Lesson
1
Number and Operations—Fractions
Name Use Fraction Circles to build the fractions. Write the equation.
1.
_______ × _______ = _______
Use Fraction Circles to build the fraction. Shade an equivalent fraction.
Write the equation.
2.
_______ × _______ = _______
Shade a model of the fraction. Shade an equivalent fraction.
Write the equation.
3. __
 25 
_______ × _______ = _______
Write the equivalent fraction.
4. __
​  23 ​= __
​  6 ​
5. __
​  35 ​= __
 10  
6. __
​  34 ​= __
 12  
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Hands-On Standards, Common Core Edition
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Name 4
Challenge! Write the equivalent fraction: ___
​ 12
  ​ = __
​  3  ​. Explain
how you found the answer. Write an equation showing that the
fractions are equivalent.
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67
Lesson
2
Number and Operations—Fractions
Name Use Fraction Towers to compare each set of fractions. Write
the fractions. Then write them in order from least to greatest.
1.
 ​ ___
  
​ 
3
​ ____
  
 ​
5
2.
____
​    
​
____
​    
​
​ ____   
​ 
_______________________
_______________________
Using Fraction Towers, model each fraction. Sketch the
towers. Write the fractions in order from least to greatest.
3 ​
2 ​​ __
1 ​​ __
3.​ __
5
3
8
5 ​​ __
3 ​
7 ​​ __
4.​ __
6
4
8
________________________
________________________
Write the fractions in order from least to greatest.
2 ​ and __
5.​ __
​ 85 ​
3
_____________
_______________
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Hands-On Standards, Common Core Edition
_____________
2 ​, __
7.​ __
​ 2 ​, __
​ 1 ​
8 5 3
_______________
4 ​, __
9.​ __
​ 5 ​, __
​ 2 ​
8 6 3
1 ​, __
10.​ __
​ 3 ​, __
​ 5 ​
2 5 8
_______________
_______________
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1 ,​ __
8. ​ __
​  3 ​, __
​  2 ​
4 8 6
2 ​ and __
6.​ __
​ 31 ​
8
Name Challenge! Describe rules you can use for comparing fractions
when the numerators are the same and the denominators are
different. Describe rules you can use for comparing fractions
when the numerators are different and the denominators are the
same. Draw pictures to help.
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Hands-On Standards, Common Core Edition
71
Lesson
3
Number and Operations—Fractions
Name Use Fraction Circles to model the fractional parts of each whole. Remove
one piece. Name the part of each circle that remains. Compare the parts
remaining. Then compare the pieces removed.
1.
1
8
1
10
_______________________ ________________________
___________________
Using Fraction Circles, model the fractions described. Sketch the models
and name the fractions. Write an inequality to compare the fractions.
2. a circle with __
​  15 ​removed
a circle with __
​  13 ​removed
_______________________ ________________________
___________________
Use < or > to fill in the circle to complete each inequality.
__
​  23 ​
7   ​
4. __
​  10
__
​  35 ​
5. __
​  12 ​
__
​  58 ​
6. __
​  11
  ​
12
__
​  78 ​
9   ​
7. __
​  10
__
​  78 ​
3   ​
8. __
​  10
__
​  13 ​
9. __
​  45 ​
__
​  56 ​
__
​  13 ​
7   ​
11. __
​  12
__
​  34 ​
Hands-On Standards, Common Core Edition
10. __
​  15 ​
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5   ​
3. ___
​  12
Name Challenge! Explain why the more equal sections a circle is
divided into, the smaller each section is compared to the whole
circle. Draw a picture.
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75
Lesson
4
Name Number and Operations—Fractions
Use Fraction Towers to model each sum or difference. Write
the fractions and the answer.
1.
+
_____________
2.
+_____________ = _____________
–
_____________
–_____________ = _____________
3.
__________________
+
+
+
+
_____ _________________ = ________
Using Fraction Towers, model each sum or difference. Then
sketch the models below. Complete the equation.
2 ​ + __
4.​ __
​ 1 ​ = _________
5 5
6 ​ – __
5.​ __
​ 3 ​ = _________
8 8
2  ​ + ___
6.​ ___
​  7  ​ = _______
10 10
Find each sum or difference.
8.
___
​  9  ​ + ___
​  2  ​=
  _______
10
8  ​ + ___
2  ​ + ___
5  ​ = _____
9.​ ___
​ 
​ 
12 12 12
8   ​ – ___
10.​ ___
​  5  ​ = _______
10 10
4 ​ – __
11.​ __
​ 1 ​ = _________
5 5
5 ​ – __
12.​ __
​ 2 ​ = ____________
6 6
Hands-On Standards, Common Core Edition
10
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3   ​ + ___
7  ​=
7.​ ___
​ 
  _______
12 12
Name 3 ​ +​ __
3 ​ on a number line.
Challenge! Show​ __
4 4
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79
Lesson
5
Number and Operations—Fractions
Name Use the model to answer the question. Write an equation.
1. How many thirds are in 2​ __23 ​? _________
2​ __23 ​= _________ + _________ + _________ = _________
Draw a model to answer the question. Use Fraction Towers to help you.
Write an equation.
2. How many fourths are in 1​ __14 ​? _________
1​ __14 ​= _________ + _________ = _________
Break apart each number in 2 ways. Write the equations.
4.2​ __12 ​____________________________
______________________________
______________________________
5.1​ __25 ​____________________________
______________________________
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Hands-On Standards, Common Core Edition
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3.1​ __18 ​___________________________
Name 7   in two different ways.
Challenge! Draw how to break apart 2 __
10
Write each as an equation.
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83
Lesson
6
Number and Operations—Fractions
Name Use the model to find the sum. Write an equation using mixed numbers.
Write an equation using improper fractions.
1. ____________ + ____________ = ____________
____________ + ____________ = ____________
+
Draw a model of 4 3__5  . Use Fraction Towers to help you. Use the model to
find the difference.
2.4 __35  – 2 __25  = ____________
Find the sum or difference.
4.1 __25  + 2 __15  = ____________
5.4 __78  – 2 __38  = ____________
6.5 __14  – 3 __34  = ____________
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3.2 __23  + 5 __23  = ____________
Name Challenge! Two sisters were raising money for charity. Tia ran
1   of a mile, while Jin walked 2 __
4   mile. How many miles did they
5 __
10
10
run/walk in all? How many less miles did Jin travel than Tia? Write
the equations. Explain how to find the answers.
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Hands-On Standards, Common Core Edition
87
Lesson
7
Number and Operations—Fractions
Name Use Fraction Circles to model each number. Write
the number as a fraction and as a mixed number.
1.
2.
1
3 × ​ __
 ​=______ = ______
2
1
8 × ​ __
 ​= ______ = ______
5
Using Fraction Circles, model each number. Sketch the model.
Write the number as a fraction.
1 
3. 1​ __
3
5 ​
4. 1​ __
8
1
4 × ​ __
 ​= ______
3
1
13 × ​ __
 ​= ______
8
Write each product as an improper fraction.
5.11 × __
​  14 ​= ______
6. 15 × __
​ 18 ​= ______
1
8.11 ×​ __
 ​= ______
2
9.7 × __
​  13 ​= ______
7. 19 × __
​ 15 ​= ______
1
10.13 × ___
​  10
  ​ = ______
Write each product as a mixed number.
12. 17 × __
​  18 ​= ______
13. 31 × __
​  16 ​= ______
1
14.63 × ___
​  10
  ​ = ______
15. 13 × __
​  12 ​= ______
16.29 × __
​  14 ​= ______
Hands-On Standards, Common Core Edition
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11.12 × 5__​  1 ​= _______
Name Challenge! Write how to change a mixed number to an
improper fraction. Why do the rules work?
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91
Lesson
8
Number and Operations—Fractions
Name Use the model to solve the problem. Write the answer as an improper
fraction and as a mixed number.
1. Regina has pieces of lumber that are each __
​  23 ​inch thick. If she stacks 4
pieces, how thick will her stack of lumber be?
4 × __
​  23 ​= 8 × __
​  13 ​= ____________ = ____________ inches
Draw a model to solve the problem. Write the equation.
2. Rakesh made 6 baskets in a basketball game. He got __
​  25 ​as many rebounds
as baskets. How many rebounds did Rakesh get?
6 × __
​  25 ​= ____________ = ____________ = ____________ rebounds
Multiply.
3. 3 × __
​  58 ​= ____________
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3   = ____________
4. 7 × __
 10
5. 15 × __
​  25 ​= ____________
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Hands-On Standards, Common Core Edition
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Name Challenge! Mandy and her dad are making cookies for a bake
sale. She has 2​ __34 ​cups of oats. She has two recipes to pick from.
Recipe A calls for __
​  14 ​cup of oats, and Recipe B calls for __
​  34 ​cup of
oats. She wants to make 5 batches of cookies and use as much of
the oats as possible. Which recipe should she use? Explain why.
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95
Lesson
9
Number and Operations—Fractions
Name Use Base Ten Blocks. Build the model and use it to solve the problem.
Complete the equation.
1. Melissa has 5 dimes and 9 pennies. What fraction of a dollar does
she have?
5
9
9
___
​  10
  ​ + ___
​  100
    
​ = ___
​  100
    
​ + ___
​  100
   ​ = ___
​  100
   ​ 
Use Base Ten Blocks to model the problem. Sketch the model and use it to
solve the problem. Write an equation.
2.The fourth graders are using the cafeteria for a meeting. There are 10
tables, and each table seats 10 students. When all the students are seated,
7 tables are filled, and one table has 3 students. What fraction of the seats
is being used?
__________ + __________ = __________ + __________ = __________
Find each sum.
6
9
4.​ ___
   ​ + ___
​ 
  ​ = _______
100
10
8
1
5.​ ___
  ​ + ___
​ 
   ​ = _______
10
100
6
2
___
6.​ 100
  ​ + ___
​  10
  ​ = _______
3
1
7.​ ___
  ​ + ___
​ 
   ​ = _______
10
100
1
1
8.​ ___
  ​ + ___
​ 
   ​ = _______
10
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Hands-On Standards, Common Core Edition
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5
7
3.​ ___
  ​ + ___
​ 
   ​ = _______
10
100
Name Challenge! The school is setting up a new computer lab. So
far, there are 100 desks set up in 10 rows. Four full rows of desks
have computers, and 5 desks in the next row have computers.
What fraction of the desks does NOT have a computer yet?
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99
Lesson
10
Number and Operations—Fractions
Name Use Fraction Towers to model each fraction. Then use
Base Ten Blocks to find the decimal equivalency.
1.
2.
1 ​ = ____________
__
​ 
5
4 ​ = ____________
__
​ 
8
Using Fraction Towers, model each fraction. Sketch the towers
and shade the Base Ten Flat. Write the decimal equivalency.
3 ​ = _______________
3.​ __
4
3 ​ = _______________
4.​ __
6
Write the decimal equivalent to each fraction.
3 ​ = __________
6.​ __
5
7  ​ = _________
7.​ ___
10
4 ​ = __________
8.​ __
5
2 ​ = __________
9.​ __
4
2 ​ = __________
10.​ __
5
Hands-On Standards, Common Core Edition
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3  ​ = _________
5.​ ___
10
Name Challenge! Describe a pattern that you notice in Problems 5
and 7 that relate the decimal equivalent and the denominator of
the fraction.
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103
Lesson
11
Number and Operations—Fractions
Name Let the flat equal 1 whole. Use Base Ten Blocks to model each
decimal. Use <, =, or > to complete each inequality.
2.
1.
=1
=1
___________ ____________
___________ ____________
Using Base Ten Blocks, model each decimal. Sketch the models.
Use <, =, or > to complete each inequality.
3. 0.72 and 0.58
4. 0.09 and 0.9
0.09
0.72
0.58
0.9
Use <, =, or > to complete each inequality.
0.7
6. 0.32
0.23
7. 0.08
0.1
8. 0.40
0.5
9. 0.55
0.58
10. 0.25
0.3
Hands-On Standards, Common Core Edition
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5. 0.65
Name Challenge! When the model is less than a flat, describe what
you know for sure about an inequality using the number modeled
and 1.
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Hands-On Standards, Common Core Edition
107