5 th Grade Number Sense 2.3 (5Q) Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions

$Page 1: 5 th Grade Number Sense 2.3 (5Q) Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions$
5th Grade Number Sense 2.3 (5Q)Solve simple problems, including ones arising in concrete situations, involving

the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.

Lesson to be used by EDI-trained teachers only.

DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? [email protected]

Learning Objective Name __________________________

Today, we will add fractions that have unlike1 denominators.

CFU

What are we going to do today?

Activate (or provide) Prior Knowledge

A fraction is a number that names a part of a whole or a part of a group.To add fractions with like1 denominators, add the numerators and keep the denominator.1 the same

CFUTeacher completes problem #1. Students complete problem #2. Students, you already know how to add fractions with like denominators and write your answer in simplest form. Today, we will use these skills to add fractions that have unlike denominators.

1 different

5 81. + =

9 9

4 52. + =

7 7

13

9419

9

7217

Add and write your answer in simplest form.

1

8

Numerator

Denominator

Fraction





Concept Development

To add fractions, both fractions must have a common denominator.• If the fractions have unlike denominators, then we need to find the lowest common denominator (LCD).• Create equivalent fractions so that the LCD is the new denominator.The lowest common denominator is the lowest multiple shared by a set of denominators.Equivalent fractions are fractions with the same value but different numbers in the numerator and denominator.

... 2 3 4 5 64 6 0 12

1182

... 6 9 1215 20

35 10

Equivalent Fractions

NOT Addingfractions correctly

1 3 42 5 7

35

12

610

510

1110

Adding Fractions that have Unlike Denominators

1110

51102

3 65 10

1110

1= 110

Lowest Common

Denominators

UnlikeDenominators

CFUWhich fractions are ready to be added? Explain your answer.

3 46 6

B 1 22 3

A





Equivalent Fractions

Concept Development (Clarification and CFU)

CFUGiven the list of multiples for 3 and 4 below, what is the LCD of and ?

1 22 3

UnlikeDenominators

: 2, 4, , 8, 10, , 14, 16,6 12 1 .8..2List of Multiples for 2 and 3

2 and 3 share the multiples 6, 12, 18,…

12 63

3 3

Equivalent Fractions: and 1 3 2 42 6 3 6

Finding the Lowest Common Denominator and Equivalent Fractions

: 3, , 9, ,6 12 1 15, ,8 21...3

To add fractions, both fractions must have a common denominator.• If the fractions have unlike denominators, then we need to find the lowest common denominator (LCD).• Create equivalent fractions so that the LCD is the new denominator.The lowest common denominator is the lowest multiple shared by a set of denominators.Equivalent fractions are fractions with the same value but different numbers in the numerator and denominator.

The Lowest Common Denominator is 6

23 62

2 4

13

14

List of Multiples for 3 and 43: 3, 6, 9, 12, 15, 18, 21, 24, ...4: 4, 8, 12, 16, 20, 24, 28, …





1. 2. 3.

4. 5. Sherry bought of a pound of milk

chocolate and of a pound of white

chocolate. How much chocolate does

Sherry have?

6. Tom bought of a pound of jelly

beans and of a pound of gummy

bears. How much candy did he buy?

Skill Development/Guided Practice

Add fractions that have unlike denominators.

Step #1: Read the problem carefully.Step #2: Find the lowest common denominator.

a. Make a list of multiples for each denominator value and identify the first shared multiple.Step #3: Create equivalent fractions using the lowest common denominator.Step #4: Add the new equivalent fractions.

a. Express the answer in simplest form.Step #5: Interpret3 the sum. 3 tell what it means

To add fractions, both fractions must have like denominators.

1

2

1

22

5

1

31

2

5

6

9

10

3

41

2

5

4 She has

pounds of chocolate.

11

4

2

31

5

13

15 He bought

of a pound of candy.

13

15

2

23

3

2

6

3

6

1

22

5

5

52

2

5

10

4

10

1

12

2

3

4

2

4

5

53

3

10

15

3

15

+ +

++

3

41

2

1

5

+ = 3: 3, 6, 9, 122: 2, 4, 6, 8

+ = 5: 5, 10, 15, 202: 2, 4, 6, 8, 10

4: 4, 8, 12, 162: 2, 4, 6, 8,

3: 3, 6, 9, 12, 155: 5, 10, 15, 20

2

3

3

4+

1

12=

1

3

4

81

6

4: 4, 8, 12, 1612: 12, 24, 36, 48

8: 8, 16, 24, 326: 6, 12, 18, 24

10

12

3

41

12

3

31

1

9

12

1

12+

16

24

4

81

6

3

34

4

12

24

4

24+

2

2

5

6

88

2

3

+

11

4

CFU (#2) How did I/you find the lowest common denominator? (#3) How did I/you create equivalent fractions? (#4a) How did I express the sum in simplest form?





Importance

CFUDoes anyone else have another reason as to why it is important to add fractions that have unlike denominators? (pair-share) Why is it important to add fractions that have unlike denominators? You may give me one of my reasons or one of your own. Which reason is more important to you? Why?

1. Adding fractions that have unlike denominators can help you solve real-world problems that use fractions.

2. Adding fractions that have unlike denominators will help you do well on tests.

14

James has eaten of the pie. Erick has eaten of the pie.

Together, they have eaten of the pie.

12

34

1 14 2

1 2 22 2 4

1 2 34 4 4

To add fractions, both fractions must have a common denominator.





Concept Closure

Skill Closure




a. Express the answer in simplest form.Step #5: Interpret the sum.


Summary Closure

__________________________________________________

__________________________________________________

Which of the following problems isready to be added? Explain your answer.

3 1+ =5 6

A 3 1+ =7 7

B

1.

2. Carmen bought of a pound of grapes and

of a pound of nectarines? How many pounds of

fruit did Carmen buy?

1

42

6

7

12Carmen bought of

a pound of fruit.

7

12

3

41

8

7

8

3

3

2

2

3

12

4

12

2

2

1

1

6

8

1

8+

+

1

4

2

63

41

8+ =

4: 4, 8, 12, 168: 8, 16, 24, 32

4: 4, 8, 12, 166: 6, 12, 18, 24

What did you learn today about adding fractions that have unlike denominators?

Day 1 ____________________________________________________________________

Day 2 ____________________________________________________________________





Independent Practice Name _____________________________

1. 2. 3.

4. Josephine bought two gold rings. One

contained of an ounce of gold. The

other one contained of an ounce of

gold. How much gold does she have

altogether?

5. The Smith family bought a pizza.

Jason ate of the pizza and Jamie ate

of the pizza. How much pizza was

eaten?

6. Sam bought of a pound of walnuts

and of a pound of peanuts. How

many pounds of nuts did he buy?

1

4 2

5

5

6

1

3

3

12

2

71

4

15

28 of the pizza was eaten.

15

28

4

4

7

7

8

28

7

28

+

2

7

1

42

5

13

20She has

of an ounce of gold.

13

20

5

5

4

4

5

20

8

20

+

3

63

12

9

12

3

3

He bought

of a pound of nuts.

2

2

1

1

6

12

3

12

3

4 3

4

+

3

63

12

7

8

3

4

1

4

5

61

3

7

6

1

1

2

2

5

6

2

6

+

3

83

12

15

24

3

3

2

2

9

24

6

24

+

7

83

4

13

8

1

1

2

2

7

8

6

8+

+ 6: 6, 12, 18, 243: 3, 6, 9, 12

=

4: 4, 8, 12, 16, 205: 5, 10, 15, 20

3

8+ = 8: 8, 16, 24, 32

12: 12, 24, 36, 48

7: 7, 14, 21, 284: 4, 8, 12, 16, 20, 24, 28

+ =8: 8, 16, 24, 324: 4, 8, 12, 16

6: 6, 12, 18, 2412: 12, 24, 36, 48

51

8

5

8

3

3


11

6









1. 2. 3.

4. Helena bought some vegetables. She

got of a pound of carrots and of a

pound of broccoli. What was the weight

of the vegetables altogether?

5. The Jones family bought a pizza. Eric

ate of the pizza and Herbert ate of

the pizza. How much pizza was eaten?

6. Geoff has of a pound of cashews

and buys of a pound more. How

many pounds of cashews does he have

altogether?

8

24

32

42 of the pizza was eaten.

16

21

6

6

7

7

18

42

14

42

+

3

7

11

24

She has

of a pound of vegetables.

11

24

3

3

4

4

+ 77

72He has pounds of nuts.

8

8

9

9

32

72

45

72

5

172

51

72+

2

6

14

12

2

2

1

1

3

3

11

12

3

12

7 1

16 6

+ 10

12

2

2

2

2

1

1

6

12

4

12

5

6+

37

48

4

4

3

3

28

48

9

48+

1

8

2

6

1

82

6

3

24

3

72

6

4

95

8

4

95

8

11

12

1

4

11

121

4

3

64

12

3

64

12

7

123

16

7

123

16

2

2

+ = 12: 12, 24, 364: 4, 8, 12, 16

+ =

=

+ =6: 6, 12, 18, 24, 12: 12, 24, 36, 48

12: 12, 24, 36, 4816: 16, 32, 48, 64

8: 8, 16, 24, 326: 6, 12, 18, 24

6: 6, 12, 18, 24, 30, 36, 427: 7, 14, 21, 28, 35, 42

9: 9, 18, 27, 36, 45, 54, 63, 728: 8, 16, 24, 32, 40, 48, 56, 64, 72

Periodic Review 1 Name _____________________________To add fractions, both fractions must have a common denominator.









1. 2. 3.

4. Alfredo bought some fruit. He got

of a pound of apples and of a pound

of pears. What was the weight of the

fruit altogether?

5. Juan got a bag of candy. He ate of

the candy. His sister ate of the

candy. How much of the bag of candy

was eaten?

6. Alfred has of a pound of cheese and

buys of a pound more. How many

pounds of cheese does he have

altogether?

1

45

8

4

6

3

8

9

10

1

4

of the candy was eaten.

+7

8

He has

of a pound of fruit.

7

8

2

2

1

1

2

8

5

8

+10

12

2

2

He bought of a pound of cheese.

4

4

1

1

8

12

2

12

5

6

5

6+

2

32

12

4

55

15

3

8

25

24

4

4

3

3

16

24

9

24

1

124

+

23

20

2

2

5

5

18

20

5

20

3

120+

17

15

3

3

1

1

12

15

5

15

2

115

+

1

45

8

2

32

12

4

63

8

9

101

4

4

55

15

+ = + =+ =

4: 4, 8, 12, 168: 8, 16, 24, 32

4: 4, 8, 12, 168: 8, 16, 24, 32,

2

4

2

43

8

2

2

4

8

1

1

3

8

7

8

7

8

3: 3, 6, 9, 1212: 12, 24, 36, 48

6: 6, 12, 18, 248: 8, 16, 24, 32

10: 10, 20 , 30 , 404: 4, 8, 12, 16, 20

5: 10, 15, 20, 2515: 15, 30, 45, 60










1. 2. 3.

4. Alice bought some beans. She got

of a pound of lima beans and of a

pound of pinto beans. What was the

weight of the beans altogether?

5. Alex is making some punch. It will

take of a cup of juice and of a cup

of soda. How much punch will he have

altogether?

6. Arnold has of a pound of cashews

and buys of a pound more. How

many pounds of cashews does he have

altogether?

2

5

11

16

He will have of a cup of punch.

11

16

1

1

2

2

5

16

6

16

+

26

40

She has of a pound of beans.1320

5

5

8

8

10

40

16

40

+

27

24

He bought pounds of nuts.

4

4

3

3

12

24

15

24

11

8

11

8

+

14

12

2

2

1

1

3

3

11

12

3

12

1

16

+ 10

10

10

10

2

2

1

1

6

10

4

10

11

1 +

8

12

4

4

1

1

3

3

5

12

3

12

2

3+

2

82

5

5

163

8

3

65

8

2

8 5

16

3

8

3

65

8

11

121

4

11

12

1

4

3

54

10

3

5

5

121

4

5

121

4

+ = + =4

10+ =12: 12, 24, 36, 484: 4, 8, 12, 16

5: 5, 10, 15, 2010: 10, 20, 30, 40

12: 12, 24, 36, 484: 4, 8, 12, 16

8: 8, 16, 24, 32, 405: 5, 10, 15, 20, 25, 30, 35, 40

16: 16, 328: 8, 16, 24, 32

6: 6, 12, 18, 248: 8, 16, 24, 32

13

20


3

3

9

8

7

6

2

2









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First five multiples of the numbers 2 through 20. Creating Equivalent (equal) Fractions





Denominators

must be the same to add fractions.

Original ProblemProblem re-written with new

equivalent fractions.

Documents

5 th Grade Number Sense 2.3 (5Q) Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions