Moorestown Upper Elementary School
Summer Packet
Incoming Fourth Graders
Name:_____________________________________________________________
Third Grade Math Teacher:_____________________________________
Updated June 2014
Preparing for 4th Grade Math
The purpose of the packet is to help you review and reinforce concepts and topics that are necessary for
success in fourth grade math.
Instructions:
Complete all sections of this packet. You will return this completed packet to your math teacher the Friday
after Labor Day. All work must be shown and final answers should be circled. Be neat and methodical in
your work.
It may be necessary to seek assistance on some questions/concepts...that is fine!
Websites that may be of assistance:
www.mathforum.org/dr.math Use this web site if you have a math question that you need answered.
www.allmath.com This website will provide you with links to games, reference, general math help and
resources.
www.mathforum.com This online community includes teachers, students, researchers, parents and educators
who have an interest in math and math education. The site includes Ask Dr. Math, Problems of the Week,
discussion groups and much more.
www.AAAmath.com. Customized by grade level and topic, AAA Math features explanations of various
mathematical topics, practice problems and fun, challenging games.
www.coolmath.com This fully interactive site allows the user to sharpen basic math skills, play games and
explore new math concepts.
www.figurethis.org Created by the National Council of Teachers of Mathematics, this site helps families enjoy
mathematics outside school through a series of fun and engaging challenges.
www.mathdrills.com This website provides additional practice worksheets and answer keys by concept.
http://www.mathdrills.com/http:www.figurethis.orghttp:www.coolmath.comhttp:www.AAAmath.comhttp:www.mathforum.comhttp:www.allmath.comwww.mathforum.org/dr.math
0 0
Name Date
Place Value
Write each number in standard form.
1. 1.
2. 2,000 + 400 + 70 + 7 2.
3. nine hundred eighty-two 3.
Write each number in word form.
4. 4,050 4.
5. 5. 6,408
Compare. Use >,
Name Date
Vocabulary- Place Value
Using the word bank below, complete each
sentence by writing the correct word or words in
the blank.
1. The symbol > means . 1.
2. One thousand, thirty-five is an example of writing a
number in .
2.
3. 3. The value given to a digit by its place in a number
is called .
4. When we , we change the value of a 4.
number to one that is easier to work with.
5. 5. The usual way of writing numbers that shows only
its digits, not words, is called .
6. 6. The symbol < means .
7. The symbol = means . 7.
2
is greater than is equal to is less than
word form place value round
standard form
Name Date
Addition
Find each sum. Identify the addition property.
1. (4 + 3) + 6 =
4 + (3 + 6) = 1.
2. 12 + 0 = 2.
Estimate. Round each addend to its greatest
place value.
3. 3. 349
+ 252
4. 412
+ 187
5. 284
+ 146 4.
5.
6. 6. 772
+ 334
7. 509
+ 399
8. 398
+ 223 7.
8.
9. Tobias buys lunch once a week. About how many
times does he buy lunch in a year?
9.
Find each sum. Estimate to check
for reasonableness. 10.
10. 1,905
+ 4,590
11. 6,988
+ 1,988 11.
12. Manuel has 45 baseball cards, 12 football
cards, and 39 basketball cards. Is it
reasonable to say that Manuel has about
80 sports cards? Explain.
12.
3
Name Date
Vocabulary- Addition
Match each vocabulary word to its definition. Write the
letter of the answer on the line provided.
1. Associative Property of Addition A. a number close to the exact
number
B. to rename a number using
place value 2. Commutative Property of
Addition
C. states that the sum of any
number and zero is the number 3. parentheses
4. estimate D. states that the way addends are
grouped does not change the sum
5. Identity Property of
Addition E. states that the order in which
numbers are added does not
change the sum
6. regroup
F. symbols which show grouping
7. Use the pictures above to write an example of the Associative Property
of Addition.
4
Name Date
Make a 10 or 100 to subtract mentally.
1. 77 – 69 = 1.
2. 532 – 199 = 2.
Estimate. Round each number to the greatest
place value.
3.
4.
3. 389
– 252
4. 87
– 42
5. 284
– 146 5.
6.
7.
6. 772
– 334
7. 509
– 99
8. 398
23 8.
–
9. Tobias counted 89 cars on his way to school. He
counted 75 cars on the way home. To the nearest ten,
about how many more cars did he count on his way to
school?
9.
Subtract. Use addition to check your answer. 10.
10. 4,590
– 1,905
11. 6,988
– 1,988 11.
12.
12. 500
– 139
13. 1,000
– 753
14. 7,000
– 1,286 13.
14.
5
Subtraction
Name Date
Vocabulary- Subtraction
Match each definition to the corresponding vocabulary
word. Write the letter for your answer on the line provided.
6
A. a number close to the exact
number
1. subtraction
B. to rename a number using
place value
2. difference
C. two operations that can undo
each other, such as addition and
subtraction
3. subtraction sentence
D. an operation that tells the
difference, when some or all are
taken away
4. estimate
E. the answer to a subtraction
problem
5. inverse operations
F. a number sentence in which one
quantity is taken away from
another quantity
6. regroup
[******] [******)
@@@@
Name Date
Understanding Muliplication
Write an addition and a multiplication sentence
for each of the following.
1. 5 groups of 7
1.
2. 4 groups of 2
2.
Use the Commutative Property of Multiplication
to find each missing number.
3. 3 × 6 = 18 6 × = 18
3. 4. 8 × 3 = 24 3 × 8 =
4.
Multiply.
5. 6 × 2 = 5.
6. 4 × 3 = 6.
7. There are 3 rows of apples with 5 apples in each
row. How many apples are there altogether?
Write two multiplication sentences.
7.
Solve.
8. Pedro is collecting insects on a hike. He has 3 jars, and
places 5 insects in each jar. Write an addition and a
multiplication sentence to express how many insects he
collects. How many insects does Pedro have in all?
8.
7
t
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Name Date
Vocabulary- Understanding Multiplication
Match each definition to its vocabulary term. Write the
correct letters on the lines provided.
Multiplication
8
A. An operation on two numbers to find
their product.
1. array
B. The property that states that the
order in which two numbers are
multiplied does not change the
product.
2. Commutative Property of
C. A new set made by combining
parts from other sets.
3. tree diagram
D. The answer to a multiplication
problem.
2 × 3 = 6
4. equal groups
E. A number that is multiplied by
another number.
5. factor
F. Groups that have the same
number of objects.
6. combination
G. A way to show all possible
combinations using “branches.”
7. multiplication
H. An arrangement of items into
equal rows and columns.
Row
Column
8. product
I I I I I I I I I I I
I I I I I I I I I I I I I
[ *****) [*****] [*****]
Name Date
Use counters to find how many are in each group.
1. 12 counters
3 equal groups
1. in each group
2. 16 counters
2 equal groups
in each group 2.
Use repeated subtraction to divide.
3.
0 1 2 3 4 5 6 7 8 9 10 3.
10 ÷ 5 =
4. 4. 0 1 2 3 4 5 6 7 8 9 10 11 12
12 ÷ 2 =
Write a related division and multiplication sentence
for each.
5. 5.
6. 6.
9
Understanding Division
-
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Name Date
Vocabulary-Understanding Division
DddddddDiDivisioj
Match each definition to its vocabulary word(s). Write the
matching letters on the lines provided.
10
A. A way to divide by sharing one
object at a time until all the
objects are gone.
1. array
B. To separate into equal groups, to
find the number of groups, or to find
the number in each group.
2. division
C. Operations, such as multiplication and
division, which undo each other.
3. divisor
D. A way to subtract the same number
over and over again until you reach 0.
4. fact family
E. The answer to a division problem.
5. quotient
F. A group of related facts using the
same number.
5 × 3 = 15
3 × 5 = 15
15 ÷ 3 = 5
15 ÷ 5 = 3
6. inverse operations
G. The number by which the
dividend is being divided.
10)30
7. partition
H. An arrangement of items in rows and
columns.
Row
Column
8. repeated subtraction
Name Date
Multiplication and Division Patterns
Write an addition and a multiplication sentence
for each of the following.
1. 4 groups of 2
2. 6 groups of 5
1.
2.
Multiply or divide.
3. 6 ÷ 2 =
4. 3 × 2 =
5. 5 × 5 =
6. 4 × 2 =
7. 10 × 6 =
8. 12 ÷ 2 =
9. 10 × 4 =
10. 7 × 5 =
11. 15 ÷ 5 =
3.
4.
5.
6.
7.
8.
9.
10.
11.
Solve.
12. Don is collecting rocks in his yard. He has 3 jars, and
places 5 rocks in each jar. Write an addition
sentence and a multiplication sentence to express how
many rocks he collects in all. How many rocks does
Don have in all?
12.
13. Mason has 60 magazines. If each shelf on his
nightstand fits 10 magazines, how many shelves
will his magazines take up?
14. Luisa needs storage cases for her collection of 40
CDs. If each case holds 5 CDs, how many cases
will Luisa need?
13.
14.
11
Name Date
Vocabulary – Multiplication and Division Patterns
Using the word bank below, complete each sentence by
writing the correct word in each blank. Then answer
the questions.
1. An arrangement of objects into rows and columns of the
same length is a(n) .
2. The answer of a division problem is the .
3. To find the number of groups is to .
4. To divide or share equally among groups is to .
5. The number to be divided is the .
6. The product of a given number and any other whole number
is a(n) .
7. A number multiplied by another number is a(n) .
8. Use this space to draw and label a division fact. Be sure
to label each number as a dividend, divisor, or quotient.
9. How will you remember which numbers in a division problem
are the dividend, divisor, and quotient?
12
array dividend multiple quotient
divide factor partition
Name Date
Multiplication and Division
Multiply.
1. 2 × 3 =
2. 5 × 0 =
3. 7 × 4 =
4. 4 × 8 =
5. 9 × 1 =
6. 8 × 3 =
7. 4 × 3 =
8. 1 × 0 =
1.
2. 3.
4. 5.
6.
7.
8.
Divide.
9. 28 ÷ 4 =
10. 20 ÷ 4 =
11. 27 ÷ 3 =
12. 30 ÷ 3 =
13. 1)4
14. 4)4
15. 3)21
16. 1)7
9.
10.
11.
12.
13.
14.
15.
16.
Solve.
17. Ten students are carrying backpacks. Each backpack
holds 3 books. How many books are the students
carrying altogether?
18. Carla’s mother bought 6 cases of milk. Each case holds 4
cartons of milk. How many cartons of milk did Carla’s
mother buy?
17.
18.
1 13
Name Date
Vocabulary- Multiplication and Division
Write a definition of each boldface word on the line
below it.
1. Katie used the known fact, 7 × 3 = 21, to find the product of
7 × 6, because she knows that 6 is a double of 3.
2. 12 ÷ 4 = 3 is the inverse operation of 3 × 4 = 12.
3. The students were asked to decompose the number 6 into
two equal addends of 3 + 3.
4. The Identity Property of Multiplication shows that of 2 × 1 = 2.
5. The Zero Property of Multiplication shows that of 6 × 0 = 0.
14
Name Date
Applying Multiplication and Division
Use the inverse operation to find each unknown.
1. 22 ÷ 2 =
2 × = 22
The unknown is 1.
2. 35 ÷ 7 =
7 × = 35
The unknown is 2.
3. 32 ÷ 8 =
8 × = 32
3. The unknown is
4. 36 ÷ 12 =
12 × = 36
4. The unknown is
5. 44 ÷ 4 =
4 × = 44
5. The unknown is
6. 54 ÷ 6 =
6 × = 54
6. The unknown is
Solve.
7. Three students are carrying pencil cases. Each pencil case
can hold 12 pencils. How many pencils are the students
carrying altogether? 7.
8. Stan’s mother bought 6 cases of orange juice. Each
case holds 8 bottles of juice. How many bottles of
juice did Stan’s mother buy in all? 8.
15
Name Date
Vocabulary- Applying Multiplication and Division
Write a description of each boldface word on the line below it.
1. I used the known fact 4 × 6 = 24, to find the product of
8 × 6, because 8 is the double of 4.
2. The 11s facts show a pattern. When a single digit number is
multiplied by 11, the product is the digit repeated.
3. A related fact to 3 × 11 = 33 is 33 ÷ 11 = 3.
4. If Kathy multiplies 6 × 5, or 5 × 6, the product is 30, because
of The Commutative Property of Multiplication.
16
Name Date
Properties and Equations
Use the Distributive Property to find each product.
1. 6 × 11 =
2. 12 × 5 =
3. 4 × 9 =
1.
2.
3.
Find each missing factor.
4.
5.
6.
4. 4 × ( × 3) = 24
5. (5 × 2) × = 50
6. 3 × ( × 5) = 60
Use numbers and operations to write each phrase as
an expression.
7. 54 and 67
8. 5 groups with 3 in each group
9. half of 24
7.
8.
9.
Evaluate each expression if x = 4 and y = 5.
10. (x + y) × 2 =
11. 3 × (y × 6) =
12. (x × y) × 4 =
10.
11.
12.
Write an equation using any letter for the unknown.
Then solve. Check for reasonableness.
13. Jesse bought 3 tennis balls for $6. How much did each
tennis ball cost?
13.
14. George has $5. Amie has twice as much. How much
money does Amie have?
14.
15. Franklin buys 3 packs of baseball cards for $2 each.
How much change will he receive if he gives the
cashier $10?
15.
17
Name Date
Vocabulary-Properties and Equations
Using the word bank below, complete each sentence by
writing the correct word in the blank. Then find the
words in the word search.
1. To find the value of an expression, I
the expression.
An contains an equal sign to show that two 2.
expressions are equal.
are mathematical processes, such as 3.
addition, subtraction, multiplication, and division.
A can be a letter or symbol that is used to 4.
represent an unknown quantity.
The Property of Multiplication allows you to 5.
decompose one factor into addends that are easier to work with.
A combination of numbers and operations that represent a
quantity is called an .
6.
7. The property that makes multiplying three factors easier by
stating that the grouping of factors does not change the product
is the Property of Multiplication.
Word Search
Hint: Look forwards, backwards, up and down to find the words.
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Associative equation expression variable
Distributive evaluate operations
[ill]
- -
- -
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00 00
Name Date
Fractions
Write the fraction for the part that is shaded. Then
write the fraction for the part that is not shaded.
1. 1. 2.
2.
Complete each number sentence to show
equivalent fractions.
3.
3.
4.
4.
5.
5.
6.
6.
Compare the fractions. Write >,
- . [ ] . [ ]
Name Date
Vocabulary- Fractions
Using the word bank below, complete each sentence by
writing the correct word or words in the blank.
1. The number above the bar in a fraction is called the
.
In
, the symbol “” represents . 3.
4. The number below the bar in a fraction is called the
.
5.
is a number that names part of a whole or part of a set,
and is called a(n) .
6. Fractions that name the same number are called
.
Complete the examples below using vocabulary from the
word bank above.
8.
_7.
9. 10.
20
denominator fraction less than
equivalent fractions greater than numerator
Name Date
Measurement
Read each question carefully. Write your answer
on the line provided.
Choose the most appropriate unit to measure each
capacity. Write milliliter or liter.
1. 2. 1.
2.
Choose the most appropriate unit to measure each
mass. Write gram or kilogram.
3. 4. 3.
4.
Write an equation with a symbol for the unknown.
Then solve.
5. Find the total capacity of the liquid shown in the
containers below.
5.
200 150 100 50
mL mL mL mL
200 150 100 50
mL mL mL mL
6. Daniella buys a bottle of juice. The bottle contains
600 milliliters of juice. She drinks half of the juice.
How many milliliters of juice did she drink?
Solve.
7. Jansen’s guitar practice started at 6:00 and ended at
8:00. How long did his guitar practice last?
8. It took Diana 70 minutes to clean her room. She
finished at 10:40 A.M. What time did she start?
6.
7.
8.
21
Name Date
Vocabulary- Measurement
Match each definition to the corresponding vocabulary word.
Write your answers on the lines provided.
A. One metric unit of mass equal to
1,000 grams
1. capacity
B. A smaller metric unit of mass, about
equal to a paper clip
2. time interval
C. The amount of material in an object 3. milliliter
D. The time that passes from the start to
the end of an activity
4. gram
E. A metric unit of capacity about equal to
the amount of liquid in a large water
bottle
5. liter
F. The amount a container can hold 6. mass
G. A device used for measuring time 7. kilogram
H. A metric unit of capacity about equal to a
small dropper of water
8. analog clock
22
~ Favorite Fruit Juice ~
f-
f-
f- ,__ -
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Name Date
Represent and Interpret Data
For Exercises 1–4, refer to the bar graph.
12
10
8
6
4
2
0 Apple Grape Orange Pineapple
Juice Flavor
1. 1. Which flavor of juice is the favorite?
2. 2. Which flavor of juice is the least favorite?
3. 3. How many students chose pineapple as their favorite?
4. How many students chose either apple or grape as
their favorite? 4.
5. A pictograph key shows 8 symbols. Each
symbol represents 4 people who ride their bike to
school. How many people ride their bike to school? 5.
6. In the line plot below, how many students scored
94 points or higher on their math quiz?
X X X
6.
23
Nu
mb
er o
f S
tud
ents
Math Quiz Scores
X
X X X X X X
88 90 92 94 96 98 100
Name Date
Vocabulary – Represent and Interpret Data
Using the word bank below, complete each sentence by
writing the correct word or words in the blank.
1. The information that has been collected is called
the .
2. A graph that uses columns of Xs above a line to show
frequency of data is a(n) .
3. A set of numbers that represent the data is
a(n) .
4. A graph that uses pictures or symbols to represent data is
a(n) .
5. To read or study the data on a graph is to
the data.
6. A graph that compares data by using bars of different
lengths or heights to show values is a(n) .
Read each statement. Choose from pictograph, bar graph,
or line plot to help each student display their information.
Justify your choice.
7. Justine wants to show how often she feeds her fish.
8. Meiko wants to display how many students have a pet turtle.
24
bar graph analyze pictograph
data line plot scale
I I
Name Date
Find the perimeter of each figure.
1. 1. 2. 9 cm
7 cm 5 cm
2. 8 cm
Find the area of each shaded figure.
3. 4. 3.
4.
Find the perimeter and area of each figure.
5. 6. 1 ft 1 ft
4 cm 5 cm 5. 2 cm 3 ft
5 cm
6. 4 ft
Draw and label a rectangle that has the same area, but a
different perimeter than the rectangle shown.
4 cm
7.
7.
3 cm
25
1 ft 1 ft
2 ft
Perimeter and Area
Name Date
Vocabulary- Perimeter and Area
Write a description of each bold-faced word on the line below it.
1. The living room and the kitchen together form a
composite figure.
2. Sonja measured the area of her bedroom in square units.
3. Traci solved the math problem by decomposing one of
the factors.
4. The perimeter of a soccer field is 320 yards.
5. Arielle followed the formula, length × width = Area, to find
how much paper would cover her math book.
6. Julio worked with his teacher to measure the area of their
classroom in meters.
26
v
0 0 0 ~ D
Name Date
Geometry
Classify each polygon.
1. 2. 1.
2.
3. 4. 3.
4.
5.
5. 6.
6.
7.
7. Identify the figure. List two attributes of the figure.
Name the shape.
8. Iris got a framed picture for her birthday. What
figure is it? 8.
9. Jay partitioned this figure into 2 equal areas.
What fraction of the rectangle’s area does each
9.
section represent?
27
Name Date
Vocabulary- Geometry
Write a description for each boldface word(s) on the line below
each sentence.
1. One attribute of a square is that it has 4 right angles.
2. A honeycomb is the shape of a hexagon.
3. The polygon can be partitioned into equal areas.
4. The rectangle and the octagon are examples of polygons.
5. A square and a rectangle are both examples of quadrilaterals.
6. The streets were parallel to each other.
7. Two rays that share an endpoint are called angles.
28
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