G6 m2-a-lesson 4-t

Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models

Date: 4/10/2336

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•2Lesson 4


Student Outcomes Students use visual models such as fraction bars and area models to divide fractions by fractions with different

denominators.

Students make connections between visual models and multiplication of fractions.

Classwork

Opening Exercise (2 minutes)

Begin class with a review of equivalent fractions. Ask each student for a new example of an equivalent fraction. Students need to share how they know that the new fraction is equivalent to the old fraction.

Opening Exercise

Write at least three equivalent fractions for each fraction below. Be sure to show how the two fractions are related.

a.23

Sample solutions include 46,69,812,1015,1218.

b.1012

Sample solutions include 56,1518,2024,2530,3036.

Example 1 (3 minutes)

For the first example, students will be asked to solve a word problem using the skills they used in Lesson 3 to divide fractions with the same denominator.

Molly purchased 138

cups of strawberries. This can also be represented as 118

. She eats 28

cups in a serving.

How many servings did Molly purchase?MP.1

http://creativecommons.org/licenses/by-nc-sa/3.0/deed.en_US



Date: 4/10/2337



This question is really asking me how many 28

are in 118

or, in other words, to divide eleven eighths by

two eighths. I can use a model to show that there are 5 12

servings in the 118

cups of strawberries.

Example 1

Molly purchased 118

cups of strawberries. She eats 28

in a serving. How many servings did Molly purchase?

Use a model to prove your answer.

0 18

28

38

48

58

68

78

88

98

108

118

128


Now imagine that Molly’s friend Xavier purchased 118

cups of strawberries and that he eats 34

cup servings.

How many servings has he purchased?

He has purchased 116

servings or 1 and 56

servings. (This would be answered last after a brief

discussion using the questions that follow.)

What is this question asking us to do?

I am being asked to divide 118

cups into 34

cup servings.

How does the problem differ from the first example?

The denominators are different.

What are some possible ways that we could divide these two fractions?

MP.1

1 +¿ 1 +¿ 1 +¿ 1 +¿ 1 +¿

12=5 12



Date: 4/10/2338



I could change 34

to 68

. These fractions are equivalent. I scaled up from 34

by multiplying the top

and bottom by 2.



Date: 4/10/2339



Example 2

Now imagine that Molly’s friend Xavier purchased 118

cups of strawberries and that he eats 34

cup servings. How many

servings has he purchased? Use a model to prove your answer.

0 18

28

38

48

58

68

78

88

98

108

118

128

There are 1 and 56

servings.


34÷23

What is this question asking us to do?

23

of what is 34

or how many 23

are in 34

.

Lead students through a brief discussion about this example:

Is your answer larger or smaller than one? Why?

Since 23

is less than 34

, we will have an answer that is larger than 1.

Why is this question more difficult to model than the questions in Lesson 3?

The fractions do not have common denominators.

How can we rewrite this question to make it easier to model?

We can create equivalent fractions with like denominators and then model and divide.

We can also think of this as 912÷812or nine twelfths divided by eight twelfths. 9 units ÷ 8 units =

98

or

1 18

units.

1 +¿ 56

MP.1



Date: 4/10/2340





Date: 4/10/2341



Example 3

Find the quotient: 34÷23

. Use a model to show your answer.

Exercises 1–5 (20 minutes)

Students will work in pairs or alone to solve more questions about division of fractions with unlike denominators.

Exercises 1–5

A model should be included in your solution.

1.62÷34

We could rewrite this problem to ask 124÷34=¿

123

=4.

1 +¿ 1 +¿ 1 +¿ 1

0 112

212

312

412

512

612

712

812

912

1012

0 14

24

34

44

54

64

74

84

94

104

88

18

MP.1



Date: 4/10/2342



2.23÷25

We could rewrite this problem to ask 1015÷615

= 106

or 146

.

0 115

215

315

415

515

615

715

815

915

1015

1115

3.78÷12

We could rewrite this as 78÷48=74

or 134

.

48

88

1 +¿ 34

4.35÷14

This can be rewritten as 1220÷520

=125

=2 25

.

1 +¿ 46



Date: 4/10/2343



1 +¿ 1 +¿ 25

5.54÷13

We can rewrite this as 1512÷412

=¿fifteen twelfths ÷ four twelfths ¿ 154

=3 34

.

Closing (10 minutes)

When dividing fractions, is it possible to get a whole number quotient?

When dividing fractions, is it possible to get an answer that is larger than the dividend?

When you are asked to divide two fractions with different denominators, what is one possible way to solve?

Exit Ticket (5 minutes)

0 112

212

312

412

512

612

712

812

912

1012

1112

1 1312

1412

1512



Date: 4/10/2344



Name ___________________________________________________ Date____________________


Exit Ticket

Draw a model to support your answer to the division questions.

1.94÷38

2.35÷23



Date: 4/10/2345



Exit Ticket Sample Solutions

Draw a model to support your answer to the division questions.

1.94÷38


¿ eighteen eighths divided by three eighths ¿ 183

¿6.

2.35÷23


=¿ nine fifteenths divided by ten fifteenths or 9units ÷ 10units.

So this is equal to 910

.

0 115

215

315

415

515

615

715

815

915

1015

1115

9 units

10units



Date: 4/10/2346



Problem Set Sample Solutions

The following problems can be used as extra practice or a homework assignment.

1.89÷49

Eight ninths ÷ four ninths = 2.

0 19

29

39

49

59

69

79

89

99

109

119

2.910÷410

Nine tenths ÷ four tenths ¿2 14

.

1 1 14

3.35÷13

915÷515

¿ nine fifteenths ÷ five fifteenths ¿ 95=1 4

5.

0 115

215

315

415

515

615

715

815

915

1015



Date: 4/10/2347



1 +¿ 45

4.34÷15

1520÷420

=¿fifteen twentieths ÷ four twentieths = 154

.

1 +¿ 1 +¿ 1 +¿ 34

¿ 3 34

44

+¿ 44

+¿ 44

+¿ 34

¿ 154


Education

G6 m2-a-lesson 4-t