Tier 2 Mathematics Intervention
Module: Building, Comparing, & Ordering Fractions (BCOF)
Teacher Display Masters
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency
ESTARINTERVENTION
Mathematics Institute for Learning Disabilities and Difficulties
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 1
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 2
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 3
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 4
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 5
Module BCOF Lesson 1 Practice
Use fraction bars to help solve.
1.) 1 sandwich shared equally with 4 friends. How much of the sandwich does each friend get?
Equal share:
Draw the equal share.
2.) 1 apple is shared equally with 2 friends. How much does each friend get?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 6
Module BCOF Lesson 1 Practice
3.) Natalie, Javier, and Andrea want to share 1 brownie equally. Natalie divided the brownie, shown below, and said it was equal because they got a piece. Is she correct? Why or why not?
Is she correct?
Why or why not?
Divide the rectangle to show an equal share.
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 7
Module BCOF Lesson 1
Practice Key
Use fraction bars to help solve.
1.) 1 sandwich shared equally with 4 friends. How much of the sandwich does each friend get?
Equal share:
Draw the equal share.
2.) 1 apple is shared equally with 2 friends. How much does each friend get?
Equal share: one-half or of an apple
one-fourth or of a sandwich
21
41
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 8
Module BCOF Lesson 1
Practice Key
3.) Natalie, Javier, and Andrea want to share 1 brownie equally. Natalie divided the brownie, shown below, and said it was equal because they got a piece. Is she correct? Why or why not?
Is she correct?
Why or why not?
Divide the rectangle to show an equal share.
Equal share:
bigger and 1 piece is smaller.
The pieces are not equal, 1 piece is
one-third or of a brownie
No, she is not correct.
31
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 9
Module BCOF Lesson 1
Independent Practice
Write a fraction to represent the shaded amount for each whole.
1.)
2.)
Look at the model below.
3.) Which statement is true?
A There are no equal parts.
B There are 5 equal parts.
C There are 6 equal parts.
D Each part is .
Use fraction bar models to help solve.
4.) 1 sandwich was shared equally with 6 friends. How much does each friend get?
6
Equal share:
17
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Module BCOF Lesson 1
Independent Practice
5.) 1 sheet of paper was shared equally with 5 students. How much of the sheet of paper should each student get?
Choose the best answer.
6.) 1 loaf of bread was shared equally with 8 people. How much bread each person got.
A 8 loaves of bread
B one-eighth of a loaf of bread
C one-sixth of a loaf of bread
D of a loaf of bread
Equal share:
81
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 11
Write a fraction to represent the shaded amount for each whole.
1.)
2.)
Look at the model below.
3.) Which statement is true?
A There are no equal parts.
B There are 5 equal parts.
C There are 6 equal parts.
D Each part is .
Use fraction bar models to help solve.
4.) 1 sandwich was shared equally with 6 friends. How much does each friend get?
17
6
Equal share:
Module BCOF Lesson 1
Independent Practice Key
21
32
one-sixth or of a sandwich61
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5.) 1 sheet of paper was shared equally with 5 students. How much of the sheet of paper should each student get?
Choose the best answer.
6.) 1 loaf of bread was shared equally with 8 people. How much bread each person got.
A 8 loaves of bread
B one-eighth of a loaf of bread
C one-sixth of a loaf of bread
D of a loaf of bread
Equal share:
81
Module BCOF Lesson 1
Independent Practice Key
one-fifth or of a sheet of paper51
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 13
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 14
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Module BCOF Lesson 2 Practice
Use fraction bars or the picture to help solve.
1.) 8 friends share 2 bananas equally. How much of a banana does each friend get?
2.) 3 sandwiches shared equally with 5 students. How much of a sandwich does each student get?
Equal share:
Equal share:
sandwiches
students
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 16
Use fraction bars or the picture to help solve.
1.) 8 friends share 2 bananas equally. How much of a banana does each friend get?
2.) 3 sandwiches shared equally with 5 students. How much of a sandwich does each student get?
Equal share:
Equal share:
sandwiches
students
Module BCOF Lesson 2
Practice Key
two-eighths or of a banana
three-fifths or of a sandwich
82
53
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 17
Module BCOF Lesson 2
Independent Practice6
1.) Cut the loaf of bread to share between 8 friends.
2.) What fraction of the bread does each friend get?
3.) 12 students share 1 large sheet of paper. Choose the answer that shows how much of the sheet of paper each student receives.
A 12 C
111
B 1 D
112
Use the picture to solve.
4.) 6 students share 3 candy bars equally. How much does each student get?
Equal share:
candy bars
students
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Module BCOF Lesson 2
Independent Practice
Choose the correct answer.
6.) 4 friends share 3 hot dogs equally. Which model shows 1 friend’s equal share?
A
B
C
D
5.) 2 ice cream bars were shared equally between 3 friends. How much did each friend get?
Equal share:
ice cream bars
friends
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 19
1.) Cut the loaf of bread to share between 8 friends.
2.) What fraction of the bread does each friend get?
3.) 12 students share 1 large sheet of paper. Choose the answer that shows how much of the sheet of paper each student receives.
A 12 C
111
B 1 D
112
Use the picture to solve.
4.) 6 students share 3 candy bars equally. How much does each student get?
Equal share:
candy bars
students
6Module BCOF
Lesson 2 Independent Practice Key
one-half or of an ice cream bar21
81
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 20
Choose the correct answer.
6.) 4 friends share 3 hot dogs equally. Which model shows 1 friend’s equal share?
A
B
C
D
5.) 2 ice cream bars were shared equally between 3 friends. How much did each friend get?
Equal share:
ice cream bars
friends
Module BCOF Lesson 2
Independent Practice Key
two-third or of an ice cream bar32
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 21
Module BCOF Lesson 3
Engaged Practice
Kathy has 5 mini pies and 7 friends to share with. If Kathy gives an equal share to herself and her friends, what portion of a whole pie will each person receive?
Friend’s equal share:
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Friend’s equal share:
Kathy has 5 mini pies and 7 friends to share with. If Kathy gives an equal share to herself and her friends, what portion of a whole pie will each person receive?
Module BCOF Lesson 3
Engaged Practice Key
of a pie85
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 23
Mo
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Equ
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 25
Module BCOF Lesson 3 Practice
1.) 3 children share 3 sandwiches equally: 1 turkey, 1 ham, and 1 roast beef. Draw a picture to show how much sandwich each child gets.
2.) Ann Marie and Sara each have some cake. Ann Marie has three-thirds of a cake. Sara has 1 cake. Does Ann Marie have more cake than Sara? Draw a picture to show your answer.
Equal share:
Does Ann Marie have more cake?
Why?
Ann Marie Sara
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 26
Module BCOF Lesson 3
Practice Key
1.) 3 children share 3 sandwiches equally: 1 turkey, 1 ham, and 1 roast beef. Draw a picture to show how much sandwich each child gets.
2.) Ann Marie and Sara each have some cake. Ann Marie has three-thirds of a cake. Sara has 1 cake. Does Ann Marie have more cake than Sara? Draw a picture to show your answer.
Equal share:
Does Ann Marie have more cake?
Why?
Ann Marie Sara
No
equals 1 whole
three-thirds or or 1 whole sandwich
student
33
33
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 27
Module BCOF Lesson 3
Independent Practice
Choose the correct answer.
1.) 3 friends share a pizza equally. Which model represents equal shares?
2.) Mr. Smith would like to share a meatloaf between 9 family members. How much of the whole meatloaf does each family member get?
A 1
B
19
C 18
D 9
3.) 7 people shared 1 large brownie. How much brownie does each person receive?
A 7
B 1
C
17
D
18
4.) Divide the rectangles into fourths.
A B C D
7
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 28
Module BCOF Lesson 3
Independent Practice
Draw a picture to solve.
5.) 2 chocolate bars were shared equally between 2 friends. How much does each friend get?
Equal share:
6.) 6 taffy sticks shared equally between 6 friends. How much does each friend get? Use the space below to draw 1 friend’s equal share.
Equal share:
7.) Select the answer that does NOT show 1 whole.
A 44 C
78
B
D
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Module BCOF Lesson 3
Independent Practice Key7
Choose the correct answer.
1.) 3 friends share a pizza equally. Which model represents equal shares?
2.) Mr. Smith would like to share a meatloaf between 9 family members. How much of the whole meatloaf does each family member get?
A 1
B
19
C 18
D 9
3.) 7 people shared 1 large brownie. How much brownie does each person receive?
A 7
B 1
C
17
D
18
4.) Divide the rectangles into fourths.
A B C D
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 30
Module BCOF Lesson 3
Independent Practice Key
Draw a picture to solve.
5.) 2 chocolate bars were shared equally between 2 friends. How much does each friend get?
Equal share:
6.) 6 taffy sticks shared equally between 6 friends. How much does each friend get? Use the space below to draw 1 friend’s equal share.
Equal share:
7.) Select the answer that does NOT show 1 whole.
A 44 C
78
B
D
1 whole bar or of a bar
1 whole stick or of a bar
chocolate bars
1 friend
22
66
taffy sticks
1 friend
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 31
Module BCOF Lesson 4
Engaged Practice
Read the story and draw a picture of the equal share.
1.) 1 cupcake shared equally among 4 friends.
Equal share:
2.) 5 apples shared equally among 6 people.
Equal share:
3.) 4 cheese sticks shared equally among 8 children.
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 32
Module BCOF Lesson 4
Engaged Practice Key
Read the story and then, draw a picture of the equal share.
1.) 1 cupcake shared equally among 4 friends.
Equal share:
2.) 5 apples shared equally among 6 people.
Equal share:
3.) 4 cheese sticks shared equally among 8 children.
Equal share:
of a cupcake
of an apple
or of a cheese stick
41
65
21
84
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 33
Module BCOF Lesson 4
Modeled Practice #1
4 bars of clay are shared equally among 3 students. How much clay did each student receive?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 34
Module BCOF Lesson 4
Modeled Practice #2
4 different colored bars of clay are shared equally among 3 students so that each student receives the same amount of each color. What portion of the 4 clay bars does each student get?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 35
Module BCOF Lesson 4
Modeled Practice #3
6 sticks of taffy are shared equally with 4 children. How much will each child receive?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 36
4 bars of clay are shared equally among 3 students. How much clay did each student receive?
Equal share:
Module BCOF Lesson 4
Modeled Practice #1 Key
one and one-third or 1 bars of clay31
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 37
4 different colored bars of clay are shared equally among 3 students so that each student receives the same amount of each color. What portion of the 4 clay bars does each student get?
Equal share:
Module BCOF Lesson 4
Modeled Practice #2 Key
four-thirds or bars of clay34
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 38
6 sticks of taffy are shared equally with 4 children. How much will each child receive?
Equal share:
Module BCOF Lesson 4
Modeled Practice #3 Key
six-fourths or or 1 of sticks of taffy46
42
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 39
Module BCOF Lesson 4 Practice
Draw the equal share for 1 person.
1.) 3 sandwiches were shared equally between 2 people. How much did each person get?
Equal share:
2.) 5 hot dogs were shared equally among 3 students so that each student received the same amount. How much of the hot dogs did each student receive?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 40
Module BCOF Lesson 4
Practice Key
Draw the equal share for 1 person.
1.) 3 sandwiches were shared equally between 2 people. How much did each person get?
Equal share:
2.) 5 hot dogs were shared equally among 3 students so that each student received the same amount. How much of the hot dogs did each student receive?
Equal share:
or 1 of hot dogs32
35
or 1 of a sandwich21
23
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 41
Module BCOF Lesson 4
Independent Practice6
Choose the correct answer.
1.) Which fraction is equivalent to 1 whole.
A
510 C
110
B
910 D
1010
2.) Which picture represents equal shares?
A
B
C
D
Draw pictures to represent the equal share.
3.) 2 containers of clay shared equally among 4 students.
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 42
Module BCOF Lesson 4
Independent Practice
Draw pictures to represent the equal share.
4.) 6 bars of clay shared equally among 4 students. How much does each student get?
Equal share:
5.) 7 candy bars shared equally among 6 friends. How much does each friend get?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 43
Module BCOF Lesson 4
Independent Practice
Choose the correct answer.
6.) 12 licorice ropes shared equally among 7 friends. Which shows how much each student gets?
A
B
C
D
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 44
Module BCOF Lesson 4
Independent Practice Key6
Choose the correct answer.
1.) Which fraction is equivalent to 1 whole.
A
510 C
110
B
910 D
1010
2.) Which picture represents equal shares?
A
B
C
D
Draw pictures to represent the equal share.
3.) 2 containers of clay shared equally among 4 students.
Equal share: or of clay21
42
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 45
Module BCOF Lesson 4
Independent Practice Key
Draw pictures to represent the equal share.
4.) 6 bars of clay shared equally among 4 students. How much does each student get?
Equal share:
5.) 7 candy bars shared equally among 6 friends. How much does each friend get?
Equal share: or 1 candy bars61
67
or 1 or 1 bars of clay62
21
64
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 46
Module BCOF Lesson 4
Independent Practice Key
Choose the correct answer.
6.) 12 licorice ropes shared equally among 7 friends. Which shows how much each student gets?
A
B
C
D
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 47
Module BCOF Lesson 5
Engaged Practice
Match the scenario with the equal share picture.
1.) 2 pieces of gum shared equally between 3 friends. How much is each friend’s equal share?
A
B
C
D
2.) 3 cookies are shared equally by 2 friends. How much of the cookies does each friend get?
3.) There are 5 pieces of colored ribbon. 3 sisters equally share the pieces of ribbon. What is 1 sister’s equal share?
4.) 6 popcorn balls are shared equally between 4 family members. How much of a popcorn ball does each family member receive?
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 48
Module BCOF Lesson 5
Engaged Practice Key
Match the scenario with the equal share picture.
1.) 2 pieces of gum shared equally between 3 friends. How much is each friend’s equal share?
A
B
C
D
2.) 3 cookies are shared equally by 2 friends. How much of the cookies does each friend get?
3.) There are 5 pieces of colored ribbon. 3 sisters equally share the pieces of ribbon. What is 1 sister’s equal share?
4.) 6 popcorn balls are shared equally between 4 family members. How much of a popcorn ball does each family member receive?
C
D
A
B
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 49
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 50
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 51
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 52
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 53
Module BCOF Lesson 5 Practice
Draw a picture and write the addition equation.
1.) 5 chocolate bars are being shared by 4 friends, so each gets the same amount. How many chocolate bars does each friend get?
Equal share:
Equation:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 54
Module BCOF Lesson 5
Practice Key
Draw a picture and write the addition equation.
1.) 5 chocolate bars are being shared by 4 friends, so each gets the same amount. How many chocolate bars does each friend get?
Equal share:
Equation:
or 1 chocolate bars41
41
41
41
41
41
45
45
+ + + + =
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 55
Module BCOF Lesson 5
Independent Practice
1.) Divide the squares into thirds.
Choose the best answer.
2.) 11 children attended the birthday party. The children ate the whole birthday cake. Each child received the same amount of cake. How much birthday cake did each child receive?
A
111
B 11 C 1 D
211
3.) Look at the model below.
Which statement is true?
A Each part is .
B Each part is .
C Each part is half.
D Each part is unequal.
14
13
6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 56
Module BCOF Lesson 5
Independent Practice
Draw a picture and write the addition equation.
4.) 6 chocolate bars shared equally among 4 friends. How many chocolate bars does each friend get?
5.) 5 brownies shared equally among 3 friends. How many brownies does each friend get?
Equal share:
Equation:
Equal share:
Equation:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 57
Module BCOF Lesson 5
Independent Practice
Choose the best answer.
6.) 5 people share 6 candy bars equally. Which is the correct addition sentence for the equal share?
A 15 + 1
5 + 15 + 1
5 + 15 = 5
25
B
16 + 1
6 + 16 + 1
6 + 16 = 5
6
C 15 + 1
5 + 15 + 1
5 + 15 + 1
5 = 65
D 15 + 1
5 + 15 + 1
5 + 15 + 1
5 + 15 = 7
35
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 58
1.) Divide the squares into thirds.
Choose the best answer.
2.) 11 children attended the birthday party. The children ate the whole birthday cake. Each child received the same amount of cake. How much birthday cake did each child receive?
A
111
B 11 C 1 D
211
3.) Look at the model below.
Which statement is true?
A Each part is .
B Each part is .
C Each part is half.
D Each part is unequal.
14
13
6Module BCOF
Lesson 5 Independent Practice Key
accept other reasonable divisions
or
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 59
Draw a picture and write the addition equation.
4.) 6 chocolate bars shared equally among 4 friends. How many chocolate bars does each friend get?
5.) 5 brownies shared equally among 3 friends. How many brownies does each friend get?
Equal share:
Equation:
Equal share:
Equation:
Module BCOF Lesson 5
Independent Practice Key
six-fourths or or one and two-fourths or 1 42
41
41
41
41
41
46
41
46
+ + + + =+
or 1 32
31
31
31
31
31
35
35
+ + + + =
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 60
Choose the best answer.
6.) 5 people share 6 candy bars equally. Which is the correct addition sentence for the equal share?
A 15 + 1
5 + 15 + 1
5 + 15 = 5
25
B
16 + 1
6 + 16 + 1
6 + 16 = 5
6
C 15 + 1
5 + 15 + 1
5 + 15 + 1
5 = 65
D 15 + 1
5 + 15 + 1
5 + 15 + 1
5 + 15 = 7
35
Module BCOF Lesson 5
Independent Practice Key
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 61
Module BCOF Lesson 6
Modeled Practice
Marcia ordered a sandwich, but only ate half. The next day, she decided to share the remaining half of her sandwich. She cut the half of the sandwich into thirds to share with her 2 friends and herself. What portion of the whole sandwich did Marcia’s friends receive?
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 62
Module BCOF Lesson 6
Modeled Practice Key
Marcia ordered a sandwich, but only ate half. The next day, she decided to share the remaining half of her sandwich. She cut the half of the sandwich into thirds to share with her 2 friends and herself. What portion of the whole sandwich did Marcia’s friends receive?
21
61
61
61
61+ ++ = 1 whole sandwich
of a sandwich
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 63
Module BCOF Lesson 6 Practice
Use fraction bars to find the answer.
1.) Rachel divided the sandwich using fifths. Can you divide the same sandwich using sixths?
Your sandwich
Rachel = Your sandwich=
2.) Thomas wants to share half of his sandwich using fourth-sized pieces. How
many pieces does he have to share?
Write an equation to show the pieces equal to 1 whole sandwich.
12
+
5 6=
6= 1
5= 1
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 64
Module BCOF Lesson 6
Practice Key
Use fraction bars to find the answer.
1.) Rachel divided the sandwich using fifths. Can you divide the same sandwich using sixths?
Your sandwich
Rachel = Your sandwich=
2.) Thomas wants to share half of his sandwich using fourth-sized pieces. How
many pieces does he have to share?
Write an equation to show the pieces equal to 1 whole sandwich.
12
+
5 6=
6= 1
5= 15 56 6
2 pieces
41 1 whole sandwich
41 =+
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 65
Module BCOF Lesson 6
Independent Practice7
Draw a picture and write the addition equation.
1.) 5 granola bars were shared equally among 3 hikers. How much of a granola bar did each hiker get?
Equal share:
Equation:
2.) 10 ounces of water shared equally among 4 hikers. How many ounces did each hiker get?
Equal share:
Equation:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 66
Module BCOF Lesson 6
Independent Practice
3.) Which addition sentence represents the model below?
A 34
B 34 + 3
4 + 34
C 14 + 1
4 + 14
D 14 + 1
4 + 14 + 1
4
4.) What equal share does the shaded portion of the model below represent?
of a sandwich
5.) How can a whole sandwich be divided equally using one-sixth pieces?
Write the addition equation.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 67
Module BCOF Lesson 6
Independent Practice
6.) Anita wants to share one-half of her sandwich using one-eighth pieces.
How many pieces will she have?
Write the addition sentence to show the pieces equal to 1 whole sandwich.
Choose the correct answer.
7.) Which the addition expression represents the model?
A 12 + 1
8 + 18 + 1
8 + 18
B 18 + 1
8 + 18 + 1
8
C 12 + 1
4 + 14 + 1
4 + 14
D 15 + 1
5 + 15 + 1
5 + 15
12
+
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 68
Module BCOF Lesson 6
Independent Practice Key7
Draw a picture and write the addition equation.
1.) 5 granola bars were shared equally among 3 hikers. How much of a granola bar did each hiker get?
Equal share:
Equation:
2.) 10 ounces of water shared equally among 4 hikers. How many ounces did each hiker get?
Equal share:
Equation:
or 1 granola bars32
31
31
31
31
31
35
35
+ + + + =
2 or 2 or ounces of water21
410
41
41
41
41
41
41
41
41
41
41
410
42
+ + ++ ++ ++ =+ =412
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 69
Module BCOF Lesson 6
Independent Practice Key
3.) Which addition sentence represents the model below?
A 34
B 34 + 3
4 + 34
C 14 + 1
4 + 14
D 14 + 1
4 + 14 + 1
4
4.) What equal share does the shaded portion of the model below represent?
of a sandwich
5.) How can a whole sandwich be divided equally using one-sixth pieces?
Write the addition equation. 61
61
61
61
61
61
66
61+ + + ++ = == =
34
31
or 1
11
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 70
Module BCOF Lesson 6
Independent Practice Key
6.) Anita wants to share one-half of her sandwich using one-eighth pieces.
How many pieces will she have?
Write the addition sentence to show the pieces equal to 1 whole sandwich.
Choose the correct answer.
7.) Which the addition expression represents the model?
A 12 + 1
8 + 18 + 1
8 + 18
B 18 + 1
8 + 18 + 1
8
C 12 + 1
4 + 14 + 1
4 + 14
D 15 + 1
5 + 15 + 1
5 + 15
12
+ 81
81
81
81+ + + = 1 whole sandwich
8 pieces
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 71
Mo
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 72
Mo
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12
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4445
2123
4246
4843
4741
or 1
21
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 73
Module BCOF Lesson 7
Modeled Practice #1
3 sandwiches are shared equally among 8 students. What portion of a sandwich does each student get?
Equal share:
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 74
Module BCOF Lesson 7
Modeled Practice #2
5 feet of rope needs to be cut into 3 equal pieces. What is the length of each part?
Equal share:
1 20
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Module BCOF Lesson 7
Modeled Practice #1 Key
3 sandwiches are shared equally among 8 students. What portion of a sandwich does each student get?
Equal share: of a sandwich83
10
82
83
81
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 76
Module BCOF Lesson 7
Modeled Practice #2 Key
5 feet of rope needs to be cut into 3 equal pieces. What is the length of each part?
Equal share: or 1 feet of rope32
35
33
30
36
1 20
31
32
34
35
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Use the fraction bar and the number line to show the equal shares.
1.) The race was 3 miles long. There were 4 water stops equally spaced along the race. How far apart was each water stop?
Does her model represent the correct equal share? If not, draw the correct number line below
2.) Rachel and Sydney want to share 3 sandwiches equally. Sydney drew the number line to repesent the amount each girl would receive.
Equal share:
1 20
3
1
3
2 10
10
Module BCOF Lesson 7 Practice
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 78
Use the fraction bar and the number line to show the equal shares.
1.) The race was 3 miles long. There were 4 water stops equally spaced along the race. How far apart was each water stop?
Does her model represent the correct equal share? If not, draw the correct number line below
2.) Rachel and Sydney want to share 3 sandwiches equally. Sydney drew the number line to repesent the amount each girl would receive.
Equal share:
3
1
3
2 10
Module BCOF Lesson 7
Practice Key
of a mile
No
43
21
22
20
23
24
1 20
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 79
Module BCOF Lesson 7
Independent Practice7
Choose the best answer.
1.) Which fraction is the same as 1 whole?
A
33
B 11 C
13 D
14
2.) Which of the following models does not represent 1 whole?
D
CA
B
Find the equal share.
3.) What fraction is missing from the number line?
10
A
13
B 2 C
14 D
12
4.) 2 celery stalks shared equally among 8 friends. How much does each friend get?
Equal share:
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 80
Module BCOF Lesson 7
Independent Practice
6.) 6 licorice ropes shared equally with 4 friends. How much does each friend get?
Equal share:
5.) 4 sandwiches shared equally among 8 students. How much does each student get?
Equal share:
1 20
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 81
Module BCOF Lesson 7
Independent Practice
Choose the correct answer.
7.) Which number line shows an equal share when 3 sandwiches are shared equally with 4 people?
A
4
1
4
2
4
3
4
4 4
51 20
B
4
1
4
2
4
3 10
C
3
1
3
2
3
3 3
41 20
D
3
1
3
2 10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 82
7Module BCOF
Lesson 7 Independent Practice Key
Choose the best answer.
1.) Which fraction is the same as 1 whole?
A
33
B 11 C
13 D
14
2.) Which of the following models does not represent 1 whole?
D
CA
B
Find the equal share.
3.) What fraction is missing from the number line?
10
A
13
B 2 C
14 D
12
4.) 2 celery stalks shared equally among 8 friends. How much does each friend get?
Equal share: or of a celery stalk41
82
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 83
Module BCOF Lesson 7
Independent Practice Key
6.) 6 licorice ropes shared equally with 4 friends. How much does each friend get?
Equal share:
5.) 4 sandwiches shared equally among 8 students. How much does each student get?
Equal share: or of a sandwich84
21
or 1 of licorice rope42
46
41
45
42
46
40
43
47
44
48
1 20
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 84
Module BCOF Lesson 7
Independent Practice Key
Choose the correct answer.
7.) Which number line shows an equal share when 3 sandwiches are shared equally with 4 people?
A
4
1
4
2
4
3
4
4 4
51 20
B
4
1
4
2
4
3 10
C
3
1
3
2
3
3 3
41 20
D
3
1
3
2 10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 85
Module BCOF Lesson 8
Engaged Practice
0 1
0 1
0 1
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Module BCOF Lesson 8
Engaged Practice Key
0 1
0 1
0 1
33
30 3
132
55
50 5
251
54
53
44
40 4
142
43
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 87
Jaso
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. Wh
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 88
Mo
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Jaso
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The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 89
Module BCOF Lesson 8 Practice
Place each fraction on the number line.
1.) Divide the number line into fourths. Shade
4
1
of the line.
1 20
2.) Divide the number line into eights. Shade 18
1
of the line.
1 20
3.) Shade 5
2
of the line.
1 20
4.) Shade 16
4
of the line.
1 20
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 90
Choose the correct answer.
5.) Which number line is shaded to represent 5 sandwiches shared equally with 4 people?
A
15
4 20
B
14
1 20
C
1
5
21
20
D
1
4
11
20
Module BCOF Lesson 8 Practice
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 91
Module BCOF Lesson 8
Practice Key
Place each fraction on the number line.
1.) Divide the number line into fourths. Shade
4
1
of the line.
2.) Divide the number line into eights. Shade 18
1
of the line.
3.) Shade 5
2
of the line.
4.) Shade 16
4
of the line.
1 20
1 20
1 20
1 20
41
81
51
61
85
65
42
82
52
62
86
66
40
80
50
60
43
83
63
87
84
64
88
811
611 6
31621 6
41
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 92
Module BCOF Lesson 8
Practice Key
Choose the correct answer.
5.) Which number line is shaded to represent 5 sandwiches shared equally with 4 people?
A
15
4 20
B
14
1 20
C
1
5
21
20
D
1
4
11
20
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 93
Module BCOF Lesson 8
Independent Practice7
Use the fraction bars to find the equal share.
1.) 4 people share 5 pieces of fabric. How much will each person get?
Equal share:
2.) 4 pizzas shared equally with 3 friends. How much pizza does each friend get?
A 3
4 or 1 3
1 B 4
3 C 3 D 2
1
3.) Which equation represents the shaded portion in the model below?
A 51
+ 51
= 102
B 1 + 1 = 510
C 61
+ 61
+ 61
= 63
D 61
+ 61
= 62
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 94
Module BCOF Lesson 8
Independent Practice
6.) Divide the number line into fourths. Shade 1 4
3
.
1 20
1 20
Divide the number line into thirds.
5.) Shade 3
2
.
4.) Divide the number line into the fifths. Shade 5
2
.
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 95
Choose the best answer.
7.) Which number line shows an equal share of 3 sandwiches equally shared between 4 people?
A
8
71 20
B
4
3 1 20
C
3
41 20
D
4
1 1 20
Module BCOF Lesson 8
Independent Practice
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 96
7Module BCOF
Lesson 8 Independent Practice Key
Use the fraction bars to find the equal share.
1.) 4 people share 5 pieces of fabric. How much will each person get?
Equal share:
2.) 4 pizzas shared equally with 3 friends. How much pizza does each friend get?
A 3
4 or 1 3
1 B 4
3 C 3 D 2
1
3.) Which equation represents the shaded portion in the model below?
A 51
+ 51
= 102
B 1 + 1 = 510
C 61
+ 61
+ 61
= 63
D 61
+ 61
= 62
1 pieces of fabric41
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 97
Module BCOF Lesson 8
Independent Practice Key
6.) Divide the number line into fourths. Shade 1 4
3
.
Divide the number line into thirds.
5.) Shade 3
2
.
4.) Divide the number line into the fifths. Shade 5
2
.
1 20
51
41
54
52
42
55
40
50
53
43
441 20
1 1 1
10
31
32
41
42
43
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 98
Module BCOF Lesson 8
Independent Practice Key
Choose the best answer.
7.) Which numberline shows an equal share of 3 sandwiches equally shared between 4 people?
A
8
71 20
B
4
3 1 20
C
3
41 20
D
4
1 1 20
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 99
Module BCOF Lesson 9
Engaged Practice
Draw a line to match the fractions to the model or words.
32
• • four-fifths
one-half • • 43
85
• •
three-fourths • • two-thirds
• •
• • one-sixth
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 100
Module BCOF Lesson 9
Engaged Practice Key
Draw a line to match the fractions to the model or words.
32
• • four-fifths
one-half • • 43
85
• •
three-fourths • • two-thirds
• •
• • one-sixth
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 101
Mo
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= =
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 102
Mo
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Equ
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3131
31
32
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32
6161
61
646161
64
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 103
Module BCOF Lesson 9 Practice
Shade the equivalent fractions.
1.) What fraction is equivalent to 31
that has 6 as a denominator?
Shade the amounts below.
3
1=
6=
2.) What fraction is equivalent to 43
that has 8 as a denominator?
Shade the amounts below.
4
3=
8=
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Use your flipbook to find the answer.
3.) Amanda and Jonathon are working on a fraction assignment. Amanda thinks that there are many fractions equivalent to one-half. Jonathon disagrees. Is Amanda or Jonathon correct? Defend your answer using drawings or the flipbook.
Module BCOF Lesson 9 Practice
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 105
Module BCOF Lesson 9
Practice Key
Shade the equivalent fractions.
1.) What fraction is equivalent to 31
that has 6 as a denominator?
Shade the amounts below.
2.) What fraction is equivalent to 43
that has 8 as a denominator?
Shade the amounts below.
4
3=
8=
3
1=
6=
6
2
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Use your flipbook to find the answer.
3.) Amanda and Jonathon are working on a fraction assignment. Amanda thinks that there are many fractions equivalent to one-half. Jonathon disagrees. Is Amanda or Jonathon correct? Defend your answer using drawings or the flipbook.
Module BCOF Lesson 9
Practice Key
21
42
63
84
105
126= = = = =
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Module BCOF Lesson 9
Independent Practice6
Choose the best answer.
1.) Which equation describes the model below?
A 21
+ 81
+ 81
+ 81
+ 81
= 1 whole
B 41
+ 41
+ 41
+ 41
= 1 whole
C 21
+ 61
+ 61
+ 61
= 1 whole
D 31
+ 61
+ 61
+ 61
= 1 whole
2.) What equal share does the shaded model below represent?
of a sandwich
3.) Draw a model to show the equal share when 3 sandwiches are shared equally with 4 friends.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 108
Module BCOF Lesson 9
Independent Practice
Shade the equivalent fractions.
4.) What fraction is equivalent to 65
that has 12 in the denominator?
Shade the amounts below.
6
5=
12=
5.) What fraction is equivalent to 52
that has 10 in the denominator?
Shade the amounts below.
5
2=
10=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 109
Module BCOF Lesson 9
Independent Practice
Choose the best answer.
6.) Which fraction is equivalent to 43
that has 12 as a denominator?
4
3=
12=
A 1211
B 1612
C 1312
D 129
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Module BCOF Lesson 9
Independent Practice Key6
Choose the best answer.
1.) Which equation describes the model below?
A 21
+ 81
+ 81
+ 81
+ 81
= 1 whole
B 41
+ 41
+ 41
+ 41
= 1 whole
C 21
+ 61
+ 61
+ 61
= 1 whole
D 31
+ 61
+ 61
+ 61
= 1 whole
2.) What equal share does the shaded model below represent?
of a sandwich
3.) Draw a model to show the equal share when 3 sandwiches are shared equally with 4 friends.
64
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 111
Module BCOF Lesson 9
Independent Practice Key
Shade the equivalent fractions.
4.) What fraction is equivalent to 65
that has 12 in the denominator?
Shade the amounts below.
6
5=
12=
5.) What fraction is equivalent to 52
that has 10 in the denominator?
Shade the amounts below.
5
2=
10=
4
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 112
Module BCOF Lesson 9
Independent Practice Key
Choose the best answer.
6.) Which fraction is equivalent to 43
that has 12 as a denominator?
4
3=
12=
A 1211
B 1612
C 1312
D 129
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 113
Module BCOF Lesson 10
Engaged Practice
Shade the equivalent fractions.
Which fraction is equivalent to 41
that has 8 in the denominator?
Shade the amounts below.
4
1=
8=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 114
Module BCOF Lesson 10
Engaged Practice Key
Shade the equivalent fractions.
Which fraction is equivalent to 41
that has 8 in the denominator?
Shade the amounts below.
4
1=
8=
2
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Mo
dul
e BC
OF
Less
on
10
Mo
del
ed P
ract
ice
#1
Equ
iva
len
t Fr
ac
tion
s:=
Ton
y h
as
of
a c
an
dy
ba
r. Je
ssic
a h
as
o
f a
ca
nd
y b
ar.
Wh
o h
as
the
gre
ate
st p
ort
ion
of
a c
an
dy
ba
r?
4386
10
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 116
Mo
dul
e BC
OF
Less
on
10
Mo
del
ed P
ract
ice
#2
Equ
iva
len
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ac
tion
s:01
Sho
w t
ha
t 42
of
a b
an
an
a a
nd
84
of
a b
an
an
a a
re t
he
sam
e a
mo
un
t.
=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 117
Mo
dul
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OF
Less
on
10
Mo
del
ed P
ract
ice
#1 K
ey
Equ
iva
len
t Fr
ac
tion
s:=
Ton
y h
as
of
a c
an
dy
ba
r. Je
ssic
a h
as
o
f a
ca
nd
y b
ar.
Wh
o h
as
the
gre
ate
st p
ort
ion
of
a c
an
dy
ba
r?
4386
10
2
4386
8185
8387
8286
84
4142
43
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 118
Mo
dul
e BC
OF
Less
on
10
Mo
del
ed P
ract
ice
#2 K
ey
Sho
w t
ha
t 42
of
a b
an
an
a a
nd
84
of
a b
an
an
a a
re t
he
sam
e a
mo
un
t.
Equ
iva
len
t Fr
ac
tion
s:
1
=
8183
858241
8442
8643
87
4284
0
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 119
Module BCOF Lesson 10
Practice
Shade the fraction bar and divide the number line to show that the fractions are equivalent.
1.) Show that 43
of a sandwich is equivalent to 86
of a sandwich.
2.) Show that 32
of a foot is equivalent to 64
of a foot.
0 1
43
42
41
0 1
32
31
43
86
32
64
List fractions equivalent to 21
.
3.) = = = = =21
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Module BCOF Lesson 10
Practice Key
Shade the fraction bar and divide the number line to show that the fractions are equivalent.
1.) Show that 43
of a sandwich is equivalent to 86
of a sandwich.
2.) Show that 32
of a foot is equivalent to 64
of a foot.
0 1
43
42
41
32
31
43
86
32
64
List fractions equivalent to 21
.
3.) = = = = =21
61
81
63
83
62
82
64
84
65
85
86
87
42
63
84
105
126
0 1
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Module BCOF Lesson 10
Independent Practice6
Choose the best answer.
1.) Which model shows an equal share when 4 sandwiches are shared equally with 3 friends?
A
B
C
D
Write an equation.
2.) Emilie ate half her hamburger and saved the other half. The next day, she shared the half with her sister. Write the equation for the model below.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 122
Module BCOF Lesson 10
Independent Practice
A 63 B 6
4 C 65 D 6
2
5
1
0 1
54
53
52
51
10
2
Shade the fraction bars.
4.) Show that 51
of a candy bar is equivalent to 102
of a candy bar.
Choose the best answer.
3.) Shade the fraction to find the equivalent fraction to 43
.
3
2=
6=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 123
Module BCOF Lesson 10
Independent Practice
Divide and shade the number line.
5.) Show that 63
of a candy bar is equivalent to 126
of a candy bar.
0 1
64
65
62
63
61
Choose the best answer.
6.) Which number line shows 52
is equivalent to 104
.
A
10
B
10
C
10
D 10
63
126
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 124
Module BCOF Lesson 10
Independent Practice Key6
Choose the best answer.
1.) Which model shows an equal share when 4 sandwiches are shared equally with 3 friends?
A
B
C
D
Write an equation.
2.) Emilie ate half her hamburger and saved the other half. The next day, she shared the half with her sister. Write the equation for the model below.
21
41
41+ +=1 whole
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 125
Module BCOF Lesson 10
Independent Practice Key
Choose the best answer.
3.) Shade the fraction to find the equivalent fraction to 43
.
A 63 B 6
4 C 65 D 6
2
Shade the fraction bars.
4.) Show that 51
of a candy bar is equivalent to 102
of a candy bar.
5
1
10
2
0 1
54
53
52
51
3
2=
6=
101
104
102
105
103
106
108
107
109
4
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 126
Module BCOF Lesson 10
Independent Practice Key
Divide and shade the number line.
5.) Show that 63
of a candy bar is equivalent to 126
of a candy bar.
0 1
64
65
62
63
61
63
126
Choose the best answer.
6.) Which number line shows 52
is equivalent to 104
.
A
10
B
10
C
10
D 10
121
124
122
125
123
126
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Module BCOF Lesson 11
Engaged Practice
10
Use the fraction bars or the number line to show that the fractions are equivalent.
31
62
=
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10
Module BCOF Lesson 11
Engaged Practice Key
Use the fraction bars or the number line to show that the fractions are equivalent.
31
62
=
31
31
32
62
61
63
62
64
65
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Mo
dul
e BC
OF
Less
on
11
Mo
del
ed P
ract
ice
She
et
Mic
ha
el h
as
a w
ho
le p
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nu
t b
utt
er a
nd
jelly
sa
nd
wic
h. H
e c
uts
his
san
dw
ich
into
2 p
art
s.
=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 130
Mo
dul
e BC
OF
Less
on
11
Mo
del
ed P
ract
ice
She
et K
ey
Mic
ha
el h
as
a w
ho
le p
ea
nu
t b
utt
er a
nd
jelly
sa
nd
wic
h. H
e c
uts
his
san
dw
ich
into
2 p
art
s.
=× ×
22
2
21
21 42
2
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Module BCOF Lesson 11
Practice
Find the equivalent fraction. Use the fraction bars to help you solve.
1.) Michael now wants to share half of his sandwich with 6 people. What fraction represents the pieces he is sharing with his friends?
2.) 3.)=
2 ×
1 ×
10
=2 ×
1 ×
6
=2 ×
1 ×
8
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Module BCOF Lesson 11
Practice Key
Find the equivalent fraction. Use the fraction bars to help you solve.
1.) Michael now wants to share half of his sandwich with 6 people. What fraction represents the pieces he is sharing with his friends?
2.) 3.)=
2 ×
1 ×
10
=2 ×
1 ×
6
=2 ×
1 ×
8
33
3
44
4 5
5
5
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Module BCOF Lesson 11
Independent Practice
Write an equation.
1.) Write an equation to show the pieces equal to 1 whole sandwich.
+
Shade the equivalent fractions.
2.) What fraction is equivalent to 43
that has 8 as a denominator?
Shade the amounts below.
8
=
=
5
12
4
3
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Module BCOF Lesson 11
Independent Practice
Find the equivalent fraction.
3.) Jason wants to share 21
of his sandwich with 4 friends. What fraction
represents the pieces he shares with his friends?
4.) Sarah wants to share 31
of her sandwich with 2 friends. What fraction
represents the amount she is sharing?
=2 ×
1 ×
=3 ×
1 ×
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Module BCOF Lesson 11
Independent Practice
Choose the best answer.
5.) Choose the multiplication sentence that matches the model below.
A 6
4
×
×=
3
3
3
2C 6
4
×
×=
2
2
3
1
B 6
4
×
×=
2
2
3
2D 6
3
×
×=
2
2
3
2
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Module BCOF Lesson 11
Independent Practice Key
Write an equation.
1.) Write an equation to show the pieces equal to 1 whole sandwich.
12
+
Shade the equivalent fractions.
2.) What fraction is equivalent to 43
that has 8 as a denominator?
Shade the amounts below.
4
3
8
=
=
5
16
16
16
++
6
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Module BCOF Lesson 11
Independent Practice Key
Find the equivalent fraction.
3.) Jason wants to share 21
of his sandwich with 4 friends. What fraction
represents the pieces he shares with his friends?
4.) Sarah wants to share 31
of her sandwich with 2 friends. What fraction
represents the amount she is sharing?
=2 ×
1 ×
=3 ×
1 × 2
5
2
5
2
5
6
10
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Module BCOF Lesson 11
Independent Practice Key
Choose the best answer.
5.) Choose the multiplication sentence that matches the model below.
A 6
4
×
×=
3
3
3
2C 6
4
×
×=
2
2
3
1
B 6
4
×
×=
2
2
3
2D 6
3
×
×=
2
2
3
2
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Module BCOF Lesson 12
Engaged Practice
Show that 21
and 84
are equivalent fractions.
=
2 ×
1 ×
8
4
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Module BCOF Lesson 12
Engaged Practice Key
Show that 21
and 84
are equivalent fractions.
=
2 ×
1 ×
8
422
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Mo
dul
e BC
OF
Less
on
12
Mo
del
ed P
ract
ice
She
et
01
=××
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Mo
dul
e BC
OF
Less
on
12
Mo
del
ed P
ract
ice
She
et K
ey
01
=××
121
125
123
127
122
126
124
128
1212
1211
1210
129
120
2 3
8 12
4 4
32
31
33
30
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Module BCOF Lesson 12
Practice
Find the equivalent fraction.
1.) Linda measures her pencil to be 31
of a foot long. Matt says his pencil is
twice as long because his pencil is 62
of a foot long.
Why does he think his pencil is twice as long?
Match game
0 1
= ×
×=
×
×
Is Matt correct? Why or why not?=
3 ×
1 ×
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Find the equivalent fraction.
1.) Linda measures her pencil to be 31
of a foot long. Matt says his pencil is
twice as long because his pencil is 62
of a foot long.
Is Matt correct? Why or why not?
Why does he think his pencil is twice as long?
Match game
0 1
Module BCOF Lesson 12
Practice Key
= ×
×=
×
×
=3 ×
1 ×
32
31
33
30
64
62
66
60
63
61
65
2 2
2 6
answers will vary
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Module BCOF Lesson 12
Independent Practice
Choose the best answer.
1.) Choose the model that shows a fraction equivalent to 21
?
A
B
C
D
2.) Which equivalent fractions are shown by the models below?
A 34 = 6
8
B 12 = 4
8
C 24 = 1
2
D 24 = 4
8
7
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Module BCOF Lesson 12
Independent Practice
Use the fraction bars or number line to help find the equivalent fractions.
3.)
4.)
5.) Use the number line to show that 41
of a sandwich and 123
of a sandwich are the same amount.
6.) Show that 21
of a candy bar and 42
of a candy bar are the same
amount.
=5 ×
1 ×
10
=3 ×
2 ×
12 10
10=
4 ×
1 ×
12
3
10=
2 ×
1 ×
4
2
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Module BCOF Lesson 12
Independent Practice
Choose the best answer.
7.) Which equivalent fractions is shown by the model below?
10
A 24 = 5
12
B 14 = 3
12
C 24 = 6
12
D 12 = 2
4
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Module BCOF Lesson 12
Independent Practice Key
Choose the best answer.
1.) Choose the model that shows a fraction equivalent to 21
?
A
B
C
D
2.) Which equivalent fractions are shown by the models below?
A 34 = 6
8
B 12 = 4
8
C 24 = 1
2
D 24 = 4
8
7
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Use the fraction bars or number line to help find the equivalent fractions.
3.)
4.)
5.) Use the number line to show that 41
of a sandwich and 123
of a sandwich are the same amount.
6.) Show that 21
of a candy bar and 42
of a candy bar are the same
amount.
=5 ×
1 ×
10
=3 ×
2 ×
12
10=
4 ×
1 ×
12
3
10=
2 ×
1 ×
4
2
Module BCOF Lesson 12
Independent Practice Key
10
2
2
4
4
8
3
3
2
2
2
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Module BCOF Lesson 12
Independent Practice Key
Choose the best answer.
7.) Which equivalent fractions is shown by the model below?
10
A 24 = 5
12
B 14 = 3
12
C 24 = 6
12
D 12 = 2
4
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Module BCOF Lesson 13
Engaged Practice
1.) Find a fraction equivalent to 21
.
2.) Find a fraction equivalent to 31
.
10
=2 ×
1 ×
=3 ×
1 ×
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 152
1.) Find a fraction equivalent to 21
.
2.) Find a fraction equivalent to 31
.
10
=2 ×
1 ×
=3 ×
1 ×
Module BCOF Lesson 13
Engaged Practice Key
answers will vary
answers will vary
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Mo
dul
e BC
OF
Less
on
13
Mo
del
ed P
ract
ice
She
et
=
4 sa
nd
wic
he
s sh
are
d b
etw
ee
n 1
0 fr
ien
ds.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 154
Mo
dul
e BC
OF
Less
on
13
Mo
del
ed P
ract
ice
She
et K
ey
=
4 sa
nd
wic
he
s e
qu
ally
sh
are
d a
mo
ng
10
frie
nd
s.
104 52
10452
÷÷
22
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Module BCOF Lesson 13
Practice
Is there a way Allie and Robert can share the parts so each person gets only 1 larger part? Use bold lines to show the equal share.
Use the fraction bar to find the equivalent fraction.
1.) Allie, Robert, and 4 of their friends are sharing 2 sandwiches equally. They know they can cut each sandwich into 6 parts and share 1 with each person, but there will be many small parts to share.
=6
2
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Module BCOF Lesson 13
Practice
Use the fraction bar to find the equivalent fraction.
1.)
2.)
=4
2
=8
6 ÷÷
÷÷
4
2
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Module BCOF Lesson 13
Practice Key
Use the fraction bar to find the equivalent fraction.
1.) Allie, Robert, and 4 of their friends are sharing 2 sandwiches equally. They know they can cut each sandwich into 6 parts and share 1 with each person, but there will be many small parts to share.
Is there a way Allie and Robert can share the parts so each person gets only 1 larger part? Use bold lines to show the equal share.
=6
2 ÷÷ 3
1
2
2
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Module BCOF Lesson 13
Practice Key
Use the fraction bar to find the equivalent fraction.
1.)
2.)
=4
2 ÷÷
=8
6 ÷÷
3
2
2
1
2
2
4
2
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Module BCOF Lesson 13
Independent Practice7
1.) Select ALL models that are equivalent to 31
.
A 26 B
2
8
C 25 D 4
12
2.) What fraction is equivalent to 42
and shown on the number line?
10
42
3.) Choose the model that shows a fraction equivalent to 21
.
A 46 B
3
6
C 34 D 5
12
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Module BCOF Lesson 13
Independent Practice
=10
6
=8
2
=6
4
÷
÷
÷
÷÷
÷
Use the fraction bars to find the equivalent fraction.
4.)
5.)
6.)
3
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Module BCOF Lesson 13
Independent Practice
Choose the best answer.
7.) Which model shows a fraction that is equivalent to 108
?
A 45
B
34
C 35
D 46
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Module BCOF Lesson 13
Independent Practice Key
1.) Select ALL models that are equivalent to 31
.
A 26 B
2
8
C 25 D 4
12
2.) What fraction that is equivalent to 42
is shown on this number line?
10
42
3.) Choose the model that shows a fraction equivalent to 21
.
A 46 B
3
6
C 34 D 5
12
8
421or
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Module BCOF Lesson 13
Independent Practice Key
Use the fraction bars to find the equivalent fraction.
4.)
5.)
6.)
=10
6
=8
2
=6
4
÷
÷
÷
÷÷
÷
3
5
3
2
2
4
1
2
2
2
2
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 164
Module BCOF Lesson 13
Independent Practice Key
Choose the best answer.
7.) Which model shows a fraction that is equivalent to 108
?
A 45
B
34
C 35
D 46
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 165
Module BCOF Lesson 14
Engaged Practice
1.) Use fraction bars to find the equivalent fraction.
2.)
=4
3
=6
4 ÷÷ 3
8
××
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 166
Module BCOF Lesson 14
Engaged Practice Key
1.) Use fraction bars to find the equivalent fraction.
2.)
=4
3
=6
4 ÷÷ 3
8
××
6
2
2
2
2
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 167
Mo
dul
e BC
OF
Less
on
14
Mo
del
ed P
ract
ice
01
128
01
128
8 sa
nd
wic
he
s a
re s
ha
red
eq
ua
lly b
etw
ee
n 1
2 fr
ien
ds.
=12
8
÷÷
=12
8
÷÷
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 168
Mo
dul
e BC
OF
Less
on
14
Mo
del
ed P
ract
ice
Key
01
128
01
128
8 sa
nd
wic
he
s a
re s
ha
red
eq
ua
lly b
etw
ee
n 1
2 fr
ien
ds.
=12
8
÷÷
=12
8
÷÷
64
22
32
44
1212
1211
1210
129
120
121
122
123
124
125
126
127
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 169
Module BCOF Lesson 14
Practice
Use fraction pieces and the number line to find equivalent fractions.
Raul shared 8 brownie bars equally with 4 of his friends. An equal share looked like this:
1). Use 41
parts to find a fraction that is equivalent to 84
.
2.) Use 21
parts to find a fraction that is equivalent to 84
.
=8
4
÷
÷
=8
4
÷
÷
0 1
84
0 1
84
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 170
Use fraction pieces and the number line to find equivalent fractions.
Raul shared 8 brownie bars equally with 4 of his friends. An equal share looked like this:
1). Use 41
parts to find a fraction that is equivalent to 84
.
2.) Use 21
parts to find a fraction that is equivalent to 84
.
0 1
84
0 1
84
=8
4
÷
÷
Module BCOF Lesson 14
Practice Key
=8
4
÷
÷
4
2
2
2
2
1
4
4
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 171
Module BCOF Lesson 14
Independent Practice6
1.) Divide the model below to find the equivalent fraction.
2.) Choose the fraction equivalent to 1 whole that makes the equation true.
A 2 B
3
3 C
4
4 D 5
8 =
4
3 ×
×
=3
2 ×
× 12
8
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3.) Choose the equation that describes the model below.
A
B
C
D
=10
5 ÷
÷
2
2
2
5
=10
5 ÷
÷
5
5
1
2
=8
4 ÷
÷
4
4
1
2
Module BCOF Lesson 14
Independent Practice
=10
4 ÷
÷
2
2
2
5
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 173
Module BCOF Lesson 14
Independent Practice
Use fraction pieces and number line to find the equivalent fraction.
4.) Jason shared 4 candy bars equally with his 12 friends. An equal share looked like this:
Use 61
parts to find a fraction that is equivalent to 124
.
0 1
124
=12
4 ÷
÷
5.) Use 31
parts to find a fraction that is equivalent to 124
.
0 1
124
=12
4 ÷
÷
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 174
Module BCOF Lesson 14
Independent Practice
Choose the best answer.
6.) Choose the number line that shows a fraction equivalent to 86
.
A
10
42
B
10
64
C
1021
D 10
43
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1.) Divide the model below to find the equivalent fraction.
2.) Choose the fraction equivalent to 1 whole that makes the equation true.
A 2 B
3
3 C
4
4 D 5
Module BCOF Lesson 14
Independent Practice Key6
8 =
4
3 ×
×
=3
2 ×
× 12
8
1
6
2
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 176
Module BCOF Lesson 14
Independent Practice Key
3.) Choose the equation that describes the model below.
A
B
C
D
=10
5 ÷
÷
2
2
2
5
=10
5 ÷
÷
5
5
1
2
=8
4 ÷
÷
4
4
1
2
=10
4 ÷
÷
2
2
2
5
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 177
Module BCOF Lesson 14
Independent Practice Key
Use fraction pieces and number line to find the equivalent fraction.
4.) Jason shared 4 candy bars equally with his 12 friends. An equal share looked like this:
Use 61
parts to find a fraction that is equivalent to 124
.
0 1
124
=12
4 ÷
÷
5.) Use 31
parts to find a fraction that is equivalent to 124
.
0 1
124
=12
4 ÷
÷
2
22
6
1
4
4
3
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 178
Module BCOF Lesson 14
Independent Practice Key
Choose the best answer.
6.) Choose the number line that shows a fraction equivalent to 86
.
A
10
42
B
10
64
C
1021
D 10
43
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Module BCOF Lesson 15
Engaged Practice
Look at each problem and determine if the equations match the model. If they do not match, write the correct equation.
1.)
Correct? Y or N
Correct? Y or N
2.)
3.)
Correct? Y or N
5
3
÷
÷=
2
2
10
6
3
2
÷
÷=
2
2
6
4
8
4
×
×=
2
2
4
2
10
=4
2
=6
4
=10
6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 180
Module BCOF Lesson 15
Engaged Practice Key
Look at each problem and determine if the equations match the model. If they do not match, write the correct equation.
1.)
Correct? Y or N
=4
2
=6
4
=10
6
Correct? Y or N
2.)
3.)
Correct? Y or N
5
3
÷
÷=
2
2
10
6
3
2
÷
÷=
2
2
6
4
8
4
×
×=
2
2
4
2
10
÷÷
2 22 1
××
2 122 8
÷÷
2 52 3
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Mo
dul
e BC
OF
Less
on
15
Mo
del
ed P
ract
ice
#1
Jua
n’s
mo
m b
ake
d a
ca
ke f
or J
ua
n’s
birt
hd
ay.
Aft
er e
atin
g 2
pie
ce
s o
f th
e c
ake
, Ju
an
ha
d
53
of
a t
he
ca
ke le
ft t
o s
ha
re w
ith h
is fr
ien
ds
tha
t st
op
pe
d b
y to
wish
him
a h
ap
py
birt
hd
ay.
Ho
w c
an
Ju
an
cu
t th
e
rem
ain
ing
ca
ke e
qu
ally
to
ma
ke e
no
ug
h p
iec
es
for h
is fr
ien
ds?
=53
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 182
Mo
dul
e BC
OF
Less
on
15
Mo
del
ed P
ract
ice
#2
Jua
n d
id s
o w
ell
find
ing
th
e fi
rst
eq
uiv
ale
nt
fra
ctio
n f
or h
is c
ake
, th
at
his
mo
m a
ske
d h
im t
o h
elp
he
r with
a c
oo
kie
ba
ske
t. T
his
time
Ju
an
’s m
om
sta
rts
with
124
of
a c
oo
kie
ba
ske
t a
nd
wa
nts
to
kn
ow
wh
at
third
of
the
ba
ske
t is
left
. Ho
w c
an
Ju
an
fin
d a
n e
qu
iva
len
t fr
ac
tion
th
at
ha
s a
de
no
min
ato
r of
3?
=124
3
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 183
Mo
dul
e BC
OF
Less
on
15
Mo
del
ed P
ract
ice
#1 K
ey
Jua
n’s
mo
m b
ake
d a
ca
ke f
or J
ua
n’s
birt
hd
ay.
Aft
er e
atin
g 2
pie
ce
s o
f th
e c
ake
, Ju
an
ha
d
53
of
a t
he
ca
ke le
ft t
o s
ha
re w
ith h
is fr
ien
ds
tha
t st
op
pe
d b
y to
wish
him
a h
ap
py
birt
hd
ay.
Ho
w c
an
Ju
an
cu
t th
e
rem
ain
ing
ca
ke e
qu
ally
to
ma
ke e
no
ug
h p
iec
es
for h
is fr
ien
ds?
=53
××2
102
6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 184
Mo
dul
e BC
OF
Less
on
15
Mo
del
ed P
ract
ice
#2 K
ey
Jua
n d
id s
o w
ell
find
ing
th
e fi
rst
eq
uiv
ale
nt
fra
ctio
n f
or h
is c
ake
, th
at
his
mo
m a
ske
d h
im t
o h
elp
he
r with
a c
oo
kie
ba
ske
t. T
his
time
Ju
an
’s m
om
sta
rts
with
124
of
a c
oo
kie
ba
ske
t a
nd
wa
nts
to
kn
ow
wh
at
third
of
the
ba
ske
t is
left
. Ho
w c
an
Ju
an
fin
d a
n e
qu
iva
len
t fr
ac
tion
th
at
ha
s a
de
no
min
ato
r of
3?
=124
3÷÷
441
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 185
Module BCOF Lesson 15
Practice
1.) In science class, Tony measures the length of an insect to be 43
of an
inch. Tony’s teacher says all measurements must be in eighths. What is the
length of the insect in eighths?
2.) Lucy is learning to compare fractions and needs to find a fraction that is
equivalent to 129
that has a denominator of 4. Can you help her?
Hint: If you have 12 parts and 4 equal groups, how many parts are in each group?
What would these two lengths look like on a ruler?
0 1
=4
3
=12
9
8
4
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Module BCOF Lesson 15
Practice
Draw a line to match the equivalent fractions.
64
•
• 32
× or ÷ by
31
•
• 21
× or ÷ by
105
•
• 43
× or ÷ by
86
•
• 62
× or ÷ by
0 1105
0 186
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 187
Module BCOF Lesson 15
Practice Key
1.) In science class, Tony measures the length of an insect to be 43
of an
inch. Tony’s teacher says all measurements must be in eighths. What is the
length of the insect in eighths?
2.) Lucy is learning to compare fractions and needs to find a fraction that is
equivalent to 129
that has a denominator of 4. Can you help her?
Hint: If you have 12 parts and 4 equal groups, how many parts are in each group?
What would these two lengths look like on a ruler?
0 1
=4
3
=12
9
8
4
43
86
××
22 6
÷÷
33 3
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Module BCOF Lesson 15
Practice Key
Draw a line to match the equivalent fractions.
64
•
• 32
× or ÷ by
31
•
• 21
× or ÷ by
105
•
• 43
× or ÷ by
86
•
• 62
× or ÷ by
0 1105
0 186
2
2
5
2
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Module BCOF Lesson 15
Independent Practice6
1.) Choose the equation that describes the model below.
A 21
= 62 C 3
1 = 9
3
B 51
= 93 D 3
1 = 6
2
2.) Which fraction is equivalent to 1 whole?
4
1
÷
÷=
12
3
A 1 B 22 C 3
3 D 14
3.) Choose the number line that shows a fraction equivalent to 63
.
A
10
21
B
10
52
C
1043
D 10
41
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Module BCOF Lesson 15
Independent Practice
Choose the best answer.
6.) Which equation would require multiplication to find the equivalent fraction?
A 129
4= C 5
310
=
B 82
4= D 6
43
=
4.) Find a fraction that is equivalent to 41
with a denominator of 12 using the
model below.
5.) Find a fraction that is equivalent to 41
with a denominator of 12 using the
model below.
=4
1
12
=8
6
4
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Module BCOF Lesson 15
Independent Practice Key6
1.) Choose the equation that describes the model below.
A 21
= 62 C 3
1 = 9
3
B 51
= 93 D 3
1 = 6
2
2.) Which fraction is equivalent to 1 whole?
4
1
÷
÷=
12
3
A 1 B 22 C 3
3 D 14
3.) Choose the number line that shows a fraction equivalent to 63
.
A
10
21
B
10
52
C
1043
D 10
41
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 192
Module BCOF Lesson 15
Independent Practice Key
Choose the best answer.
6.) Which equation would require multiplication to find the equivalent fraction?
A 129
4= C 5
310
=
B 82
4= D 6
43
=
4.) Find a fraction that is equivalent to 41
with a denominator of 12 using the
model below.
5.) Find a fraction that is equivalent to 41
with a denominator of 12 using the
model below.
=4
1
12
=8
6
4
××
33 3
÷÷
22 3
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Module BCOF Lesson 16
Modeled Practice #1
Two friends walk to school each morning. Natalie walks 43
of a mile. Jason
says he walks farther because he walks 86
of a mile. Is he correct?
Is Jason correct? Why or why not?
0 1
=4
3
8
6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 194
Module BCOF Lesson 16
Modeled Practice #2
Michael has 52
of a sandwich. Robert has
105
of a sandwich. Robert thinks
their sandwiches are the same size. Is he correct?
Is Robert correct? How do you know?
=5
2
×
×
5
2=
10
5
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Module BCOF Lesson 16
Modeled Practice #1 Key
Two friends walk to school each morning. Natalie walks 43
of a mile. Jason
says he walks farther because he walks 86
of a mile. Is he correct?
Is Jason correct? Why or why not?
0 1
=4
3
××
22
8
6
43
44
41
40
42
86
87
88
80 8
183
82
84
85
No, they walk the same distance.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 196
Module BCOF Lesson 16
Modeled Practice #2 Key
Michael has 52
of a sandwich. Robert has
105
of a sandwich. Robert thinks
their sandwiches are the same size. Is he correct?
Is Robert correct? How do you know?
=5
2
×
×
5
2=
10
5
No, the fractions are not equivalent.
22 4
10
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Module BCOF Lesson 16
Practice
Determine if the two fractions are equivalent using models. Write “=” (equivalent) or “=” (not equivalent) in the circle.
1.)
2.)
0 1
4
2
8
5
4
1
12
3
=
=
4
2
4
1
8
12
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 198
Module BCOF Lesson 16
Practice
Write “=” or “=” in the circle.
3.)
0 1
4.)
0 1
3
1
6
3
4
3
12
9
=
=
3
1
4
3
6
12
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 199
Module BCOF Lesson 16
Practice Key
Determine if the two fractions are equivalent using models. Write “=” (equivalent) or “=” (not equivalent) in the circle.
1.)
2.)
4
2
8
5
4
1
12
3
=
=
4
2
4
1
8
12
××
22 4
××
33 3
=
=
43
44
41
40
42
86
87
88
80 8
183
82
84
850 1
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Module BCOF Lesson 16
Practice Key
Write “=” or “=” in the circle.
3.)
4.)
3
1
6
3
4
3
12
9
=
=
3
1
4
3
6
12
0 1
××
22 2
××
33 9
=
=
33
44
31
41
30
40
32
42
43
66
1212
60
120
61
63
62
64
65
125
1210
1211
121
126
122
127
123
128
124
129
0 1
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Module BCOF Lesson 16
Independent Practice6
Choose the best answer.
1.) Which fraction equivalent to 1 whole goes in the box?
12
4
×
×=
3
1
A 22 B 4
4 C 41 D 1
4
2.) Choose the equation that describes the shaded portion of the model below.
A 81
= 82 C 5
1 = 10
2
B 82
= 82 D 4
2 = 8
4
3.) Which equation would require division to find the equivalent fraction.
A 126
4= C 3
26
=
B 43
12= D 5
110
=
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Module BCOF Lesson 16
Independent Practice
Determine if the two fractions are equivalent using models. Write “=” (equivalent) or “=” (not equivalent) in the circle.
4.)
5.)
6
2
3
1
=6
2
3
0 1
4
3
8
7
=4
3
8
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 203
Module BCOF Lesson 16
Independent Practice
6.)
0 1
5
3
10
6
=5
3
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 204
Module BCOF Lesson 16
Independent Practice Key6
Choose the best answer.
1.) Which fraction equivalent to 1 whole goes in the box?
12
4
×
×=
3
1
A 22 B 4
4 C 41 D 1
4
2.) Choose the equation that describes the shaded portion of the model below.
A 81
= 82 C 5
1 = 10
2
B 82
= 82 D 4
2 = 8
4
3.) Which equation would require division to find the equivalent fraction.
A 126
4= C 3
26
=
B 43
12= D 5
110
=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 205
Module BCOF Lesson 16
Independent Practice Key
Determine if the two fractions are equivalent using models. Write “=” (equivalent) or “=” (not equivalent) in the circle.
4.)
5.)
6
2
3
1
=6
2
3
4
3
8
7
=4
3
8××
22 6
=
43
44
41
40
42
86
87
88
80 8
183
82
84
850 1
÷÷
22 1
=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 206
6.)
0 1
5
3
10
6
=5
3
10
Module BCOF Lesson 16
Independent Practice Key
××
22 6
=
55
51
50
52
54
53
1010
100 10
5101
106
102
107
103
108
104
109
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 207
Module BCOF Lesson 17
Engaged Practice
> < =
Write “>,” “<,” or “=” in the circle.
1.) 23 17
2.) 124 368
3.) 173 173
4.) 475 468
5.) 3,645 3,445
6.) 1.037 13,077
7.)
0 10 1
8.)
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Module BCOF Lesson 17
Engaged Practice Key
> < =
Write “>,” “<,” or “=” in the circle.
1.) 23 17
2.) 124 368
3.) 173 173
4.) 475 468
5.) 3,645 3,445
6.) 1.037 13,077
7.)
0 10 1
8.)
<
=
>
>
<
>
<
>
Greater than Less than Equal
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 209
Mo
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Mo
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ract
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#1
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 210
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Mo
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01
01
01
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Mo
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Mo
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#1 K
ey
103 107105
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 212
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Mo
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01
01
01
4344
4140
42
8687
8880
8183
8284
85
42 12282
1212120
1251210
1211121
126122
127123
128124
129
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Module BCOF Lesson 17
Practice
Draw and use the fraction bar models to solve.
1.) Mark’s friend Phillip is offering him 61
of a candy bar. Phillip says he is
being generous, because he only gets 31
of the candy bar, which is
smaller, because 3 is less than 6. Is Phillip correct?
Use the number line to solve.
2.) Is 85
less than or greater than 83
?
Draw a model to support your answer.
8
5
8
3
6
1
3
1
0 1
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Module BCOF Lesson 17
Practice Key
Draw and use the fraction bar models to solve.
1.) Mark’s friend Phillip is offering him 61
of a candy bar. Phillip says he is
being generous, because he only gets 31
of the candy bar, which is
smaller, because 3 is less than 6. Is Phillip correct?
Use the number line to solve.
2.) Is 85
less than or greater than 83
?
Draw a model to support your answer.
8
5
8
3
6
1
3
1
86
87
88
80
81
83
82
84
85
0 1
<
>
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 215
Module BCOF Lesson 17
Independent Practice7
1.) Solve to find the equivalent fraction. Compete the model.
2.) Solve to find the equivalent fraction. Complete the model.
0 1
3.) Choose the fraction that is equivalent to 42
.
A 82 C 12
5
B 21 D 3
2
×
×=
5
3
10
÷
÷=
8
6
4
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Module BCOF Lesson 17
Independent Practice
Draw a model and write “>” or “<” in the circle.
5.) Is 32
less than or greater than 102
?
0 1
0 1
Write “=” (equivalent) or “=” (not equivalent) in the circle.
4.) Are 32
and 126
equivalent?
3
2
12
6
=6
2
12
3
2
10
2
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Module BCOF Lesson 17
Independent Practice
6.) Is 62
less than or greater than 65
?
6
2
6
5
7.) Choose the letter of the inequality shown by the models.
A 53
< 86 C 5
2 > 8
2
B 62
= 82 D 5
2 < 6
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 218
Module BCOF Lesson 17
Independent Practice Key7
1.) Solve to find the equivalent fraction. Compete the model.
2.) Solve to find the equivalent fraction. Complete the model.
3.) Choose the fraction that is equivalent to 42
.
A 82 C 12
5
B 21 D 3
2
×
×=
5
3
10
÷
÷=
8
6
4
43
44
41
40
42
86
87
88
80 8
183
82
84
850 1
22 3
22 6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 219
Module BCOF Lesson 17
Independent Practice Key
Draw a model and write “>” or “<” in the circle.
5.) Is 32
less than or greater than 102
?
0 1
0 1
Write “=” (equivalent) or “=” (not equivalent) in the circle.
4.) Are 32
and 126
equivalent?
3
2
12
6
=6
2
12
3
2
10
2
××
44 8
333
1
30 3
2
1010
100 10
5101
106
102
107
103
108
104
109
=
>
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Module BCOF Lesson 17
Independent Practice Key
6.) Is 62
less than or greater than 65
?
6
2
6
5
7.) Choose the letter of the inequality shown by the models.
A 53
< 86 C 5
2 > 8
2
B 62
= 82 D 5
2 < 6
2
<
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 221
Module BCOF Lesson 18
Engaged Practice
0 1
1.) Mark 21
on the number line.
2.) Divide the number line into eights. Label 81
on the number line. Is 81
closer to 0 or 1?
3.) Find 43
on the number line and label it.
Is 43
closer to 0 or 1?
Is 43
greater than or less than 21
?
4.) Name 2 fractions on the number line greater than 21
.
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Module BCOF Lesson 18
Engaged Practice Key
1.) Mark 21
on the number line.
2.) Divide the number line into eights. Label 81
on the number line. Is 81
closer to 0 or 1?
3.) Find 43
on the number line and label it.
Is 43
closer to 0 or 1?
Is 43
greater than or less than 21
?
4.) Name 2 fractions on the number line greater than 21
.
0 143
81
21
greater than
1
0
86
87
88
43
44
85 , , , , ,
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 223
Module BCOF Lesson 18
Modeled Practice
0 1
0 1
41
65
109
83
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 224
Module BCOF Lesson 18
Modeled Practice Key
41
65
109
83
0 141
0 1
0 163
65
61
62
64
0 183
21
109
>
<
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 225
Module BCOF Lesson 18
Practice
Place the pairs of fractions on the number line to compare them. Fill in the circle with “>” or “<”.
1.) 102
1
4
3
2.) 104
3
3
1
3.) 103
1
8
5
4.) 1012
3
10
8
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 226
Module BCOF Lesson 18
Practice
1.) Locate and label 3 fractions between 0 and 1 that are greater than 21
on the number line.
10
21
2.) Locate and label 3 fractions between 0 and 1 that are less than 32
on the number line.
10
32
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 227
Module BCOF Lesson 18
Practice Key
Place the pairs of fractions on the number line to compare them. Fill in the circle with “>” or “<”.
1.) 102
1
4
3
2.) 104
3
3
1
3.) 103
1
8
5
4.) 1012
3
10
8
<
<
<
>
123
108
43
31
85
21
21
43
21
31
21
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 228
Module BCOF Lesson 18
Practice Key
1.) Locate and label 3 fractions between 0 and 1 that are greater than 21
on the number line.
10
21
2.) Locate and label 3 fractions between 0 and 1 that are less than 32
on the number line.
10
32
answers will vary
answers will vary
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 229
Module BCOF Lesson 18
Independent Practice7
Choose the best answer.
1.) Choose the fraction that is equivalent to 32
.
A 64 C 4
3
B 82 D 6
5
2.) Choose the inequality shown by the model.
A 41
< 63 C 4
3 < 6
3
B 43
> 53 D 4
3 > 6
3
3.) Find the equivalent fraction using division.
÷
÷=
12
9
4
Place the pairs of fractions on the number line to compare them. Fill in the circle with “>” or “<”.
4.) 104
1
8
6
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 230
Module BCOF Lesson 18
Independent Practice
Place the pairs of fractions on the number line to compare them. Fill in the circle with “>” or “<”.
4.) 104
1
8
6
5.) 102
1
10
3
6.) 105
2
12
11
Choose the best answer.
7.) Which number line is correct?
A 10
43
21
B
10
81
83
C
10101
1211
D 10
84
21
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 231
Module BCOF Lesson 18
Independent Practice Key7
Choose the best answer.
1.) Choose the fraction that is equivalent to 32
.
A 64 C 4
3
B 82 D 6
5
2.) Choose the inequality shown by the model.
A 41
< 63 C 4
3 < 6
3
B 43
> 53 D 4
3 > 6
3
3.) Find the equivalent fraction using division.
÷
÷=
12
9
433 3
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 232
Module BCOF Lesson 18
Independent Practice Key
Place the pairs of fractions on the number line to compare them. Fill in the circle with “>” or “<”.
4.) 104
1
8
6
5.) 102
1
10
3
6.) 105
2
12
11
Choose the best answer.
7.) Which number line is correct?
A 10
43
21
B
10
81
83
C
10101
1211
D 10
84
21
52
21
103
1011
<
>
41
86
<
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1.)
×
×=
3
2
12
2.)
×
×=
2
1
10
3.)
×
×=
4
3
8
4.)
×
×=
3
1
6
Module BCOF Lesson 19
Engaged Practice
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 234
1.)
×
×=
3
2
12
2.)
×
×=
2
1
10
3.)
×
×=
4
3
8
4.)
×
×=
3
1
6
Module BCOF Lesson 19
Engaged Practice Key
0 1
0 1
44 8
22 6
55 5
22 2
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#1
an
d31
123
××=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 236
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#2
an
d53
107 107
53
107
××
53
01
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#1 K
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an
d31
123
××=
3 12
123
44
123
124
31
31
124
>>
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 238
Mo
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Mo
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an
d53
107 107
53
107
××
53
01
100105
1010101
51
106102
52
107103
53
108104
54
109
106
106
<<
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 239
Module BCOF Lesson 19
Practice
2.)
×
×=
2
1
8
5
2
1
8
5
8
4
1.) Sam ran 41
of a mile. Raquel ran 83
of a mile. Who ran farther?
×
×=
4
1
8
2
8
3
4
1
8
3
3.)
×
×=
5
2
10
3
5
2
10
3
10
4
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 240
Module BCOF Lesson 19
Practice
Look at the table of distances run at the track meet. Put the distances in order from least to greatest.
Runner Distance (mile) Equivalent Fraction
Jacob3
1=
3
1
Mandy4
2=
4
2
Javi6
5=
6
5
Yessica12
3=
12
3
Put the equivalent fractions in order from least to greatest:
, , ,
Put the original fractions in order from least to greatest:
, , ,
Who ran the greatest distance?
Who ran the least distance?
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 241
Module BCOF Lesson 19
Practice Key
2.)
×
×=
2
1
8
5
2
1
8
5
8
4
1.) Sam ran 41
of a mile. Raquel ran 83
of a mile. Who ran farther?
×
×=
4
1
8
2
8
3
4
1
8
3
3.)
×
×=
5
2
10
3
5
2
10
3
10
4
2
4
2
8
8
10
2
4
2
2
4
4
>
<
<
<
>
<
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 242
Module BCOF Lesson 19
Practice Key
Look at the table of distances run at the track meet. Put the distances in order from least to greatest.
Runner Distance (mile) Equivalent Fraction
Jacob3
1=
3
1
Mandy4
2=
4
2
Javi6
5=
6
5
Yessica12
3=
12
3
Put the equivalent fractions in order from least to greatest:
, , ,
Put the original fractions in order from least to greatest:
, , ,
Who ran the greatest distance?
Who ran the least distance?
12
12
12
12
3
10
6
4
124
31
126
42
1210
65
123
123
Javi
Jessica
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 243
Module BCOF Lesson 19
Independent Practice7
Use the number lines, as needed, to fill in “>” or “<”.
1.)
6
4
8
4
1
1
0
0
2.)
12
5
12
7
10
3.)
10
2
4
3
10
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 244
Module BCOF Lesson 19
Independent Practice
4.)
×
×=
2
1
2
1
6
4
6
4
5.)
×
×=
3
2
3
2
12
9
12
9
6.)
×
×=
6
2
12
5
6
2
12
5
Find the equivalent fraction and then compare using the > or < symbol.
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 245
Module BCOF Lesson 19
Independent Practice
Choose the best answer.
7.) Which inequality shown below is correct?
A 106
> 86
12×
×=
2
2
6
4
C 127
> 64
8×
×=
2
2
4
3
B 81
< 43
12×
×=
4
4
3
1
D 53
< 52
10×
×=
2
2
5
4
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 246
Module BCOF Lesson 19
Independent Practice Key7
Use the number lines, as needed, to fill in “>” or “<”.
1.)
6
4
8
4
1
1
0
0
2.)
12
5
12
7
10
3.)
10
2
4
3
10
>
<
<
125
126
127
102
64
21
43
84
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 247
Module BCOF Lesson 19
Independent Practice Key
4.)
×
×=
2
1
2
1
6
4
6
4
5.)
×
×=
3
2
3
2
12
9
12
9
6.)
×
×=
6
2
12
5
6
2
12
5
Find the equivalent fraction and then compare using the > or < symbol.
3
2
6
12
12
6
12
4
12
3
2
3
4
8
3
4
4
8
<
<
>
>
<
<
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 248
Choose the best answer.
7.) Which inequality shown below is correct?
A 106
> 86
12×
×=
2
2
6
4
C 127
> 64
8×
×=
2
2
4
3
B 81
< 43
12×
×=
4
4
3
1
D 53
< 52
10×
×=
2
2
5
4
Module BCOF Lesson 19
Independent Practice Key
6
8
4
8
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 249
Module BCOF Lesson 20
Engaged Practice
Compare the fractions.
1.) 12
3
12
9
2.) 5
4
5
1
3.) 10
10
10
2
Order the fractions from greatest to least.
4.) 41
, 43
, 42
5.) 88
, 83
, 85
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 250
Module BCOF Lesson 20
Engaged Practice Key
Compare the fractions.
1.) 12
3
12
9
2.) 5
4
5
1
3.) 10
10
10
2
Order the fractions from greatest to least.
4.) 41
, 43
, 42
5.) 88
, 83
, 85
<
>
>
42
85
41
83
43
88
,
,
,
,
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 251
Mo
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20
Mo
del
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ract
ice
8454
6254
01
8543
=
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 252
Mo
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Mo
del
ed P
ract
ice
Key
8454
6254
01
8543
=4 83 5
8 86 6
Like
num
era
tor
< < >
>
6254
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 253
Module BCOF Lesson 20
Practice
Select the strategy, then compare the fractions.
1.)8
5
4
3 Like numerator/denominator
Number line
Find a common denominator
2.)12
3
10
9 Like numerator/denominator
Number line
Find a common denominator
3.)6
4
6
2 Like numerator/denominator
Number line
Find a common denominator
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 254
Module BCOF Lesson 20
Practice
4.)8
6
5
1 Like numerator/denominator
Number line
Find a common denominator
5.)10
7
12
7 Like numerator/denominator
Number line
Find a common denominator
6.)6
2
12
5 Like numerator/denominator
Number line
Find a common denominator
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 255
Module BCOF Lesson 20
Practice Key
Select the strategy, then compare the fractions.
1.)8
5
4
3 Like numerator/denominator
Number line
Find a common denominator
2.)12
3
10
9 Like numerator/denominator
Number line
Find a common denominator
3.)6
4
6
2 Like numerator/denominator
Number line
Find a common denominator
<
>
<
86
×× =
22
43
0 1129
123
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 256
Module BCOF Lesson 20
Practice Key
4.)8
6
5
1 Like numerator/denominator
Number line
Find a common denominator
5.)10
7
12
7 Like numerator/denominator
Number line
Find a common denominator
6.)6
2
12
5 Like numerator/denominator
Number line
Find a common denominator
>
<
>
124
×× =
22
62
0 186
51
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 257
Module BCOF Lesson 20
Independent Practice6
Choose the best answer.
1.) Choose the number line that has the fraction correctly placed.
2.) Choose the factor that is used to find the equivalent fraction.
12×
×=
3
2
A 11
B 12
C 33
D 44
A
10
41
B
10
31
C
1087
D 10
21
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 258
Module BCOF Lesson 20
Independent Practice
Compare the fractions using one of the following strategies:
• Like numerators or denominators
• Number line
• Find a common denominator
3.)8
7
4
3
4.)12
3
2
1
5.)6
4
10
4
Choose the best answer.
6.) Which inequality correctly compares the fractions?
A 106
> 86 C 12
7 > 6
4
B 81
< 43 D 5
3 < 5
2
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 259
Module BCOF Lesson 20
Independent Practice Key6
Choose the best answer.
1.) Choose the number line that has the fraction correctly placed.
2.) Choose the factor that is used to find the equivalent fraction.
12×
×=
3
2
A 11
B 12
C 33
D 44
A
10
41
B
10
31
C
1087
D 10
21
The Meadows Center for Preventing Educational Risk—Mathematics InstituteThe University of Texas at Austin ©2012 University of Texas System/Texas Education Agency 260
Module BCOF Lesson 20
Independent Practice Key
Compare the fractions using one of the following strategies:
• Like numerators or denominators
• Number line
• Find a common denominator
3.)8
7
4
3
4.)12
3
2
1
5.)6
4
10
4
Choose the best answer.
6.) Which inequality correctly compares the fractions?
A 106
> 86 C 12
7 > 6
4
B 81
< 43 D 5
3 < 5
2
>
>
<
86
×× =
22
43
0 121
123