Download Answers to Parent Pages L55-L70

Number and Operations in Base Ten
→ Use place value understanding and properties of operations to perform
multi-digit arithmetic.
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Lesson 53
Lesson 54
CC.3.NBT.1
CC.3.NBT.1
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CC.3.NBT.2
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CC.3.NBT.3
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CC.3.NBT.3
Round to the Nearest Ten or Hundred . . . .
Estimate Sums . . . . . . . . . . . . . . . .
Estimate Differences . . . . . . . . . . . . .
Mental Math Strategies for Addition . . . . .
Algebra • Use Properties to Add . . . . . .
Use the Break Apart Strategy to Add . . . . .
Use Place Value to Add . . . . . . . . . . .
Mental Math Strategies for Subtraction . . .
Use Place Value to Subtract . . . . . . . . .
Combine Place Values to Subtract . . . . . .
Problem Solving • Use the Distributive
Property . . . . . . . . . . . . . . . . . . .
Multiplication Strategies with Multiples of 10
Multiply Multiples of 10 by 1-Digit Numbers .
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Number and Operations—Fractions
© Houghton Mifflin Harcourt Publishing Company
→ Develop understanding of fractions as numbers.
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Lesson 62
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CC.3.NF.1
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CC.3.NF.1
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CC.3.NF.2a
CC.3.NF.2b
CC.3.NF.3a
CC.3.NF.3b
CC.3.NF.3c
CC.3.NF.3d
CC.3.NF.3d
CC.3.NF.3d
CC.3.NF.3d
CC.3.NF.3d
Equal Parts of a Whole . . . . . . . . . . . . . .
Equal Shares . . . . . . . . . . . . . . . . . . .
Unit Fractions of a Whole . . . . . . . . . . . .
Fractions of a Whole . . . . . . . . . . . . . . .
Fractions of a Group . . . . . . . . . . . . . . .
Find Part of a Group Using Unit Fractions . . . .
Problem Solving • Find the Whole Group Using
Unit Fractions . . . . . . . . . . . . . . . . . .
Fractions on a Number Line . . . . . . . . . . .
. .121
. .123
Model Equivalent Fractions . . . . . . . . . .
Equivalent Fractions . . . . . . . . . . . . . .
Relate Fractions and Whole Numbers . . . . .
Problem Solving • Compare Fractions . . . .
Compare Fractions with the Same Denominator
Compare Fractions with the Same Numerator .
Compare Fractions . . . . . . . . . . . . . . .
Compare and Order Fractions . . . . . . . . .
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v
Name
LESSON
55
1
Equal Parts of a Whole
CC.3.NF.1
OBJECTIVE Explore and identify equal parts of a whole.
When you divide a shape into equal parts, each part
must be exactly the same size.
This rectangle is divided into 2 equal parts, or halves.
This rectangle is divided into 3 equal parts, or thirds.
This rectangle is divided into 4 equal parts, or fourths.
Write the number of equal parts. Then write the name
for the parts.
1.
2.
4
3.
2
equal parts
3
equal parts
fourths
equal parts
thirds
halves
Write whether each shape is divided into equal parts
or unequal parts.
5.
© Houghton Mifflin Harcourt Publishing Company
4.
equal
parts
6.
unequal
parts
Draw lines to divide the squares into equal parts.
7. 3 thirds
Number and Operations–Fractions
8. 6 sixths
equal
parts
Possible lines are shown.
9. 8 eighths
109
Name
1
Equal Parts of a Whole
CC.3.NF.1
Write the number of equal parts.
Then write the name for the parts.
1.
2.
4
3
equal parts
equal parts
thirds
fourths
3.
4.
2
6
equal parts
halves
equal parts
sixths
Write whether the shape is divided into equal parts or unequal parts.
unequal
parts
equal
parts
Problem Solving
7. Diego cuts a round pizza into
eight equal slices. What is the
name for the parts?
eighths
110
8. Madison is making a place mat.
She divides it into 6 equal parts
to color. What is the name for the
parts?
sixths
Lesson 55
© Houghton Mifflin Harcourt Publishing Company
6.
5.
Name
LESSON
56
1
Equal Shares
CC.3.NF.1
OBJECTIVE Divide models to make equal shares.
Six brothers share 5 sandwiches equally. How much
does each brother get? Draw to model the problem.
Step 1 Draw 5 squares for the sandwiches.
Step 2 There are 6 brothers. Draw lines to divide
each sandwich into 6 equal parts.
Step 3 Each brother will get 1 equal part from each sandwich.
So, each brother gets 5 sixths of a sandwich.
Draw lines to show how much each person gets.
Write the answer. Check students’ lines. Possible answers are given.
2. 6 friends share 3 fruit bars
equally.
© Houghton Mifflin Harcourt Publishing Company
1. 4 sisters share 3 pies equally.
3 fourths, or 1 half and 1 fourth,
3 sixths, or 1 half, of a fruit bar
of a pie
Number and Operations–Fractions
111
Name
1
Equal Shares
CC.3.NF.1
For 1–2, draw lines to show how much
each person gets. Write the answer.
For 2–3, check students’ lines.
1. 6 friends share 3 sandwiches equally.
Possible answer: 1 half or
3 sixths of a sandwich
2. 8 classmates share 4 pizzas equally.
Possible answer: 4 eighths, or
1 half, of a pizza
Possible answer: 1 whole and
1 fourth, or 5 fourths, of a
granola bar
Problem Solving
Possible answers are given.
4. Three brothers share 2 sandwiches
equally. How much of a sandwich
does each brother get?
112
5. Six neighbors share 4 pies equally.
How much of a pie does each
neighbor get?
2 thirds, or 1 half and 1 sixth, of
4 sixths, or 1 half and 1 sixth,
a sandwich
of a pie
Lesson 56
© Houghton Mifflin Harcourt Publishing Company
3. 4 teammates share 5 granola bars equally.
Draw to show how much each person
gets. Shade the amount that one person
gets. Write the answer.
Name
1
Unit Fractions of a Whole
LESSON
57
CC.3.NF.1
OBJECTIVE Use a fraction to name one part of a whole that is divided into
equal parts.
A fraction is a number. It names part of a whole or part of a group.
The top number tells how many equal parts are being counted.
The bottom number tells how many equal parts are in the whole.
A unit fraction names 1 equal part of a whole. It always has 1
as its top number.
How much is 1 part of a fruit bar that is cut into 8 equal parts?
Step 1 Use fraction strips. Make a strip showing 8 equal parts, or eighths.
Step 2 Shade 1 of the parts and name it.
© Houghton Mifflin Harcourt Publishing Company
__.
This fraction is called 1
8
1.
So, 1 part of a fruit bar that can be divided into 8 equal parts is __
8
Write the number of equal parts in the whole.
Then write the fraction that names the shaded part.
2.
1.
4
equal parts
1
__
4
Number and Operations–Fractions
3.
3
1
__
3
equal parts
6
equal parts
1
__
6
113
Name
1
Unit Fractions of a Whole
CC.3.NF.1
Write the number of equal parts in the whole.
Then write the fraction that names the shaded part.
2.
1.
6
2
equal parts
equal parts
1
__
2
1
__
6
3.
4.
4
3
equal parts
1
__
equal parts
1
__
3
4
Draw a picture of the whole. Check students’ drawings.
1 is
5. __
3
Problem Solving
Possible drawings are shown.
7. Tyler made a pan of cornbread.
He cut it into 8 equal pieces and
ate 1 piece. What fraction of the
cornbread did Tyler eat?
1
__
8
114
8. Anna cut an apple into 4 equal
pieces. She gave 1 piece to her
sister. What fraction of the apple
did Anna give to her sister?
1
__
4
Lesson 57
© Houghton Mifflin Harcourt Publishing Company
1 is
6. __
8
Name
1
Fractions of a Whole
LESSON
58
CC.3.NF.1
OBJECTIVE Read, write, and model fractions that represent more than one part of a
whole that is divided into equal parts.
Some shapes can be cut into equal parts.
A fraction can name more than 1 equal part of a whole.
Write a fraction in words and in numbers to name the shaded part.
How many equal parts make up the whole shape? 6 equal parts
How many parts are shaded? 3 parts
So, 3 parts out of 6 equal parts are shaded. Read: three sixths. Write: _36
1. Shade three parts out of eight equal parts. Write a fraction
in words and in numbers to name the shaded part.
Read:
three
Write:
3
__
8
Possible shading is shown.
eighths
© Houghton Mifflin Harcourt Publishing Company
Write the fraction that names each part. Write a fraction
in words and in numbers to name the shaded part.
3.
2.
Each part is
four
sixths
4
__
6
Number and Operations–Fractions
1
__
6
.
4.
Each part is
two
2
__
4
1
__
4
fourths
.
Each part is
five
1
__
8
.
eighths
5
__
8
115
Name
1
Fractions of a Whole
CC.3.NF.1
Write the fraction that names each part. Write a fraction
in words and in numbers to name the shaded part.
2.
1.
Each part is
three
1
__
6
1
__
.
Each part is
five
sixths
3
__
8
.
eighths
5
__
8
6
3.
4.
1
__
Each part is
two
3
1
__
.
Each part is
three
thirds
2
__
4
.
fourths
3
__
4
3
Shade the fraction circle to model the fraction.
Then write the fraction in numbers.
8
__
4
__
6
8
Problem Solving
7. Emma makes a poster for the
school’s spring concert. She divides
the poster into 8 equal parts. She
uses two of the parts for the title.
What fraction of the poster does
Emma use for the title?
8. Lucas makes a flag. It has 6 equal
parts. Five of the parts are red.
What fraction of the flag is red?
2
__
8
5
__
6
116
Lesson 58
© Houghton Mifflin Harcourt Publishing Company
6. eight out of eight
5. four out of six
Name
LESSON
59
1
Fractions of a Group
CC.3.NF.1
OBJECTIVE Model, read, and write fractional parts of a group.
Adam has a collection of cars.
What fraction names the shaded part of the collection?
Step 1 Count how many cars are shaded. There are 3 shaded cars.
This number will be the numerator, or the top number of the fraction.
Step 2 Count the total number of cars. 8 This number will be the
denominator, or the bottom number of the fraction.
Step 3 Read the fraction: three eighths, or three out of eight.
3 of Adam’s cars are shaded.
So, __
8
Write a fraction to name the shaded part of each group.
© Houghton Mifflin Harcourt Publishing Company
1.
2.
2
__
4
3
__
4
Write a whole number and a fraction greater than 1
to name the part filled.
4.
3.
Think: 1 can = 1
Think: 1 pan = 1
2
Number and Operations–Fractions
6
__
3
2
12
___
6
117
Name
1
Fractions of a Group
CC.3.NF.1
Write a fraction to name the shaded part of each group.
2.
1.
6 or __
3
__
8
1
3
__, or __
6
2
4
Write a whole number and a fraction greater
than 1 to name the part filled. Think: 1 container = 1
4.
3.
8
__
4
2
18
___
6
3
Draw a quick picture. Then, write a fraction
Possible shading is shown.
to name the shaded part of the group.
6. Draw 6 circles.
Make 3 groups.
Shade 1 group.
5. Draw 4 circles.
Shade 2 circles.
3
4
© Houghton Mifflin Harcourt Publishing Company
1, or __
2
__
2
__
6
Problem Solving
7. Brian has 3 basketball cards and
5 baseball cards. What fraction of
Brian’s cards are baseball cards?
5
__
8
118
8. Sophia has 3 pink tulips and
3 white tulips. What fraction
of Sophia’s tulips are pink?
3
1
__, or __
6
2
Lesson 59
Name
LESSON
60
Find Part of a Group Using Unit Fractions
OBJECTIVE Find fractional parts of a group using unit fractions.
1
CC.3.NF.1
1 of them.
Lauren bought 12 stamps for postcards. She gave Brianna __
6
How many stamps did Lauren give to Brianna?
Step 1 Find the total number of stamps. 12 stamps
Step 2 Since you want to find __16 of the group, there should be
1
.
6 equal groups. Circle one of the groups to show __
6
1 of the stamps. How many stamps are in 1 group? 2 stamps
Step 3 Find __
6
1 of 12 = 2
So, Lauren gave Brianna 2 stamps. __
6
Circle equal groups to solve. Count the number
of shapes in 1 group.
© Houghton Mifflin Harcourt Publishing Company
1 of 8 =
1. __
4
1 of 16 =
3. __
4
Check students’ circles.
1 of 9 =
2. __
3
2
4
Number and Operations–Fractions
1 of 18 =
4. __
6
3
3
119
Name
1
Find Part of a Group Using Unit Fractions
CC.3.NF.1
Circle equal groups to solve. Count the number Check students’ circles.
of items in 1 group.
1 of 12 =
1. __
4
3
1 of 16 =
2. __
8
1 of 12 =
3. __
3
4
1 of 9 =
4. __
3
3
1 of 18 =
5. __
6
3
1 of 4 =
6. __
2
2
Problem Solving
7. Marco drew 24 pictures. He drew
1
__
of them in art class. How many
6
pictures did Marco draw in art
class?
4 pictures
120
8. Caroline has 16 marbles. One
eighth of them are blue. How
many of Caroline’s marbles are
blue?
2 marbles
Lesson 60
© Houghton Mifflin Harcourt Publishing Company
2
Name
LESSON
61
Problem Solving • Find the Whole Group
Using Unit Fractions
1
CC.3.NF.1
OBJECTIVE Solve fraction problems by using the strategy draw a diagram.
There are 3 apple juice boxes in the cooler. One fourth
of the juice boxes in the cooler are apple juice. How many
juice boxes are in the cooler?
Read the Problem
What do I need to find?
I need to find
boxes
how many juice
are in the cooler.
What information do I need to use?
There are
3
apple juice boxes.
One fourth of the juice boxes are
apple juice.
© Houghton Mifflin Harcourt Publishing Company
How will I use the information?
I will use the information in the
problem to draw a diagram.
Solve the Problem
Describe how to draw a diagram
to solve.
The denominator in 1_4 tells you
that there are 4 parts
in the whole group.
Draw 4 circles to
show
4
parts.
Since 3 juice boxes are 1_4 of
the group, draw 3
counters in the first circle.
Since there are 3
counters in the first circle,
draw 3 counters in
each of the remaining
circles. Then count all
of the counters.
So, there are 12 juice
boxes in the cooler.
1. Max has 3 beta fish in his fish
tank. One half of his fish are
beta fish. How many fish does
Max have in his tank?
6 fish
Number and Operations–Fractions
2. Two boys are standing in line.
One sixth of the students in line
are boys. How many students
are standing in line?
12 students
121
Name
Problem Solving • Find the Whole Group
Using Unit Fractions
1
CC.3.NF.1
Draw a quick picture to solve. Check students’ work.
1. Katrina has 2 blue ribbons for her hair.
One fourth of all her ribbons are blue. How
many ribbons does Katrina have in all?
8 ribbons
2. One eighth of Tony’s books are mystery
books. He has 3 mystery books. How
many books does Tony have in all?
24 books
3. Brianna has 4 pink bracelets. One third
of all her bracelets are pink. How many
bracelets does Brianna have?
12 bracelets
4. Ramal filled 3 pages in a stamp album. This is
one sixth of the pages in the album. How many
pages are there in Ramal’s stamp album?
© Houghton Mifflin Harcourt Publishing Company
18 pages
5. Jeff helped repair one half of the bicycles in a bike
shop last week. If Jeff worked on 5 bicycles, how
many bicycles did the shop repair in all last week?
10 bikes
6. Layla collects postcards. She has 7 postcards from
Europe. Her postcards from Europe are one third
of her total collection. How many postcards in all
does Layla have?
21 postcards
122
Lesson 61
Name
LESSON
62
Fractions on a Number Line
1
CC.3.NF.2a,
CC.3.NF.2b
OBJECTIVE Represent and locate fractions on a number line.
Use the fraction strips to help name the points on the number line.
1.
Draw a point to show __
3
Step 1 The denominator is 3, so use fraction strips for thirds. Place
the fraction strips above the number line. Use the fraction
strips to divide the number line into three equal lengths.
Step 2 Label each mark on the number line.
Think: The distance between each mark is 1_3 of the total
distance, so count the number of 1_3 lengths.
1.
Step 3 Draw a point on the number line to show __
3
0
1
3
1
3
1
1
3
0
3
1
3
2
3
3
3
0 of 3
equal lengths
1 of 3
equal lengths
2 of 3
equal lengths
3 of 3
equal lengths
© Houghton Mifflin Harcourt Publishing Company
2.
1. Complete the number line. Draw a point to show __
4
0
1
4
1
4
0
4
1
4
1
1
4
1
2
3
4
4
4
4
4
Write the fraction that names the point.
0
1
6
1
6
A
0
6
2. point A
1
__
6
Number and Operations–Fractions
1
6
2
6
1
6
3
6
1
6
B
1
1
6
5
6
3. point B
6
6
4
__
6
123
Name
Fractions on a Number Line
1
CC.3.NF.2a,
CC.3.NF.2b
Use fraction strips to help you complete the number line.
Then locate and draw a point for the fraction.
__
1. 1
3
0
1
1
3
0
3
3
2. __
4
1
3
0
2
3
3
3
1
1
4
0
4
1
2
3
4
4
4
4
4
Write the fraction that names the point.
0
8
1
1
8
3. point A
A
3
8
2
__
8
4
8
B
6
8
C
8
8
5
__
4. point B
8
7
__
5. point C
8
Problem Solving
6. Jade ran 6 times around her
neighborhood to complete a total
of 1 mile. How many times will
she need to run to complete
5
_ of a mile?
6
5 times
124
7. A missing fraction on a number
line is located exactly halfway
between 3_6 and 5_6 . What is the
missing fraction?
4
__
6
Lesson 62
© Houghton Mifflin Harcourt Publishing Company
0
Name
LESSON
63
Model Equivalent Fractions
1
CC.3.NF.3a
OBJECTIVE Model equivalent fractions by using area models and number lines.
Equivalent fractions are two or more fractions that name
the same amount.
You can use fraction circles to model equivalent fractions.
__.
Find a fraction that is equivalent to 1
2
1
__ = __
2
4
Step 1 Look at the first circle. It is divided into
2 equal parts. Shade one part to show 1_2 .
1
2
1
2
1
4
2
1
1 is equivalent to 2
__.
So, __
1
4
2
1 = __
__
2
4
1
Step 3 Count the number of parts shaded now.
There are 2 parts out of 4 parts shaded.
4
Step 2 Draw a line to divide the circle into
4 equal parts because 4 is the denominator
in the second fraction.
4
4
Shade the model. Then divide the pieces to find
the equivalent fraction. Possible shading is shown.
© Houghton Mifflin Harcourt Publishing Company
1.
2.
2
1 = ____
__
4
8
3.
2
8
4.
4
2 = ____
__
3
Number and Operations–Fractions
4
1 = ____
__
6
6
3 = ____
__
4
8
125
Name
Model Equivalent Fractions
1
CC.3.NF.3a
Shade the model. Then divide the pieces to find the
equivalent fraction. Check students’ shadings.
1.
2.
2
4
2 = ____
__
4
8
1 = ____
__
3
6
Use the number line to find the equivalent fraction.
0
4
1
4
2
4
0
2
3
4
1
2
4
4
2
2
2
1 = ____
__
2
4
4.
0 1 2 3 4 5 6 7 8
8 8 8 8 8 8 8 8 8
0
4
1
4
2
4
3
4
4
4
6
3
__ = ____
4
8
Problem Solving
5. Mike says that 3_3 of his fraction
model is shaded blue. Ryan
says that 6_6 of the same model
is shaded blue. Are the two
fractions equivalent? If so, what is
another equivalent fraction?
__
Yes; possible answer: 4
4
126
6. Brett shaded 4_8 of a sheet of
notebook paper. Aisha says he
shaded 1_2 of the paper. Are the
two fractions equivalent? If
so, what is another equivalent
fraction?
__
Yes; possible answer: 2
4
Lesson 63
© Houghton Mifflin Harcourt Publishing Company
3.
Name
LESSON
64
Equivalent Fractions
1
CC.3.NF.3b
OBJECTIVE Generate equivalent fractions by using models.
3 of a sheet of wrapping paper.
Kaitlyn used __
4
3
__.
__ = __
Find a fraction that is equivalent to 3
4
4
8
Step 1 The top fraction strip is divided into 4 equal
parts. Shade 3_4 of the strip to show how much
paper Kaitlyn used.
Step 2 The bottom strip is divided into 8 equal
parts. Shade parts of the strip until the
same amount is shaded as in the top strip.
6 parts of the bottom strip are shaded.
1
4
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
8
6
3
__ = __
4
8
6 is equivalent to 3
__.
So, __
8
4
Each shape is 1 whole. Shade the model
to find the equivalent fraction.
© Houghton Mifflin Harcourt Publishing Company
1.
2.
2
1 = ____
__
3
6
2
1
__ = ____
4
8
3.
16
4
__ = ____
2
8
Number and Operations–Fractions
127
Name
Equivalent Fractions
1
CC.3.NF.3b
Each shape is 1 whole. Shade the model to find the
equivalent fraction.
1.
2.
3
1 = ____
__
2
6
6
3
__ = ____
4
8
Circle equal groups to find the equivalent fraction.
4.
3.
2
4
__ = ____
6
3
1
2 = ____
__
4
2
5. May painted 4 out of 8 equal
parts of a poster board blue.
Jared painted 2 out of 4 equal
parts of a same-size poster board
red. Write fractions to show
which part of the poster board
each person painted.
4; Jared __
2
May: __
8
© Houghton Mifflin Harcourt Publishing Company
Problem Solving
Check students’ drawings.
4
6. Are the fractions equivalent?
Draw a model to explain.
yes
128
Lesson 64
Name
LESSON
65
Relate Fractions and Whole Numbers
1
CC.3.NF.3c
OBJECTIVE Relate fractions and whole numbers by expressing whole numbers as fractions and
recognizing fractions that are equivalent to whole numbers.
A fraction greater than 1 has a numerator greater
than its denominator.
Jason ran 2 miles and Tyra ran 6_3 miles. Did Jason and
Tyra run the same distance?
Step 1 Use fraction strips to show the distances.
Use 2 whole strips to show Jason’s distance.
Use six _31 -strips to show Tyra’s distance.
Jason
Tyra
1
1
3
1
1
3
1
3
1
3
1
3
1
3
2=6
1=3
3
3
Step 2 Compare the fraction strips.
Since the fraction strips for 2 and 6_3 are the same length,
they are equal.
© Houghton Mifflin Harcourt Publishing Company
So, Jason and Tyra ran the same distance.
Use the number line to find whether the two numbers
are equal. Write equal or not equal.
'
'
+
__ and 1
1. 4
4
equal
Number and Operations–Fractions
(
(
+
)
+
3
2. 1 and __
4
not equal
*
+
+
+
4
__ and __
3. 1
4
4
not equal
129
Name
Relate Fractions and Whole Numbers
1
CC.3.NF.3c
Use the number line to find whether the two numbers
are equal. Write equal or not equal.
1
0
0
6
1
6
2
6
3
6
4
6
5
6
6
6
6
2. 1 and __
6
__ and 1
1. 0
6
not equal
6
__ and __
3. 1
6
6
equal
not equal
Each shape is 1 whole. Write a fraction greater than 1
for the parts that are shaded.
5.
4.
2=
4
__
2
6.
4=
12
___
3
12
___
3=
4
1=
8
__
8
Problem Solving
8. Rachel jogged along a trail that
was 1_4 of a mile long. She jogged
along the trail 8 times. How many
miles did Rachel jog in all?
8
__ , or 2 miles
4
130
9. Jon ran around a track that was
1
_ of a mile long. He ran around
8
the track 24 times. How many
miles did Jon run in all?
24
___ , or 3 miles
8
Lesson 65
© Houghton Mifflin Harcourt Publishing Company
7.
Name
LESSON
66
Problem Solving • Compare Fractions
1
CC.3.NF.3d
OBJECTIVE Solve comparison problems by using the strategy act it out.
Nick walked 2_4 mile to the gym. Then he walked 3_4 mile to the store.
Which distance is shorter?
Read the Problem
Solve the Problem
What do I need to find?
I need to find which distance
is shorter.
What information do I need to use?
Nick walked
2
__
4
Then he walked
store.
mile to the gym.
3
__
4
mile to the
How will I use the information?
I will use fraction strips and
compare
© Houghton Mifflin Harcourt Publishing Company
the lengths of
the models to find which distance
is shorter.
1. Mariana and Shawn each had
6 pages to read. Mariana read
2
_ of her pages. Shawn read 1_
3
3
of his pages. Who read more
pages? Explain.
Mariana; Possible explanation:
2 > __
1
__
3 3
Number and Operations–Fractions
1
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
Compare the lengths.
3
2
__
__
<
4
4
The length of the 2_4 model is less
than the length of the 3_4 model.
So, the distance to the gym is
shorter.
2. Carlos ran 3_8 of the race course.
Lori ran 3_6 of the same race
course. Who ran farther?
Explain.
3
__ > __
Lori; Possible explanation: 3
6 8
131
Name
Problem Solving • Compare Fractions
1
CC.3.NF.3d
Solve.
1. Luis skates 2_3 mile from his home to
school. Isabella skates 2_4 mile to get to
school. Who skates farther?
Think: Use fraction strips to act it out.
Luis
2. Sandra makes a pizza. She puts
mushrooms on 2_8 of the pizza. She adds
green peppers to 5_8 of the pizza. Which
topping covers more of the pizza?
green peppers
3. The jars of paint in the art room have
different amounts of paint. The green
paint jar is 4_8 full. The purple paint jar is
_4
6
full. Which paint jar is less full?
the green paint jar
_2
3
© Houghton Mifflin Harcourt Publishing Company
4. Jan has a recipe for bread. She uses
cup of flour and 1_3 cup of chopped
onion. Which ingredient does she use
more of, flour or onion?
flour
5. Edward walked 3_4 mile from his home to
the park. Then he walked 2_4 mile from
the park to the library. Which distance
is shorter?
2 mile
__
4
132
Lesson 66
Name
LESSON
67
Compare Fractions with the Same
Denominator
1
CC.3.NF.3d
OBJECTIVE Compare fractions with the same denominator by using models and reasoning strategies.
Pete’s Prize Pizzas makes a special pizza. Of the toppings,
_1
4
is peppers and 3_4 is ham. Does the pizza have
more peppers or ham?
1 and __
3.
Compare __
4
4
Step 1 The denominators of both fractions are the same, 4.
Use fraction circles divided into fourths to model
the fractions.
Step 2 Shade 1 part of the first circle to show 1_4 .
Shade 3 parts of the second circle to show 3_4 .
Step 3 Compare. 3 parts is more than 1 part.
3
__
1
__
>
4
4
© Houghton Mifflin Harcourt Publishing Company
So, the pizza has more ham.
Compare. Write < , > , or =.
1.
2.
2
1
__
__
6 > 6
2
__
3. 1
< __
3
3
Number and Operations–Fractions
3
__
__
4. 5
8 > 8
2 = __
2
__
4
4
3
__
__
5. 1
4 < 4
4
__
6. 4
= __
8
8
133
Name
Compare Fractions with the
Same Denominator
1
CC.3.NF.3d
1
3
1. __
> __
4
4
0
__
__
2. 3
>
6
6
1
__
3. 1
= __
2
2
6
__
__
4. 5
6 < 6
5
__
5. 7
> __
8
8
3
__
6. 2
< __
3
3
0
__
__
7. 8
8 > 8
1
__
8. 1
= __
6
6
2
__
__
9. 3
4 > 4
2
__
__
10. 1
6 < 6
0
__
__
11. 1
2 > 2
3
__ = __
12. 3
8
8
4
__
13. 1
< __
4
4
4
__
14. 5
> __
8
8
6
__
15. 4
< __
6
6
Problem Solving
16. Ben mowed 5_6 of his lawn in
one hour. John mowed 4_6 of his
lawn in one hour. Who mowed
less of his lawn in one hour?
John
134
17. Darcy baked 8 muffins. She put
blueberries in 5_8 of the muffins.
She put raspberries in 3_8 of the
muffins. Did more muffins have
blueberries or raspberries?
blueberries
Lesson 67
© Houghton Mifflin Harcourt Publishing Company
Compare. Write < , > , or = .
Name
LESSON
68
Compare Fractions with the Same
Numerator
1
CC.3.NF.3d
OBJECTIVE Compare fractions with the same numerator by using models and reasoning strategies.
Ryan takes a survey of his class. 1_8 of the class has dogs,
and 1_3 of the class has cats. Are there more dog owners or cat
owners in Ryan’s class?
Dog Owners
3
Step 1 Divide the first circle into 8 equal parts.
Cat Owners
3
1
__
3
1
1
1
__
8
Compare the fractions.
Shade 1_8 of the circle to show dog owners.
1
3
Step 2 Divide the second circle into
3 equal parts. Shade 1_3 of the circle to
show cat owners.
Step 3 Compare the shaded parts of the circles.
Which shaded part is larger?
1
1.
__ is larger than __
3
8
1
__
<
8
3
1
__
So, there are more cat owners than dog owners in Ryan’s class.
© Houghton Mifflin Harcourt Publishing Company
Compare. Write <, >, or =.
3
__ > __
1. 3
4
6
1
__
2. 1
< __
8
6
2
2
3. __
> __
4
6
2
__ > __
4. 2
3
6
4
__
5. 4
> __
6
8
2
__
6. 2
< __
8
4
5
__
7. 5
> __
6
8
1
__
8. 1
> __
3
4
3
__
__
9. 3
<
6
4
1
__
10. 1
= __
3
3
3
__
__
11. 3
3 > 4
2
__
__
12. 2
8 < 6
Number and Operations–Fractions
135
Name
Compare Fractions with the Same Numerator
1
CC.3.NF.3d
Compare. Write < , > , or = .
1
1
__
1. __
8 < 2
3
3
2. __
< __
8
6
2
2
3. __
> __
3
4
2
2
4. __
< __
8
3
3
3
5. __
< __
6
4
1
1
6. __
> __
2
6
5
5
__
7. __
6 > 8
4
4
8. __
= __
8
8
6
6
__
9. __
8 < 6
1 1
8 8
1 1
8 8
1
2
Problem Solving
10. Javier is buying food in the lunch
line. The tray of salad plates is 3_8
full. The tray of fruit plates is
3
_ full. Which tray is more full?
4
the fruit plate tray
136
11. Rachel bought some buttons.
Of the buttons, 2_4 are yellow
and 2_8 are red. Rachel bought
more of which color buttons?
yellow
Lesson 68
© Houghton Mifflin Harcourt Publishing Company
1 1
8 8
1 1
8 8
1
2
Name
LESSON
69
Compare Fractions
1
CC.3.NF.3d
OBJECTIVE Compare fractions by using models and strategies involving the size
of the pieces in the whole.
Mrs. Brown’s recipe uses 2_3 cup of flour. Mrs. Young’s recipe
uses 3_4 cup of flour. Which recipe uses more flour?
2 and __
3.
Compare __
3
4
• You can compare fractions using fraction strips.
Step 1 Model each fraction.
1
Step 2 Compare the lengths of the models.
The length of the 3_4 model is greater
than the length of the 2_3 model.
3
__
2
__
4 > 3
1
3
1
3
1
4
1
4
1
3
1
4
1
4
So, Mrs. Young’s recipe uses more flour.
© Houghton Mifflin Harcourt Publishing Company
4. Which is greater?
__ and __
Compare 3
6
6
• The denominators are the same, so compare the
numerators.
4.
3 < __
3 < 4, so __
6 6
3
4
__ is greater than 3
__ . __
So, 4
> __
6
6 6
6
Compare. Write <, >, or = . Write the strategy you used.
3
2
1. __
< __
8
8
5
__
2. 7
> __
8
6
same denominator
3
__
3. 3
> __
4
6
Possible strategies
are given.
missing pieces
5
__
__
4. 3
6 < 6
same numerator
Number and Operations–Fractions
same denominator
137
Name
Compare Fractions
1
CC.3.NF.3d
Possible strategies are given.
Compare. Write < , > , or = . Write the strategy you used.
3
__
__
1. 3
<
8
4
7
__
2. 2
< __
3
8
1
__
3. 3
> __
4
4
Think: The numerators are the
same. Compare the denominators.
The greater fraction will have the
lesser denominator.
same numerator
missing
same
pieces
denominator
Name a fraction that is less than or greater than the
given fraction. Draw to justify your answer. Answers and drawings will vary.
3
__ ____
5. less than 3
4 8
Problem Solving
6. At the third-grade party, two
groups each had their own pizza.
The blue group ate 7_8 pizza. The
green group ate 2_8 pizza. Which
group ate more of their pizza?
the blue group
138
7. Ben and Antonio both take the
same bus to school. Ben’s ride is
7
_ mile. Antonio’s ride is 3_ mile.
8
4
Who has a longer bus ride?
Ben
Lesson 69
© Houghton Mifflin Harcourt Publishing Company
2
1 ____
4. greater than __
3 3
Name
Compare and Order Fractions
LESSON
70
1
CC.3.NF.3d
OBJECTIVE Compare and order fractions by using models and reasoning strategies.
You can use a number line to compare and order fractions.
5 , __
2 , and __
7 from least to greatest.
Order __
8 8
8
Since you are comparing eighths, use a number line
divided into eighths.
__.
Step 1 Draw a point on the number line to show 5
8
7.
2 and __
Step 2 Repeat for __
8
8
0
8
1
8
2
8
3
8
0
4
8
5
8
6
8
7
8
8
8
1
1
2
Step 3 Fractions increase in size as you move right
on the number line. Write the fractions in order
from left to right.
© Houghton Mifflin Harcourt Publishing Company
5,
__ , __
So, the order from least to greatest is 2
8 8
7.
__
8
Write the fractions in order from least to greatest.
2 , __
2 , __
2
2. __
3 6 4
6 , __
3
4 , __
1. __
6 6 6
0
6
1
6
0
2
6
3
6
1
2
3
4, __
6
__, __
6 6 6
1 , __
1 , __
1
3. __
4 8 2
4
6
5
6
6
6
Think: When the numerators are
the same, look at the denominators
to compare the size of the pieces.
1
2, __
2, __
2
__
6 4 3
3 , __
0 , __
2
4. __
4 4 4
1, __
1
1
__, __
8 4 2
Number and Operations–Fractions
0, __
2, __
3
__
4 4 4
139
Name
Compare and Order Fractions
1
CC.3.NF.3d
Write the fractions in order from greatest to least.
4, __
1, __
3
1. __
4 4 4
4
__
4
,
3
__
4
1
__
,
4
2, __
5, __
1
2. __
,
1
__
6
2, __
2, __
2
4. __
8 8 8
5
__
8
,
2
__
8
,
2
__
6
,
4
__
6
,
3
__
6
1
__
,
8
,
2
__
8
,
5
__
6
,
3
__
4
Think: The denominators are
the same, so compare the
numerators: 4 > 3 > 1.
1, __
1, __
1
3. __
3 6 2
1
__
2
,
1
__
3
3 6 8
2
__
3
2, __
4, __
3
5. __
2
__
4
7, __
0, __
3
7. __
0
__
8
4 4 4
8 8 8
,
3
__
4
,
3
__
8
,
4
__
4
4, __
5, __
2
6. __
2
__
6
,
7
__
8
3, __
3, __
3
8. __
3
__
8
6 6 6
4 6 8
Problem Solving
9. Mr. Jackson ran 7_8 mile on Monday.
He ran 3_8 mile on Wednesday
and 5_8 mile on Friday. On which day
did Mr. Jackson run the shortest
distance?
10. Delia has three pieces of ribbon.
Her red ribbon is 2_4 foot long. Her
green ribbon is 2_3 foot long.
Her yellow ribbon is 2_6 foot long.
She wants to use the longest piece
for a project. Which color ribbon
should Delia use?
Wednesday
green
140
Lesson 70
© Houghton Mifflin Harcourt Publishing Company
Write the fractions in order from least to greatest.