Name ___________________________ Date _________
Grade 4 Summer Packet – Going into 5th Grade
For questions 3-6, which symbol belongs in the box to make a true
comparison? (use <, =, or >). Write your answer in the box.
3.
4.
5.
Twenty-seven thousand, four hundred ninety
20,000  7,000  400  10  9
6.
For questions 7-8, fill in the missing digit in the blank in each number
that will make each statement true.
7.
Four hundred twenty-six thousand, seven hundred nine = 426,7__9
8.
835,__14 > Eight hundred thirty-five thousand, eight hundred fourteen
9.
Which number when rounded to the nearest ten thousand has a value
of 290,000?
a.
286,314
b.
298,947
c.
281,769
d.
295,986
10.
Round 759,048 to the nearest hundred thousand.
11.
Circle the numbers below that have a value of 950,000 when rounded
to the nearest ten thousand.
944,806
12.
953,782
956,270
945,867
947,603
The area of a building is 709,650 square feet. What is this number
rounded to the nearest thousand square feet?
a.
700,000
b.
709,000
c.
709,700
d.
710,000
13.
14.
Which of the following is NOT equivalent to 8  7  56?
a.
56 is 7 added to itself 8 times.
b.
56 is 8 multiplied 7 times.
c.
56 is 7 times as many as 8.
d.
56 is 8 times as many as 7.
Use the equation 72  8  9 to complete the following statement.
72 is 8 times as many as ______ and 9 times as many as ______.
15.
Write a multiplication equation that is equivalent to the verbal
statement below.
Verbal statement:
16.
48 is 8 times as much as 6
Raja worked 40 hours per week for 4 weeks. Frank worked half the
amount of time Raja worked. How many hours did Frank work during
the 4 weeks? Show your work.
17. The students in the fourth grade sold 684 erasers for a fund-raiser.
They sold 4 times as many erasers as the students in the fifth grade.
How many erasers did the students in the fifth grade sell?
18. The workers at a farm collected 837 chicken eggs and 9 duck eggs. The
number of chicken eggs collected was how many times the number of
duck eggs collected?
19.
Eight buses are available for a class trip. Each bus can seat 56
students. The letter n represents the number of students that can go
on the class trip. Which equation can be used to find n ? Put a check
mark in the oval if the equation can be used.
Can be used
56  8  n
8  n  56
n  8  56
n  8  56
56  8  n
20.
A school auditorium has 32 rows of seats. Each row has 15 seats. The
letter k represents the total number of seats. Write an equation that
can be used to find k.
21.
Write an equation with a variable that could be solved to find the
answer to the word problem below. Do not solve the word problem.
Word problem: There are 133 paper cups at a party, and that is 7
times the number of people at the party. How many
people are there?
22.
Represent the word problem below by writing an equation with a
variable. The variable should represent the number of trees that Mr.
Wong’s students planted. Do not solve the word problem.
Word problem: The students in Ms. Shah’s class planted 4 more trees
than the students in Mr. Wong’s class planted. Ms.
Shah’s students planted 36 trees. What is the number
of trees that Mr. Wong’s students planted?
In questions 1-4, use the standard algorithm to add or subtract.
1)
2,746  23,694
3) 62,114  49,586
2)
92,318  23, 027
4)
4,591  1,985
5.
Which expression is equal to 3, 452  6 ?
a.
2,000  6  300  6  40  6  5  6
b.
2,000  6  400  6  30  6  5  6
c.
3,000  6  400  6  50  6  2  6
d.
3,000  6  500  6  40  6  2  6
7.
Marbles are arranged in an array that has 318 columns and 7 rows. How
many total marbles are in the array?
8.
Find 42  25. Show your work.
9. Show how to find 288  4.
10.
A rectangular array of cabbage plants in a field has 6,489 plants arranged in
9 rows. How many columns are in the array? Explain your reasoning.
11.
Find 708  6.
12.
Use an area model to explain how to find 192  8.
13.
Fill in the missing numbers in the boxes below to make equivalent fractions.
1
14.

2

10
100
Which is an equivalent fraction for
a.
1
2
b.
2
6
c.
4
6
d.
3
2
2
?
3
4
2
is equivalent to
.
10
5
15.
Draw a model and use it to explain why
16.
The 24 counters below are arranged in groups of 4 to show that
4
of the
6
total number of counters are black. Arrange the 24 counters in groups of a
different size to show another fraction that is equivalent to
4
.
6
17.
Ms. Lucas drew the model below for
3
.
4
Then she asked her students to find a fraction that is equivalent to
and draw their own model for that fraction.
For each model below, choose Yes or No to indicate whether the
3
shaded portion represents a fraction that is equivalent to .
4
 Yes
 No
 Yes
 No
 Yes
 No
 Yes
 No
3
4
18.
19.
A group of students picked up 4 bags of litter in a park. Each bag contained
n pieces of litter. The students collected 120 pieces of litter in all. Which
equation can be solved to find the number of pieces of litter in each bag?
a.
4  n  120
b.
4  120  n
c.
4  n  120
d.
4  n  120
Four cousins collected bottle caps for a school fund-raiser. Adam,
Selina, and Fiona counted the number of bottle caps they collected, as
shown in the table below. Darius did not count his bottle caps. They all
placed their bottle caps in a pile on the teacher’s desk. The teacher
counted 2,000 bottle caps in all.
Student
Adam
Number of Bottle Caps
367
Selina
922
Fiona
442
Let the number of bottle caps that Darius collected be represented as
n. Write an equation that could be used to
find n. Do not solve the equation.
20.
Jenny decides to buy two cans of juice for each guest she has invited
to a party. She buys the cans and puts 21 cans in each of 4 rooms in
her house. Represent the number of invited guests with the letter g
and write an equation with g that could be solved to find the number
of invited guests.
21.
Which number is a prime number?
22.
a.
21
b.
39
c.
43
d.
49
Is 57 a prime or composite number? Explain your answer.
23.
Put a check mark in the oval to indicate whether the number is prime or
composite.
Number
Prime
Composite
99
51
41
23
24.
List all the factor pairs for 72.
25.
The number 64 is a multiple of which of the following numbers?
26.
a.
9
c.
6
b.
8
d.
3
Which number is a multiple of 7 ?
a.
1
c.
63
b.
17
d.
89
1.
Complete the table below by filling in the missing values of B using the rule: add 15.
A
B
11
26
12
13
14
15
What pattern do you see in the sequence of numbers in the B column?
____________________________________________________
2.
The first six terms of a sequence of symbols are shown. What symbol will be the 10th symbol?
a.
b.
c.
d.
3.
Sunila described a number pattern below.


Part A:
The starting number is 13.
The rule is to add 5.
Fill in the blanks below with the first six numbers in the number pattern that Sunila
described.
_______, _______, _______, _______, _______, _______
Part B:
Describe one thing you notice about the pattern.
___________________________________________________________________________
4.
Which symbol (<, =, or >) belongs in the box below to make a true comparison? Write your
answer in the box.
2
3
1
4
Draw a picture and use it to explain your answer.
5.
Name the fraction that represents each shaded region.
_____________________
___________________
Which is greater, the fraction of Figure A that is shaded or the fraction of Figure B that is shaded?
Explain your response.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
6.
Write the two numbers in the boxes to make a true comparison.
Use 3 and 10.
7.
2
____
4
____
Shade a fractional part of each drawing. Write the fractions in the comparison to make it true.
>
____
8.
>
Is each sum equivalent to 2
yes or no.
2
? Put a check mark in the oval to select
5
Yes
2 2

5 5
5 5 1 1
  
5 5 5 5
5 5 5 5 1 1
    
5 5 5 5 5 5
5 3 4
 
5 5 5
____
No
9.
Write an equation to show
5
as a sum of two or more fractions.
8
Draw a model that
represents the equation.
Equation: _________________
Model:
10.
A pizza was cut into 6 equal slices. Andrew and Robert will share
5
of the pizza.
6
Use fractions to write two different ways that Andrew and Robert could share the pizza
between them. They do not each get the same amount.
A: __________________________
B: __________________________
In questions 11-14, add or subtract each. Write answers as proper fractions or mixed numbers. Show all
work that leads to your answer.
11.
2
5
1
4 
6
6
12.
5
7
1
4

12
12
3 3
 
4 4
13.
2
15.
In two weeks a flower grew
14.
9
3
7
4

10
10
11
3
of a foot. The first week it grew
of a foot.
12
12
How much did the flower grow in the second week? Show your work
with a model or expression.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
16.
Train A and train B left a train station at the same time and headed in the same direction. After
five minutes, train A was 5
1
7
miles from the station and train B was 2
miles from the
10
10
station. How much farther from the station is train A than train B? Show your work with an
equation or a model.
Complete the missing amounts in the following table so that the two measurements are equivalent.
Measurement
Measurement
17.
1 ft
______ in
18.
1 kg
______ g
19.
1 hr
______ min
20.
1L
______ mL
In questions 21-23, use a letter to represent the unknown, and then write an equation and use it to
solve the word problem.
21.
Brooke read 3,237 pages during the fourth grade. She read 8,421 pages in fourth and fifth
grades combined. How many pages did Brooke read in fifth grade?
Write an equation using a letter to represent the unknown.
_________________________
Use your equation to answer the question.
_____________________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
22.
Lane rode his bike 340 miles in April. In May he rode his bike 100 miles more than in April. Lane
rode a total of 960 miles in May and June. How many miles did Lane ride in June?
Write an equation using a letter to represent the unknown.
_________________________
Use your equation to answer the question.
______________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
23.
Kyle swam 40 minutes on Monday, 20 minutes on Tuesday, and 30 minutes on Wednesday.
Over the same days, Lavar swam for a total of 20 minutes less than Kyle. What is the total
amount of time, in minutes, that Lavar swam?
Write an equation using a letter to represent the unknown.
_________________________
Use your equation to answer the question.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
___________________________________________________
In questions 24-25, use the standard algorithm to add or subtract each.
24.
2,346  1,768 
25.
34,234  27,318 
1.
Use the number line below to show which whole number can be multiplied by
1
7
to get .
8
8
2.
Each circle in the model below represents one whole. Write a product to
represent the shaded parts shown in the model.
Product: ____________________________
3.
Which of the following fraction models can be used to show 3 
a.
b.
c.
d.
What is the value of 3 
2
? ________________
5
2
?
5
4.
Holly gives
1
cup of cat food to each of her 4 cats every morning. How much
3
food does Holly need each morning to feed her 4 cats?
Part A: Draw a model for the problem.
Part B: How much food does Holly need each morning to feed her 4 cats?
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
5.
The label on a box of cookies states that one serving is
1
of the box. Each of
8
the 6 people in a family ate one serving of the cookies. What fraction of the
box of cookies did the family eat?
_____________________
6.
The distance of one lap around a track is
1
mile. Casey ran 12 laps.
4
Part A: Write an expression that can be used to find the total
number of miles that Casey ran.
_____________________
Part B: How many miles did Casey run? Show your work.
______________________
7.
Jake wants to find the value of
4
27
.

10 100
Part A: What fraction can Jake write that is equal to
4
and has a
10
denominator of 100?
___________________
Part B: Show how you can use the fraction from Part A to find the value of
4
27
.

10 100
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
8.
Kelly finds
7
11
. Her work is shown in the box below.

10 100
Since the two fractions have different denominators, I wrote
with a denominator of 100.
7
10
7
7
, so I added

10 100
7
11
18
.


100 100 100
Kelly’s work contains an error. State the error that Kelly made. Show how to
find
7
11
correctly.

10 100
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
For questions 9–11, add the fractions. Write each sum as a fraction with a
denominator of 100.
9.
2
43


10 100
10.
8
6


10 100
12.
Howard placed 100 pennies in a pile. He removed 48 pennies from the pile.
Part A: Write a fraction to represent the part of the pile of pennies that
Howard removed.
______________
Part B: Write a decimal to represent the part of the pile of pennies that
Howard removed.
_______________
13.
Complete the table below with the decimal number that is equal to each
fraction.
Fraction
18
100
3
10
7
100
76
100
Decimal Number
14.
Part A: Write a fraction that represents the shaded part of the
large square.
________________
Part B: Write a decimal number that represents the shaded part
large square.
of the
________________
15.
How many square inches of felt is needed to cover the top of a rectangular
table that has a length of 92 inches and a width of 46 inches? Show your
work.
16.
Mo bought a rectangular piece of carpet for his living room, which has an
area of 96 square feet. The length of his rectangular living room is 12 feet.
What is the width, in feet, of Mo’s living room? Show your work.
18.
Student
The table shows the lengths, in inches, of the shoes of the students in Lisa’s
class.
Length of Student’s Shoe
Student
Length of Student’s Shoe
(in inches)
(in inches)
Lisa
6
1
4
Diane
6
1
2
Sangam
5
1
8
Fred
7
1
4
Melissa
6
1
2
Hal
7
1
8
Justin
8
1
8
Monique
6
1
2
Ray
7
1
4
Briyona
Connie
6
1
4
6
Part A: Make a lineplot of the data. Be sure to include labels.
Part B: What is the difference between the length of the longest shoe and the
length of the shortest shoe?
_____________
19.
The students in a study group each measured the thickness of
notebooks. The results are shown in the lineplot below.
their math
If the students stack their notebooks one on top the other, what will be the
total thickness of the stack?
a.
b.
c.
d.
7
8
3
2
8
1
2
2
7
2
8
1
inches
inches
inches
inches
20.
Mr. Bruno ordered 78 pencils for the students in his class. He ordered enough
pencils for each student to have exactly 3 pencils. How many students are in Mr.
Bruno’s class?
Mr. Bruno ordered 78 pencils for the students in his class. He
ordered enough pencils for each student to have 3 pencils. How many students are
in Mr. Bruno’s class?
Use a letter to represent the number of students in Mr. Bruno’s class. Write an
equation and use it to solve the word problem.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
____________________________________________________
21.
A group of 5 friends has a total of 74 marbles. Each of the friends is given an
equal number of marbles and there are 4 marbles left over. How many
marbles did each friend get?
Use a letter to represent the number of marbles each friend got. Write an
equation and use it to solve the word problem.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
22.
Leah scored 26 points in a basketball game. She made 7 baskets worth 2
points each, and she also made some baskets worth 3 points each. How
many 3-point baskets did Leah make in the game?
Use a letter to represent the number of 3-point baskets Leah made. Write an
equation and use it to solve the word problem.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
23.
The mass of one green block is 450 grams. The mass of one yellow
block is 0.7 kilograms.
Part A: Which block has a greater mass? How much greater is
the mass, in kilograms?
___________________________________________
___________________________________________
Part B: What is the total mass, in kilograms, of 3 green blocks and 2
yellow blocks?
__________________________________________________________
___________________________________________________________
24.
25.
On the first day of summer, the height of a plant was 9 inches. At the
3
end of the summer, the height of the plant was 3 feet. The height of
4
the plant at the end of the summer is how many times the height of
the plant at the beginning of the summer?
a.
3
b.
4
c.
5
d.
6
1
hours playing computer games. His younger sister
3
spends 45 minutes playing computer games. How many more minutes
does Jeff spend playing computer games than his sister spends?
Jeff spends 1
____________________