether their answer is larger than the second factor or smaller than the second factor as they work on the problem.

40B


Sue 4

Joe 11__234

Alan 3__434

June 3__334

Do you UNDERSTAND?Do you know HOW?

Multiplication as ScalingHow can multiplying by a fraction change the second factor?Sue knitted four scarves 4 feet long for her and her friends Joe, Alan, and June. After a month, they compared the lengths of their scarves. Some scarves had stretched and some had shrunk. The results are shown in the chart.

How had the lengths of the scarves changed?

Think of multiplication as scaling or resizing.

Without multiplying, decide which symbol belongs in the box: , , or 5.

1. 3 1 __ 2 3 2 2 __ 3 ❚ 2 2 __ 3

2. 4 __ 5 3 2 2 __ 3 ❚ 2 2 __ 3

3. 4 3 __ 5 3 4 __ 4 ❚ 4 3 __ 5

4. Reason Why does multiplying a number by 3 1 __ 2 increase its value?

5. Reason Does the scaling factor always have to be the first factor?

12. Without multiplying, order the following products from least to greatest.

2 × 3 __ 5 2 1 __ 4 3 3 __ 5 3 __ 4 3 3 __ 5 5 __ 5 3 3 __ 5

Independent Practice

Guided Practice

In 6–11, without multiplying, decide which symbol belongs in the box: , , or 5.

6. 2 1 __ 2 3 1 2 __ 3 ❚ 1 2 __ 3

8. 1 2 __ 7 3 5 __ 5 ❚ 1 2 __ 7

10. 3 3 __ 5 3 2 __ 2 ❚ 3 3 __ 5

7. 3 __ 5 3 4 4 __ 5 ❚ 4 4 __ 5

9. 1 __ 3 3 2 2 __ 5 ❚ 2 2 __ 5

11. 4 1 __ 3 3 2 2 __ 7 ❚ 2 2 __ 7


Common Core

5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number. . . explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a _ 

b  5 (n 3 a)

_____ (n 3 b)

to

the effect of multiplying a _ b

  by 1. Also 5.NF.5, 5.NF.5.a

5

5

5

Sample answer: Because 3 1 __ 2 is

greater than 1.

3 __ 4 3 3 __

5 ; 5 __

5 3 3 __

5 ; 2 3 3 __

5 ; 2 1 __

4 3 3 __

5

Sample answer: No; For example, in Exercise 3, the scaling factor came second.

Lesson

11-4A

40

MTH12_SE05_CCTK_TPC11_L04A.indd 40 15/07/11 2:58 AM

10Sue’s scarf

Joe’s scarfAlan’s scarf

June’s scarf

62 3 4 5

Draw a picture.

Perform the multiplication indicated in the chart and use a number line to compare the new lengths of the scarves.

Joe’s scarf stretched.

1 1 __ 2 3 4 4

Multiplying a number by a fraction greater than 1 results in a product greater than the starting number.

Alan’s scarf shrunk.

3 __ 4 3 4 4

Multiplying a number by a fraction less than 1 results in a product less than the starting number.

June’s scarf stayed the same length.

3 __ 3 3 4 5 4

Multiplying by a fraction equal to 1 results in a product equal to the starting number.

When you multiply by a fraction equal to 1, you are finding an equivalent fraction:4 5 4 __ 1 5 4 __ 1 3 3 __ 3 5 (4 3 3)

______ (1 3 3) 5 12 ___ 3

Step 2 Step 3

13. At a taffy pull, George stretched the taffy to 3 feet. Jose stretched

it 1 1 __ 3 times as far as George. Maria stretched it 2 __ 3 as far. Sally

stretched it 6 __ 6 as far. Who stretched it the farthest? the least?

14. Use Tools Who ran the farthest by the end of the week? Use the table below that shows the distances in miles.

Monday Tuesday Wednesday Thursday Friday

Holly 11__2 1__

2 21__

4 3__

4 11__

2

Yu 13__4 11__

2 23__

4 11__

4 1__

2

15. Persevere Joni and her friends are stretching rubber bands for an activity

in science class. Joni stretched her rubber band to 24 inches. Manuel stretched

it 2 1 __ 2 times as far. Nicole stretched it 3 __ 3 as far. Molly stretched it 3 __ 5 as far. Put the

students in order of how far they stretched their rubber bands from least to greatest.

16. Look for Patterns Make up two decimals with an answer close to the given product.

___.___ 3 ___. ___ 5 6.3

17. Reasonableness Put the following products in order from greatest to least, without multiplying.

3 3 4 __ 7 1 __ 2 3 4 __ 7 1 3 __ 4 3 4 __ 7 4 __ 4 3 4 __ 7

Problem Solving

Step 1


Jose stretched it the farthest.; Maria stretched it the least.

Yu.; Holly ran 6 1 __ 2 miles and Yu ran 7 3 __

4 miles. Yu ran 1 1 __

4 miles farther than Holly.

Molly, Nicole and Joni, Manuel

Sample answer: 9.1 3 0.7 is close to 6.3

3 3 4 __ 7 ; 1 3 __

4 3 4 __

7 ; 4 __

4 3 4 __

7 ; 1 __

2 3 4 __

7

Lesson 11-4A 41


10Sue’s scarf


June’s scarf

62 3 4 5


1

Set the Purpose Call students’ attention to the Visual Learning Bridge at the top of the page. In this lesson you will learn how to compare the size of the product to the size of one factor without multiplying as you begin to consider multiplication as scaling.

www.pearsonsuccessnet.com

Exercise 1 and 2Error InterventionIf students have difficulty deciding whether the answers to Exercises 1 and 2 are greater,

then have them multiply. For example, ask: What is 3 1 __ 2 2 2 __

3 ? [9 1 __ 3 ]

What is the product of 4 __ 5 2 2 __ 3 ? [2 2 ___ 15 ] Which exercise has a greater

product? Why? [Exercise 1 has a greater product because 2 2 __ 3 is being multiplied by a number greater than 1.]

After students have completed the Guided Practice, read the instructions for the Independent Practice together with the students. Demonstrate how to put the products in order knowing only the relationship between the multiplication expressions. Use Exercise 12 as an example.

Which is the greatest product? [2 1 __ 4 3 __ 5 ] How do you know? [ 3 __ 5 is being multiplied by a number greater than any of the others. The product is greater than 2 3 __ 5 because 2 1 __ 4 is greater than 2.] Which

is the smallest product? [ 3 __ 4 3 __ 5 ] How do you know? [ 3 __ 5 is being multiplied by a number less than 1.]

Guided Practice2

Independent Practice3

How can multiplying by a fraction change the second factor?Sue knitted four scarves 4 feet long for her and her friends Joe, Alan, and June. After a month, they compared the lengths of their scarves. Some scarves had stretched and some had shrunk. The results are shown in the chart.



3 Develop the Concept: Visual

What does it mean to scale something up or down? [to make it greater or lesser, enlarge or shrink] Whose scarf should be our starting point? [Sue, because hers has not changed in length.]

Sue 4

Joe 11__24

Alan 3__44

June 3__34

Draw a picture.Perform the multiplication indicated in the chart and use a number line to compare the new lengths of the scarves.

Step 1


40


Sue 4

Joe 11__234

Alan 3__434

June 3__334

Do you UNDERSTAND?Do you know HOW?

Multiplication as ScalingHow can multiplying by a fraction change the second factor?Sue knitted four scarves 4 feet long for her and her friends Joe, Alan, and June. After a month, they compared the lengths of their scarves. Some scarves had stretched and some had shrunk. The results are shown in the chart.



Without multiplying, decide which symbol belongs in the box: , , or 5.

1. 3 1 __ 2 3 2 2 __ 3 ❚ 2 2 __ 3

2. 4 __ 5 3 2 2 __ 3 ❚ 2 2 __ 3

3. 4 3 __ 5 3 4 __ 4 ❚ 4 3 __ 5

4. Reason Why does multiplying a number by 3 1 __ 2 increase its value?

5. Reason Does the scaling factor always have to be the first factor?

12. Without multiplying, order the following products from least to greatest.

2 × 3 __ 5 2 1 __ 4 3 3 __ 5 3 __ 4 3 3 __ 5 5 __ 5 3 3 __ 5

Independent Practice

Guided Practice

In 6–11, without multiplying, decide which symbol belongs in the box: , , or 5.

6. 2 1 __ 2 3 1 2 __ 3 ❚ 1 2 __ 3

8. 1 2 __ 7 3 5 __ 5 ❚ 1 2 __ 7

10. 3 3 __ 5 3 2 __ 2 ❚ 3 3 __ 5

7. 3 __ 5 3 4 4 __ 5 ❚ 4 4 __ 5

9. 1 __ 3 3 2 2 __ 5 ❚ 2 2 __ 5

11. 4 1 __ 3 3 2 2 __ 7 ❚ 2 2 __ 7


Common Core

5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number. . . explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a _ 

b  5 (n 3 a)

_____ (n 3 b)

to

the effect of multiplying a _ b

  by 1. Also 5.NF.5, 5.NF.5.a

5

5

5

Sample answer: Because 3 1 __ 2 is

greater than 1.

3 __ 4 3 3 __

5 ; 5 __

5 3 3 __

5 ; 2 3 3 __

5 ; 2 1 __

4 3 3 __

5

Sample answer: No; For example, in Exercise 3, the scaling factor came second.

Lesson

11-4A

40


10Sue’s scarf


June’s scarf

62 3 4 5

Draw a picture.

Perform the multiplication indicated in the chart and use a number line to compare the new lengths of the scarves.


1 1 __ 2 3 4 4



3 __ 4 3 4 4



3 __ 3 3 4 5 4


When you multiply by a fraction equal to 1, you are finding an equivalent fraction:4 5 4 __ 1 5 4 __ 1 3 3 __ 3 5 (4 3 3)

______ (1 3 3) 5 12 ___ 3

Step 2 Step 3

13. At a taffy pull, George stretched the taffy to 3 feet. Jose stretched

it 1 1 __ 3 times as far as George. Maria stretched it 2 __ 3 as far. Sally

stretched it 6 __ 6 as far. Who stretched it the farthest? the least?

14. Use Tools Who ran the farthest by the end of the week? Use the table below that shows the distances in miles.

Monday Tuesday Wednesday Thursday Friday

Holly 11__2 1__

2 21__

4 3__

4 11__

2

Yu 13__4 11__

2 23__

4 11__

4 1__

2

15. Persevere Joni and her friends are stretching rubber bands for an activity

in science class. Joni stretched her rubber band to 24 inches. Manuel stretched

it 2 1 __ 2 times as far. Nicole stretched it 3 __ 3 as far. Molly stretched it 3 __ 5 as far. Put the

students in order of how far they stretched their rubber bands from least to greatest.

16. Look for Patterns Make up two decimals with an answer close to the given product.

___.___ 3 ___. ___ 5 6.3

17. Reasonableness Put the following products in order from greatest to least, without multiplying.

3 3 4 __ 7 1 __ 2 3 4 __ 7 1 3 __ 4 3 4 __ 7 4 __ 4 3 4 __ 7

Problem Solving

Step 1


Jose stretched it the farthest.; Maria stretched it the least.

Yu.; Holly ran 6 1 __ 2 miles and Yu ran 7 3 __

4 miles. Yu ran 1 1 __

4 miles farther than Holly.

Molly, Nicole and Joni, Manuel

Sample answer: 9.1 3 0.7 is close to 6.3

3 3 4 __ 7 ; 1 3 __

4 3 4 __

7 ; 4 __

4 3 4 __

7 ; 1 __

2 3 4 __

7

Lesson 11-4A 41


Problem Solving

Students use underlying processes and mathematical tools for Exercises 13–17. Remind students to check for reasonableness when solving each problem.

Exercise 16Look for Patterns Encourage students to look for patterns that may help them find decimals that make the number sentence true. What two whole numbers can be multiplied to get a product of 63? [Sample answer: 7 and 9] How does this basic multiplication fact help to solve this problem? [Sample answer: Since I know that 7 9 5 63, I can adjust the decimals in those factors and find two numbers that make the number sentence true.]

Exercise 17Check for Reasonableness Encourage students to put the factors that are not the same in each answer choice in the desired order and see how they relate to the final answer. What would the order be from greatest to least if you simply ordered the factors? [3, 1 3 __ 4 , 4 __ 4 , 1 __ 2 ] How can you use that information to help put the answer choices in order? [Sample answer: The order is exactly the same.]

Why does multiplying by a number greater than 1 result in a product greater than the starting number? [You have one whole and then add to it to complete the multiplication.] Why does multiplying by a number less than 1 result in a product less than the starting number? [You have only a part of the starting number.]

Why does multiplying by a fraction equal to 1 result in a product equal to the starting number? [Identity Property of Multiplication 1 n 5 n] How do we know how long June’s scarf is? [Multiplying by 1 does not change the number.]

Step 2 Step 3


1 1 __ 2 4 4



3 __ 4 4 4



3 __ 3 4 5 4


When you multiply by a fraction equal to 1, you are finding an equivalent fraction:

4 5 4 __ 1 5 4 __ 1 3 __ 3 5 (4 3) ______ (1 3) 5 12 ___ 3

How do we know how long Joe’s scarf is? [Draw a line segment as long as Sue’s and then another line segment half as long.] How do we know how long Alan’s scarf is? [Divide Sue’s into 4 equal parts and use 3 of them.]


41


FormativeAssessment

Michaela, Gloria, Kris, Sammi; Michaela was the longest because she stretched it 2 1 _ 2 times as far as Gloria. Gloria and Kris were next because they did not stretch theirs longer than 18 inches. Sammi’s clay was the shortest because she stretched it only 4 _ 7 as far as Gloria and Kris.

Sammi, Kris, Gloria, Michaela; Michaela was the longest

because she stretched it 2 1 _ 2 times as far as Gloria. Gloria

was next because she did not stretch hers longer than

18 inches. Kris was next because she kept her clay the

same length by stretching it by 3 _ 3 or 1. Sammi’s clay was

the least because she stretched it only 4 _ 7 as far as Gloria

and Michaela.

Sammi, Kris, Gloria, Michaela; Michaela was the shortest because she stretched it 1 _ 2 as far as Gloria. Gloria was next because she did not stretch hers longer than 18 inches. Kris was next because she kept her clay the same length by stretching it by 3 _ 3 or 1. Sammi’s clay was the longest because she stretched it only 7 _ 4 as far as Gloria and Michaela.

CloseEssential Understanding Multiplication can be interpreted as scaling or resizing. In this lesson, you learned how to compare the size of the product to the size of one factor without multiplying as you begin to consider multiplication as scaling.

ASSESSMENT

Exercises 1-3 are worth 1 point each. Use the rubric to score Exercise 4.

Exercise 4Writing to Explain Students should use their understanding of scaling and resizing fractions to find the length of each person’s piece of modeling clay.

Suggest a Word List Students who need additional writing support can use these words in their explanations: scaling and resizing.

Student Samples3-point answer The student thoroughly explains how to find the relative lengths of each person’s piece of modeling clay. He or she then puts the names in the correct order. The answer is correct.

2-point answer The student adequately explains how to find the relative lengths of each person’s piece of modeling clay. He or she made an error in calculation or put the students in the wrong order, and the answer is incorrect.

1-point answer The student shows no understanding of how to find the relative lengths of each person’s piece of modeling clay. The answer is incorrect.

Points Prescription

0–4 Intervention

5 On-Level

6 Advanced

Quick Check Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5Q 11•4A

For 1-3, without multiplying, decide which symbol belongs in the box: <, >, or =.

1. 2 1 _ 2 × 1 1 _ 2 1 1 _ 2

2. 3 _ 5 × 1 2 _ 7 1 2 _ 7

3. 6 3 _ 4 × 5 _ 5 6 3 _ 4

4. Writing to Explain Gloria and her friends are rolling out modeling clay for an activity in math class. Gloria rolled out her clay until it was 18 inches long. Michaela rolled hers 2 1 _ 2 times as far. Kris rolled hers 3 _ 3 as far. Sammi rolled hers 4 _ 7 as far. Put the students in order of the length of their clay from least to greatest. Explain how you found your answer.

See sample student answers to the right.

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∙

Quick Check

11-4A

MTH12_ANC5_TRM_Q11_04a.indd 1 7/19/11 6:20 PM

Prescription for Differentiated InstructionUse student work on the Quick Check to prescribe differentiated instruction.

Use the Quick Check to assess students’ understanding.

4 Close/Assess and Differentiate

41A


eToolswww.pearsonsuccessnet.com



Leveled Homework


10 min

Materials Chalkboard, chalk

• Write these numbers and expressions on the chalkboard.Number A: 5Option #1: 2 2 __ 3 5

Option #2: 1 __ 4 5

Option #3: 3 __ 3 5Number B: 2Option #1: 1 1 __ 3 2

Option #2: 4 __ 4 2

Option #3: 1 __ 3 2 • Have students choose the greatest

product and least product for each number. [Number A: #1; #2; Number B: #1; #3]

Intervention

Reteaching Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5R 11•4A



Example 1: 2 1 _ 2 × 5 > 5


Example 2: 3 _ 4 × 5 < 5


Example 3: 2 _ 2 × 5 = 5


Without multiplying, decide which symbol belongs in the box:<, >, or =.

1. 3 1 _ 2 × 3 1 _ 3 3 1 _ 2

2. 2 _ 3 × 2 1 _ 3 2 1 _ 3

3. 8 2 _ 5 × 5 _ 5 8 2 _ 5

4. 3 _ 4 × 4 2 _ 3 4 2 _ 3

5. 4 1 _ 2 × 1 1 _ 3 1 1 _ 3

6. 2 _ 5 × 5 2 _ 3 5 2 _ 3

7. 3 2 _ 5 × 4 _ 4 3 2 _ 5

8. 5 _ 8 × 8 1 _ 3 8 1 _ 3

9. 5 1 _ 2 × 6 2 _ 3 6 2 _ 3

10. 3 _ 8 × 2 1 _ 3 2 1 _ 3

11. 10 2 _ 5 × 8 _ 8 10 2 _ 5

12. 1 _ 2 × 9 1 _ 3 9 1 _ 3

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,

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,

∙

∙

∙

Reteaching

11-4A

MTH12_ANC5_TRM_R11_04a.indd 2 7/19/11 7:38 PM

Practice Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5P 11•4A

Multiplication as ScalingIn 1-20, without multiplying, decide which symbol belongs in the box: <, >, or =.

1. 2 1 _ 2 × 3 2 _ 3 3 2 _ 3

3. 4 _ 5 × 4 2 _ 3 4 2 _ 3

5. 5 3 _ 5 × 2 _ 2 5 3 _ 5

7. 6 1 _ 2 × 7 2 _ 3 7 2 _ 3

9. 3 _ 5 × 8 4 _ 5 8 4 _ 5

11. 9 2 _ 7 × 3 _ 3 9 2 _ 7

13. 1 _ 3 × 1 2 _ 5 1 2 _ 5

15. 2 3 _ 5 × 4 _ 4 2 3 _ 5

17. 3 1 _ 3 × 4 2 _ 7 4 2 _ 7

19. 5 1 _ 2 × 6 2 _ 3 5 1 _ 2

2. 1 _ 3 × 9 2 _ 5 9 2 _ 5

4. 1 3 _ 5 × 6 _ 6 1 3 _ 5

6. 2 1 _ 3 × 3 2 _ 7 3 2 _ 7

8. 4 1 _ 2 × 5 2 _ 3 5 2 _ 3

10. 3 _ 5 × 6 4 _ 5 6 4 _ 5

12. 7 2 _ 7 × 7 _ 7 7 2 _ 7

14. 1 _ 3 × 8 2 _ 5 8 2 _ 5

16. 9 3 _ 5 × 3 _ 3 9 3 _ 5

18. 1 2 _ 3 × 2 2 _ 5 2 2 _ 5

20. 3 1 _ 3 × 4 _ 4 3 1 _ 3

21. Put the following products in order from least to greatest, without multiplying.

5 × 3 _ 4 , 4 1 _ 4 × 3 _ 4 , 1 _ 2 × 3 _ 4 , 3 _ 3 × 3 _ 4

22. Put the following products in order from greatest to least,

without multiplying.

6 × 2 _ 5 , 3 2 _ 3 × 2 _ 5 , 2 _ 7 × 2 _ 5 , 2 _ 2 × 2 _ 5

23. Melissa and her friends are stretching rubber bands for an

activity in science class. Melissa stretched her elastic to 10 inches. Juan stretched it 3 1 _ 2 times as far. Sara stretched it 4 _ 4 as far. Marsha stretched it 2 _ 5 as far. Put the students in order of how far they stretched their rubber bands from least to greatest.

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1 _ 2 ∙ 3 _ 4 , 3 _ 3 ∙ 3 _ 4 , 4 1 _ 4 ∙ 3 _ 4 , 5 ∙ 3 _ 4

6 ∙ 2 _ 5 , 3 2 _ 3 ∙ 2 _ 5 , 2 _ 2 ∙ 2 _ 5 , 2 _ 7 ∙ 2 _ 5

Marsha, Melissa and Sara, Juan

Practice

11-4A

MTH12_ANC5_TRM_P11_04a.indd 1 7/19/11 6:07 PM

Enrichment Master

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5E 11•4A

Step It Out!Write and answer the hidden question(s) in each problem. Then solve the problem.

1. James bought 30 ounces of sliced turkey. He used 2 _ 3 of the turkey to make sandwiches for his friends and 1 _ 5 of the turkey in an omelet. How many ounces of turkey were left?

Hidden question(s):

Solution:

2. Ellie bought 4 CDs. The rock music CD cost $12. The jazz CD cost 2 _ 3 as much as the rock music CD. The two special edition CDs each cost 3 times as much as the jazz CD. What was the cost of the 4 CDs?

Hidden question(s):

Solution:

3. Paul spent 2 1 _ 2 hours setting up his laptop. It took him 2 times as long to install his favorite computer game. How long did it take Paul to set up his laptop and install the game?

Hidden question(s):

Solution:

4. Maria cut off 1 _ 6 of a 36-inch piece of rope. Juan cut off 1 _ 4 of a 48-inch piece of rope. They compared their pieces. Whose piece is longer? How much longer?

Hidden question(s):

Solution:

5. Choose one of the problems above. Explain how you determined the hidden question and why it is necessary to answer that question in order to solve the problem.

How many hours did it take to install the game? 2 ∙ 2 1 _ 2 ∙ 5

How long is Maria’s cut piece? 1 _ 6 ∙ 36 ∙ 6 inches; How long is Juan’s cut piece? 1 _ 4 ∙ 48 ∙ 12 inches

$12 ∙ $8 ∙ $24 ∙ $24; $68

2 1 _ 2 ∙ 5 ∙ 7 1 _ 2 ; 7 1 _ 2 hours

Juan’s piece of rope is 6 inches longer: 12 ∙ 6 ∙ 6.

30 ∙ 20 ∙ 6 ∙ 4; 4 ounces

Sample answer: In Problem 3, the question asks for the time spent on two tasks, so I needed to add the two times to answer the question. Only the time for one task was given in the problem, so the hidden question had to be to find the other time.

How many ounces of turkey were used to make the sandwiches? 2 _ 3 ∙ 30 ∙ 20; How many ounces of turkey were used in the omelet? 30 ∙ 1 _ 5 ∙ 6

How much did the jazz CD cost? 2 _ 3 ∙ $12 ∙ $8; How much did the special edition CDs each cost? 3 ∙ $8 ∙ $24

Enrichment

11-4A

MTH12_ANC5_TRM_E11_04a.indd 2 7/19/11 5:35 PM

On-Level

Share your thinking while you work.

Partner Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 511-4ACenter Activity H

aWhat is the missing digit in this factor pair for 45? , 15

bWhat is the missing digit in this factor pair for 38? , 19

cWhat is the missing digit in this

factor pair for 40? , 8

dWhat is the missing digit in this factor pair for 75? , 75

eWhat is the missing digit in this factor pair for 48? , 12

fWhat is the missing digit in this


gWhat is the missing digit in this factor pair for 55? 5, 1

hWhat is the missing digit in this factor pair for 90? , 18

iWhat is the missing digit in this factor pair for 96? 8, 1

jWhat is the missing digit in this factor pair for 81? , 27

kWhat is the missing digit in this factor pair for 84? 4, 2

lWhat is the missing digit in this factor pair for 96? 3, 3

mWhat is the missing digit in this


Get Started or or

Each player tosses two number cubes. If your numbers match another player’s numbers, toss again.Decide who will read the first question. Take turns.

For Each Question

Listen to the reader. Discuss and agree on the correct answer. Every player who has that answer can remove one cube that shows the answer.

How to Win The first player who removes both cubes wins. Have fun!

If you have more time

Toss two number cubes again. Play another game. Begin with the next question in the list.

n What is the missing digit in this factor pair for 36? , 9

o What is the missing digit in this factor pair for 30? 2, 1

p What is the missing digit in this factor pair for 18? , 6

q What is the missing digit in this factor pair for 24? , 12

r What is the missing digit in this factor pair for 60? 4, 5

s What is the missing digit in this factor pair for 75? 3, 2

t What is the missing digit in this factor pair for 32? , 8

u What is the missing digit in this factor pair for 51? , 17

v What is the missing digit in this factor pair for 77? 7, 1

w What is the missing digit in this factor pair for 84? 2. 4

x What is the missing digit in this factor pair for 65? , 13

y What is the missing digit in this factor pair for 27? , 9

z What is the missing digit in this factor pair for 72? 3, 2

MTH12_ANC5_TRM_CA11_04a.indd 13 7/19/11 5:00 PM

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Partner Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 511-4ACenter Activity HH

a Which one of these is a factor pair of 110?1) 2, 55 2) 5, 21 3) 4, 28

b Which one of these is not a factor pair of 84?4) 7, 12 5) 8, 12 6) 6, 14

c Which one of these is a factor pair of 85?1) 3, 25 2) 5, 15 3) 5, 17

d Which one of these is not a factor pair of 82?4) 4, 21 5) 2, 41 6) 1, 82

e Which one of these is a factor pair of 34?1) 4, 9 2) 2, 17 3) 3, 11

f Which one of these is not a factor pair of 102?4) 2, 51 5) 6, 17 6) 8, 15

g Which one of these is not a factor pair of 72?1) 9, 8 2) 4, 36 3) 3, 24

h Which one of these is a factor pair of 76?4) 4, 19 5) 3, 26 6) 6, 12

i Which one of these is a factor pair of 106?1) 4, 24 2) 8, 14 3) 2, 53

j Which one of these is a factor pair of 108?4) 8, 14 5) 3, 36 6) 7, 16

k Which one of these is not a factor pair of 68?1) 3, 32 2) 4, 17 3) 2, 34

l Which one of these is a factor pair of 94?4) 3, 28 5) 4, 26 6) 2, 47

m Which one of these is a factor pair of 100?1) 4, 20 2) 5, 25 3) 4, 25

Get Started or or

Each player tosses two number cubes. If your numbers match another player’s numbers, toss again.Decide who will read the first question. Take turns.

For Each Question

Listen to the reader. Discuss and agree on the correct answer. Every player who has that answer can remove one cube that shows the number in front of that answer.

How to Win The first player who removes both cubes wins. Have fun!

If you have more time

Play another game. Begin with the next question in the list. Or make up your own questions like these.

n Which one of these is not a factor pair of 62?4) 2, 31 5) 1, 62 6) 3, 24

o Which one of these is a factor pair of 56?1) 4, 14 2) 3, 18 3) 7, 9

p Which one of these is not a factor pair of 84?4) 7, 12 5) 6, 19 6) 4, 21

q Which one of these is a factor pair of 96?1) 3, 24 2) 8, 12 3) 4, 22

r Which one of these is not a factor pair of 75?4) 6, 15 5) 3, 25 6) 5, 15

s Which one of these is a factor pair of 27?1) 4, 6 2) 3, 9 3) 6, 7

t Which one of these is not a factor pair of 78?4) 6, 13 5) 4, 17 6) 2, 39

u Which one of these is a factor pair of 92?1) 4, 23 2) 3, 34 3) 7, 12

v Which one of these is a factor pair of 105?4) 3, 35 5) 2, 52 6) 8, 15

w Which one of these is not a factor pair of 112?1) 4, 28 2) 8, 14 3) 8, 16

x Which one of these is a factor pair of 88?4) 8, 12 5) 6, 14 6) 4, 22

y Which one of these is not a factor pair of 32?1) 4, 16 2) 2, 16 3) 4, 8

z Which one of these is a factor pair of 54?4) 6, 8 5) 3, 18 6) 4, 9

MTH12_ANC5_TRM_CA11_04a.indd 14 7/19/11 5:00 PM

: Partner Talk Listen for evidence that a student understands why each product is greater than, less than, or equal to the original factor. For example, a student might say, “When I multiply by 1 __ 2 , my product will be less because 1 __ 2 is less than 1.

Differentiated Instruction

Fractions Fractions Fractions

41B


11-4a multiplication as scaling · 2 develop the concept: interactive 10–15 min problem-based...

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