Math Review-Fractions

Number and Operations - Fractions
*Click on the standard or the problem to go directly to desired page.
MAFS.4.NF.1.1 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5
MAFS.4.NF.3.7 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 4
Instructions and Suggestions
4

Instructions and Suggestions
 This resource is designed to address the standards in
need of re-teaching based on data.
 Provide 2-5 minutes for students to solve the problem
and about another 5 minutes to debrief the problem.
 The fifth problem for each standard is an MFAS task
pulled from CPALMs. To further guide instruction, click
on the top of the slide for the task rubric.
Back to
Start Page

MAFS.4.NF.1.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by
using visual fraction models, with attention to how the number and size of
the parts differ even though the two fractions themselves are the same
size. Use this principle to recognize and generate equivalent fractions.
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.1.1
4thGrade
Number&Operations
Fractions
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using
visual fraction models, with attention to how the number and size of the parts
differ even though the two fractions themselves are the same size. Use this
principle to recognize and generate equivalent fractions.
Select all fraction comparisons that
are true. Use visual models to prove
your answers.
A.
𝟑
𝟔
=
𝟓
𝟏𝟎
B.
𝟔
𝟖
=
𝟗
𝟏𝟐
C.
𝟑
𝟏𝟐
=
𝟏
𝟑
D.
𝟏
𝟑
=
𝟒
𝟏𝟐
E.
𝟏
𝟐
=
𝟑
𝟒
Problem 1
AnswerStandard
page

MAFS.4.NF.1.1
Problem 1
Answer Key
Problem 2Standard
page
A.
𝟑
𝟔
=
𝟓
𝟏𝟎
B.
𝟔
𝟖
=
𝟗
𝟏𝟐
C.
𝟑
𝟏𝟐
=
𝟏
𝟑
D.
𝟏
𝟑
=
𝟒
𝟏𝟐
E.
𝟏
𝟐
=
𝟑
𝟒
4thGrade
Number&Operations
Fractions

Standard 1 problem 2
AnswerStandard
page
MAFS.4.NF.1.1
Problem 2
Sara needs
𝟒
𝟏𝟐
yard of string to finish her
project. S𝐞𝐥𝐞𝐜𝐭 𝐚𝐥𝐥 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧𝐬 𝐭𝐡𝐚𝐭 𝐚𝐫𝐞
equivalent to
𝟒
𝟏𝟐
.
A.
𝟐
𝟔
B.
𝟐
𝟖
C.
𝟏
𝟒
D.
𝟏
𝟑
E.
𝟐
𝟓
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.1
Problem 2
Answer Key
Problem 3Standard
page
A.
𝟐
𝟔
B.
𝟐
𝟖
C.
𝟏
𝟒
D.
𝟏
𝟑
E.
𝟐
𝟓
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.1.1
Problem 3
Jen and Jack each drew a picture on paper that was the same size.
They cut apart their pictures to turn them into puzzles. Jen cut her
picture into 3 equal pieces. Jack cut his picture into 9 equal pieces.
Jen colored 1/3 of her puzzle. Jack colored 3/9 of his puzzle.
Jen said she colored more of her puzzle. Jack said they colored the
same amount.
Who is correct and why?
Create a model to prove your answer.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.1
Problem 3
Answer Key
Problem 4Standard
page
Possible Student Explanation:
Jack is correct. Jen’s pieces are larger, but there are fewer
pieces. Jack’s pieces are smaller, and there are more pieces.
Three of Jack’s pieces are the same size as one of Jen’s pieces.
4thGrade
Number&Operations
Fractions

MAFS.4.MD.1.1
Problem 4
AnswerStandard
page
MAFS.4.NF.1.1
Problem 4
On a sheet of graph paper draw two 12 x 12
squares.
Divide the first square into 6 equal pieces
with 5 shaded in to represent
𝟓
𝟔
.
In the second square model another
fraction that is equivalent to
𝟓
𝟔
.
Describe the similarities and differences
you notice.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.1
Problem 4
Answer Key
Problem 5Standard
page
Possible Solution and Explanation:
Each 12th takes up twice as much space as a 6th, so
𝟏
𝟔
is
equivalent to
𝟐
𝟏𝟐
. These pictures show that the two shapes are
equivalent because they take up the same amount of space in
each drawing.
4thGrade
Number&Operations
Fractions

MAFS.4.MD.1.
1
Problem 5-
AnswerStandard
page
MAFS.4.NF.1.1
Problem 5
Equivalence Using a Number Line- CPALMs Formative Assessment
* Click on link above to access the formative assessment rubric.
Use a number line like the one below to
show that
𝟏
𝟐
is equivalent to
𝟐
𝟒
.
0 1
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.1
Problem 5
Answer Key
Next
Standard
Page
Standard
page
*Click on link above to access the formative assessment rubric.
Equivalence Using a Number Line- CPALMs Formative Assessment
When dividing the space between 0
and 1 into two equal parts,
𝟏
𝟐
is in the
center. When dividing the space
between 0 and 1 into four equal
parts,
𝟐
𝟒
is in the center showing
𝟏
𝟐
is
equivalent to
𝟐
𝟒
.
Questions Eliciting Thinking
• What does the fraction
𝟐
𝟒
mean? What
does the two represent? What about the
four?
• How could we divide this interval into
four equal parts? What would that show
us?
• How can you use four equal parts to
show
𝟐
𝟒
?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.1.2
Compare two fractions with different numerators and different denominators, e.g., by
creating common denominators or numerators, or by comparing to a benchmark fraction
such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the
same whole. Record the results of comparisons with symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
Problem 1
AnswerStandard
page
Amar and Jamari each ordered a small pizza at
the Pizza Shack. Amar’s pizza was cut into 6
slices. Jamari’s pizza was cut into 5 slices.
After eating, each boy had one slice
left of their pizza.
Who had more pizza left? How do you know?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 1
Answer Key
Problem 2Standard
page
Even though they both had one slice of pizza left, Jamari had more
pizza left. Both pizza’s are the same size, but when they were cut
Amar’s was cut into 6 pieces, while Jamari’s was cut into 5 pieces. Each
of the 5 pieces were larger than each of the 6 pieces, so the final piece
would leave Jamari with more pizza than Amar.
Amar Jamari
4thGrade
Number&Operations
Fractions

dard 1 problem 2
AnswerStandard
page
MAFS.4.NF.1.2
Problem 2
Cary ran
𝟐
𝟒
of a mile. Kevin ran
𝟕
𝟏𝟎
of a mile. Who ran
farther ? How did you solve this problem?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 2
Answer Key
Problem 3Standard
page
𝟕
𝟏𝟎
of a mile is farther. I solved this problem using a
number line to see which number was larger and the
furthest distance.
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.1.2
Problem 3
Is
𝟒
𝟓
greater than, less
than, or equal to
𝟐
𝟑
?
How do you know?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 3
Answer Key
Problem 4Standard
page
𝟒
𝟓
is greater than
𝟐
𝟑
. I know this because I compared
them using a number line and the number line shows
𝟒
𝟓
is larger.
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.1.2
Problem 4
Ed measured 4/10 cup of sunflower seeds and
2/3 cup of raisins. Which fraction is larger,
4/10 or 2/3? How do you know?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 4
Answer Key
Problem 5Standard
page
Solution: 2/3
2/3 is larger than 4/10 because 2/3 is more than ½
and 4/10 is less than 1/2.
4thGrade
Number&Operations
Fractions

MAFS.4.MD.1.2
Problem 5-
AnswerStandard
page
MAFS.4.NF.1.2
Problem 5
Corn Farms-CPALMs Formative
The Nelson brothers are corn farmers. Jim
Nelson plants corn on
𝟑
𝟓
of an acre of land.
Brian Nelson plants corn on
𝟗
𝟏𝟐
of an acre of
land.
Whose portion of an acre planted in corn is
larger?
How do you know?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.1.2
Problem 5
Answer Key
Back
to Start
Page
Standard
page
Corn Farms-CPALMs Formative
𝟗
𝟏𝟐
is more than
𝟑
𝟓
. I know
because I built each fraction
with fraction tiles and
compared them to see which
was larger.
Questions Eliciting Thinking:
 Do each of the parts in this model need to
be the same size? Why or why not?
 If I want to compare these two fractions by
drawing a picture, should the whole in each
drawing be the same size? Why or why not?
 What is important to remember when
you scale a number line? Where would
𝟏
𝟐
be
on the number line? Would
𝟑
𝟓
be placed
before or after
𝟏
𝟐
? How do you know? know?
What is half of five?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same
whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording
each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an
equivalent fraction, and/or by using properties of operations and the relationship between addition and
subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and
having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.2.3
Select all the correct ways to
make the sum
𝟕
𝟏𝟎
.
A.
2
10
+
3
10
+
2
10
B.
2
10
+
5
10
C.
1
10
+
6
10
D.
3
10
+
3
10
E.
1
10
+
1
10
+
5
10
Problem 1
AnswerStandard
page
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Problem 1
Answer Key
Problem 2Standard
page
A.
𝟐
𝟏𝟎
+
𝟑
𝟏𝟎
+
𝟐
𝟏𝟎
+ + =
𝟕
𝟏𝟎
B.
𝟐
𝟏𝟎
+
𝟓
𝟏𝟎
+ =
𝟕
𝟏𝟎
C.
𝟏
𝟏𝟎
+
𝟔
𝟏𝟎
+ =
𝟕
𝟏𝟎
D.
𝟑
𝟏𝟎
+
𝟑
𝟏𝟎
+ =
𝟔
𝟏𝟎
E.
𝟏
𝟏𝟎
+
𝟏
𝟏𝟎
+
𝟓
𝟏𝟎
+ + =
𝟕
𝟏𝟎
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.2.3
Problem 2
To get the correct color Erin mixed
𝟐
𝟐
𝟔
quarts of yellow paint, 3
𝟒
𝟔
quarts of blue paint, and 1
𝟏
𝟔
quarts
of red paint. How much paint did
Erin mix? Explain and/or model
your solution.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Problem 2
Answer Key
Problem 3Standard
page
Erin mixed 7
𝟏
𝟔
quarts of paint. I drew a picture to show each color of
paint. Then, I added all of the wholes to get 6. I then noticed that there
were
𝟕
𝟔
, which is more than 1 whole, so I made the wholes 7 and then
there was
𝟏
𝟔
left. So, my answer became 7
𝟏
𝟔
.
Yellow
Blue
Red
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.2.3
Problem 3
Summer starts in 4
𝟐
𝟔
weeks.
Write the mixed number as a fraction
greater than one.
Explain how you found the solution.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Problem 3
Answer Key
Problem 4Standard
page
I got
26
6
for my solution. To get my solution I first drew my 4 wholes.
Next, I added 2 more
1
6
pieces to the bottom to represent the
2
6
. Then,
I divided each whole into 6 pieces because there are 6 pieces of
1
6
in
each whole. Next, I counted all of the
1
6
pieces and there were 26. So, I
wrote the numerator as 26 and left the denominator as 6 to
represent the number of pieces in each whole.
4thGrade
Number&Operations
Fractions

MAFS.4.MD.1.1
Problem 4
AnswerStandard
page
MAFS.4.NF.2.3
Problem 4
Anna has
𝟒
𝟔
of a medium cheese pizza.
Bob gives her
𝟒
𝟔
of a medium pepperoni
pizza.
How much pizza does Anna Marie have
now?
A.
𝟖
𝟏𝟐
B. 𝟏
𝟐
𝟏𝟐
C. 𝟏
𝟐
𝟑
D. 𝟏
𝟐
𝟔
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Problem 4
Answer Key
Problem 5Standard
page
Solution: D, 1
𝟏
𝟑
To get my answer I drew Anna’s pizza using
1
6
pieces. Next I drew
the pizza given to Anna using
1
6
pieces. Then, I counted them and
noticed there were 8 pieces. I knew this was larger than one pizza,
because the pizza’s were cut into 6 pieces. So, I took 6 pieces out to
be a whole pizza and was left with
2
6
.
A.
𝟖
𝟏𝟐
B. 𝟏
𝟐
𝟏𝟐
C. 𝟏
𝟐
𝟑
D. 𝟏
𝟐
𝟔
4thGrade
Number&Operations
Fractions
1
𝟐
𝟔

MAFS.4.MD.1.
1
Problem 5-
AnswerStandard
page
MAFS.4.NF.2.3
Problem 5
Decomposing Three Fifths- CPALMs Formative Assessment
Use a visual fraction model to show two
ways to decompose
𝟑
𝟓
. Make sure to label
each fraction part in the model, and write
an equation to show how you decomposed
𝟑
𝟓
.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.3
Problem 5
Answer Key
Next
Standard
Page
Standard
page
Decomposing Three Fifths-CPALMs Formative Assessment
+ =
𝟏
𝟓
+
𝟐
𝟓
=
𝟑
𝟓
+ =
𝟐
𝟓
+
𝟏
𝟓
=
𝟑
𝟓
How do we
use this
button to
respond?
Possible Solutions: Questions Eliciting Thinking:
 Can you make a model to
show
𝟑
𝟓
?
 Where is one of the fifths?
 How many fifths did you
need to make
𝟑
𝟓
?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.2.4 Apply and extend previous understandings of multiplication to multiply a
fraction by a whole number.Problem
1
AnswerStandard
page
Sarah is making 4 batches of
granola bars. She adds
𝟕
𝟖
cup
peanuts to each batch. Her
measuring cup holds
𝟏
𝟖
cup. How
many times must Sarah measure
𝟏
𝟖
cup of peanuts to have enough for
the granola bars. Shade the model
to show your answer.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 1
Answer Key
Problem 2Standard
page
Solution:
She will need to fill her
𝟏
𝟖
cup 28 times.
4thGrade
Number&Operations
Fractions
Apply and extend previous understandings of multiplication to multiply a
fraction by a whole number.

dard 1 problem 2
AnswerStandard
page
MAFS.4.NF.2.4
Problem 2
Jessie and Lamar are filling in the number line below.
Jessie says 2 is equivalent to
𝟗
𝟓
and Lamar says it is
equivalent to
𝟏𝟎
𝟓
. Who is correct? How do you know?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 2
Answer Key
Problem 3Standard
page
Lamar is correct because if you keep filling in the
number line, the next number is
𝟖
𝟓
, then
𝟗
𝟓
, then
𝟏𝟎
𝟓
.
Also, if you know that there are five parts to each whole
and 5 x 2 = 10 that means there are 2 wholes.
𝟖
𝟓
𝟗
𝟓
𝟏𝟎
𝟓
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.2.4
Problem 3
Rudi is comparing shark lengths. She
reads that a sandbar shark is 4
𝟏
𝟐
feet
long. A thresher shark is 3 times as long
as a sandbar shark. Complete the model
below. Then, find the length of a
thresher shark.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 3
Answer Key
Problem 4Standard
page
Solution: 13
𝟏
𝟐
Feet
4
𝟏
𝟐
x 3 =
(4 x 3) + (
𝟏
𝟐
x 3)=
12 + 1
𝟏
𝟐
= 13
𝟏
𝟐
4
𝟏
𝟐
4
𝟏
𝟐
4
𝟏
𝟐
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.2.4
Problem 4
Alma is making 3 batches of tortillas.
Each batch needs
𝟑
𝟒
cup of water. She
only has a
𝟏
𝟒
cup measure. How many
times must Alma measure
𝟏
𝟒
cup of
water to have enough for all of the
tortillas? Model your solution.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 4
Answer Key
Problem 5Standard
page
Solution:
Alma will need to fill her
𝟏
𝟒
cup measure 9 times.
4thGrade
Number&Operations
Fractions

MAFS.4.MD.1.2
Problem 5-
AnswerStandard
page
MAFS.4.NF.2.4
Problem 5
Training for a Race-CPALMs Formative
Jessica is training for a race. If
she runs
𝟓
𝟒
miles each day for 4
days, how many miles will
Jessica run in preparation for the
race?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.2.4
Problem 5
Answer Key
Next
Standard
Page
Standard
page
Training for a Race-CPALMs Formative
Solution:
Jessica will run 5 miles in
preparation for the race.
 What mathematical operation
can you use to solve this
problem? How did you
determine that?
 What equation can you write to
represent this problem? How
many times did Jessica run
𝟓
𝟒
?
 If Jessica runs two miles a day
for four days, how would you
solve that problem?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Express a fraction with denominator 10 as an equivalent fraction
with denominator 100, and use this technique to add two
fractions with respective denominators 10 and 100. For example,
express
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
.
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.3.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100,
and use this technique to add two fractions with respective denominators 10 and 100.
For example, express
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
Problem 1
AnswerStandard
page
Identify the decimal fractions of each of the
models and add.
+
One whole One whole
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 1
Answer Key
Problem 2Standard
page
Express a fraction with denominator 10 as an equivalent fraction with denominator 100,
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
Identify the decimal fractions of each of the models and
add.
+
One whole One whole
𝟑𝟔
𝟏𝟎𝟎
𝟒
𝟏𝟎
+ =
𝟕𝟔
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

dard 1 problem 2
AnswerStandard
page
MAFS.4.NF.3.5
Problem 2
Part B.
Which of the following are equivalent
to the fraction
𝟓𝟎
𝟏𝟎𝟎
?
a.
𝟓
𝟏𝟎
b.
𝟓𝟎
𝟏𝟎
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
c.
𝟓
𝟏𝟎𝟎
d.
e.
f.
𝟓𝟎
𝟏𝟎
Part A.
Create a fraction with a denominator of 100 that is
equivalent to
𝟕
𝟏𝟎
.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 2
Answer Key
Problem 3Standard
page
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
Part A.
Create a fraction with a denominator of
100 that is equivalent to
𝟕
𝟏𝟎
.
𝟕𝟎
𝟏𝟎𝟎
is equivalent to
𝟕
𝟏𝟎
Part B.
Which of the following are equivalent to
the fraction
𝟓𝟎
𝟏𝟎𝟎
?
a.
𝟓
𝟏𝟎
b.
𝟓𝟎
𝟏𝟎
c.
𝟓
𝟏𝟎𝟎
d.
e.
f.
𝟓𝟎𝟎
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.5
Problem 3
Look at the equations below.
What are the missing fractions?
a.
𝟑
𝟏𝟎
+
𝟔𝟏
𝟏𝟎𝟎
=
b.
𝟐
𝟏𝟎
+ =
𝟕𝟖
𝟏𝟎𝟎
c.
𝟓𝟒
𝟏𝟎𝟎
+
𝟒
𝟏𝟎
=
d.
𝟔
𝟏𝟎
+
𝟏𝟎𝟎
=
𝟗𝟕
𝟏𝟎𝟎
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 3
Answer Key
Problem 4Standard
page
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
Look at the equations below.
What are the missing fractions?
a.
𝟑
𝟏𝟎
+
𝟔𝟏
𝟏𝟎𝟎
=
𝟗𝟏
𝟏𝟎𝟎
b.
𝟐
𝟏𝟎
+
𝟓𝟖
𝟏𝟎𝟎
=
𝟕𝟖
𝟏𝟎𝟎
c.
𝟓𝟒
𝟏𝟎𝟎
+
𝟒
𝟏𝟎
=
𝟗𝟒
𝟏𝟎𝟎
d.
𝟔
𝟏𝟎
+
𝟑𝟕
𝟏𝟎𝟎
=
𝟗𝟕
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.5
Problem 4
Raphael has
𝟒𝟑
𝟏𝟎𝟎
of a dollar. He needs at least one dollar to
purchase a rose for his mom.
Choose all the choices below that when added to what
Raphael has would equal at least one dollar.
𝟒
𝟏𝟎
dollar
𝟓
𝟏𝟎
dollar
𝟔
𝟏𝟎
dollar
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
𝟕
𝟏𝟎
dollar
𝟖
𝟏𝟎
dollar
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 4
Answer Key
Problem 5Standard
page
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
Raphael has
𝟒𝟑
𝟏𝟎𝟎
of a dollar. He needs at least one dollar to
purchase a rose for his mom.
Choose all the choices below that when added to what
Raphael has would equal at least one dollar.
𝟒
𝟏𝟎
+
𝟒𝟑
𝟏𝟎𝟎
=
𝟖𝟑
𝟏𝟎𝟎
𝟓
𝟏𝟎
+
𝟒𝟑
𝟏𝟎𝟎
=
𝟗𝟑
𝟏𝟎𝟎
𝟔
𝟏𝟎
+
𝟒𝟑
𝟏𝟎𝟎
=
𝟏𝟎𝟑
𝟏𝟎𝟎
𝟕
𝟏𝟎
+
𝟒𝟑
𝟏𝟎𝟎
=
𝟏𝟏𝟑
𝟏𝟎𝟎
𝟖
𝟏𝟎
+
𝟒𝟑
𝟏𝟎𝟎
=
𝟏𝟐𝟑
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 5-
AnswerStandard
page
MAFS.4.NF.3.5
Problem 5
 Look at the equation below. Is the equation
true? Why or why not?
𝟖
𝟏𝟎𝟎
+
𝟐
𝟏𝟎
=
𝟐𝟖
𝟏𝟎𝟎
 Find the sum in the following equation.
𝟒
𝟏𝟎
+
𝟑𝟔
𝟏𝟎𝟎
=
Hundredths and Tenths-CPALMs Formative Assessment
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.5
Problem 5
Answer Key
Next
Standard
Page
Standard
page
Hundredths and Tenths-CPALMs Formative Assessment
𝟑
𝟏𝟎
as
𝟑𝟎
𝟏𝟎𝟎
, and add
𝟑
𝟏𝟎
+
𝟒
𝟏𝟎𝟎
=
𝟑𝟒
𝟏𝟎𝟎
• What do you know about the fraction
𝟐
𝟏𝟎
?
• To how many hundredths is
𝟐
𝟏𝟎
equal?
• When adding fractions with different denominators, what should you
be certain to do?
• Do both denominators need to be the same number in order to add
the fractions?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Use decimal notation for fractions with denominators 10 or
100. For example, rewrite 0.62 as 62/100; describe a length as
0.62 meters; locate 0.62 on a number line diagram.
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page
Next
Standard
Page

MAFS.4.NF.3.6 Use decimal notation for fractions with denominators 10 or 100. For example,
rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a
number line diagram.
Problem 1
AnswerStandard
page
Look at the two values that are shown below.
Plot these values on a number line.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 1
Answer Key
Problem 2Standard
page
Use decimal notation for fractions with denominators 10 or 100. For example,
Look at the two values that are shown below.
Plot these values on a number line.
I know that 2.5 or 2.50 is exactly in the middle of the whole numbers 2 and 3. I drew
a tick mark there. Then, I found the middle of 2 and 2.5 to find 2.25. I did the same
thing between 2.5 and 3 to find 2.75. The number2.23 is a very little less than 2.25,
so I placed that point just before 2.25. The number 2.64 is also a little less than 2.75,
so I placed that point just before 2.75 but a little farther away than the point for 2.23.
2.23 2.64
2.5
or
2.50
4thGrade
Number&Operations
Fractions

A value is shown.
6
𝟑𝟗
𝟏𝟎𝟎
What is the value in decimal form?
AnswerStandard
page
MAFS.4.NF.3.6
Problem 2
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 2
Answer Key
Problem 3Standard
page
A value is shown.
6
𝟑𝟗
𝟏𝟎𝟎
What is the value in decimal form?
6.39
6 .394thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.6
Problem 3
Select all the fractions below that are
equivalent to 0.5.
o
𝟓
𝟏𝟎
o
𝟓𝟎
𝟏𝟎
o
𝟓
𝟏𝟎𝟎
o
𝟓𝟎
𝟏𝟎𝟎
o
𝟏𝟎
𝟓
o
𝟏𝟎𝟎
𝟓𝟎
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 3
Answer Key
Problem 4Standard
page
Select all the fractions below that are
equivalent to 0.5.
o
𝟓
𝟏𝟎
o
𝟓𝟎
𝟏𝟎
o
𝟓
𝟏𝟎𝟎
o
𝟓𝟎
𝟏𝟎𝟎
o
𝟏𝟎
𝟓
o
𝟏𝟎𝟎
𝟓𝟎
4thGrade
Number&Operations
Fractions

.63 .68
MAFS.4.NF.3
Problem 4
AnswerStandard
page
MAFS.4.NF.3.6
Problem 4
Jill’s baby chick weighs
𝟔𝟔
𝟏𝟎𝟎
pound. She
plotted her chick’s weight below. Joey says
she is right, Jeffrey says she’s wrong. Who do
you agree with and why?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 4
Answer Key
Problem 5Standard
page
Joey and Jill are wrong. Jeffrey numbered the
remaining equally spaced tick marks. Jill marked .65
place rather than .66.
.63 .68.64 .65 .66 .67
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 5-
AnswerStandard
page
MAFS.4.NF.3.6
Problem 5
Fractions to Decimals-CPALMs Formative Assessment
Write the following fractions as decimals.
1.
𝟖
𝟏𝟎𝟎
2.
𝟒
𝟏𝟎
3.
𝟐𝟎
𝟏𝟎𝟎
4.
𝟕
𝟏𝟎
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.6
Problem 5
Answer Key
Next
Standard
Page
Standard
page
Write the following fractions as decimals.
1.
𝟖
𝟏𝟎𝟎
= 0.08 3.
𝟐𝟎
𝟏𝟎𝟎
= 0.2
2.
𝟒
𝟏𝟎
= 0.4 4.
𝟕
𝟏𝟎
= 0.7
Fractions to Decimals-CPALMs Formative Assessment
* What is the value of the six in the number 0.62? What is the value of the two?
* What does the number to the left of the decimal point represent? What does the
number to the right of the decimal point represent?
* Is 2/10 the same as 20/100? How do you know that? Can you represent this
visually?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Compare two decimals to hundredths by reasoning about their size.
Recognize that comparisons are valid only when the two decimals
refer to the same whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions, e.g., by using a
visual model.
Problem 1
Answer Key
Problem 2
Answer Key
Problem 3
Answer Key
Problem 4
Answer Key
Problem 5
Answer Key
Back to
Start Page

MAFS.4.NF.3.7 Compare two decimals to hundredths by reasoning about their size. Recognize
that comparisons are valid only when the two decimals refer to the same
whole. Record the results of comparisons with the symbols >, =, or <, and
justify the conclusions, e.g., by using a visual model.
Problem 1
AnswerStandard
page
Part A. Each model shown represents 1 whole.
Copy these models and shade sections in your model to
represent 0.6 and 0.9.
Part B. Write a true comparison statement using the
information above.
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Problem 1
Answer Key
Problem 2Standard
page
Compare two decimals to hundredths by reasoning about their size. Recognize
Part A. Each model shown represents 1 whole.
Copy these models and shade sections in your
model to represent 0.6 and 0.9.
0.6
0.9
Part B. Write a true comparison statement using the
information above.
0.6 < 0.9 or 0.9 > 0.6
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.7
Problem 2
Review the locations of points F and G on the
number line representing decimal numbers.
Explain why the value of point F is less than the
value of point G.
0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Problem 2
Answer Key
Problem 3Standard
page
Point F is at 0.44 and Point G is at 0.52. F is less than G because it
is closer to a whole number of lesser value and point F is farther
to the right of the next whole value making it greater.
0.44 is less than 0.52
0.44 < 0.52
0.52 > 0.44
Review the locations of points F and G on the number line
representing decimal numbers. Explain why the value of point F is
less than the value of point G.
0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.7
Problem 3
Katy weighed her sandwich by
the pound. She wrote down the
weight using a decimal number
that is greater than 0.78 of a
pound but less than 0.82 of a
pound. What is one number
Katy could have written down
to represent the weight of her
sandwich?
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Problem 3
Answer Key
Problem 4Standard
page
Katy weighed her sandwich by the pound.
She wrote down the weight using a
decimal number that is greater than 0.78
of pound but less than 0.82 of a pound.
What is one number Katy could have
written down to represent the weight of
her sandwich?
To show the weight of her
sandwich, Katy could have
written . . .
0.79, 0.80, or 0.81
4thGrade
Number&Operations
Fractions

AnswerStandard
page
MAFS.4.NF.3.7
Problem 4
Joyce planted some Alaskan fireweed. One of
the stems grew 3.7 inches in the first week
and 3.63 inches in the second week. Select all
the true comparisons of the fireweed’s growth
for the two weeks.
o 3.7 > 3.63
o 3.63 > 3.7
o 3.63 < 3.7
o 3.7 = 3.63
o 3.7 < 3.63
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Problem 4
Answer Key
Problem 5Standard
page
Joyce planted some Alaskan fireweed. One of
the stems grew 3.7 inches in the first week and
3.63 inches in the second week. Select all the
true comparisons of the fireweed’s growth for
the two weeks.
o 3.7 > 3.63
o 3.63 > 3.7
o 3.63 < 3.7
o 3.7 = 3.63
o 3.7 < 3.63
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
roblem 5-
AnswerStandard
page
MAFS.4.NF.3.7
Problem 5
Compare Decimals-CPALMs Formative Assessment
Compare each set of decimals. Use the <, =, and >
symbols to record each comparison. Explain your
reasoning.
0.34 0.4
0.9 0.90
0.07 0.6
0.53 0.52
4thGrade
Number&Operations
Fractions

MAFS.4.NF.3.7
Problem 5
Answer Key
Standard
page
 What is your strategy for comparing the decimal numbers?
 What does one square represent on a 10 x 10 grid? What does one
column represent?
 Do 0.34 and 0.4 refer to the same size whole?
 How can you use benchmark fractions (0,
𝟏
𝟒
,
𝟏
𝟐
,
𝟑
𝟒
, and 1)
to compare 0.49 and 0.8?
Compare Decimals-CPALMs Formative Assessment
Compare each set of decimals. Use the <, =, and >
symbols to record each comparison.
0.34 0.4
0.9 0.90
0.07 0.6
0.53 0.52
<
=
*Four tenths is greater than
three tenths or 40 hundredths
is greater than 34 hundredths.
𝟗
𝟏𝟎
𝐢𝐬 𝐞𝐪𝐮𝐢valent to
𝟗𝟎
𝟏𝟎𝟎
*Seven hundredths is
less than sixty
hundredths
<
*53 hundredths is
greater than 52
hundredths.
>
4thGrade
Number&Operations
Fractions

Math Review-Fractions

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