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

MATHEMATICAL PRACTICES

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

Lesson

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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

MATHEMATICAL PRACTICES

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