This document contains a review for Mrs. Labuski's math class covering lessons 1-8 on identities, operations, expressions, properties, and geometry. Students are asked to fill in blanks, write expressions, evaluate expressions, and answer questions about division, multiplication, exponents, area, perimeter, and volume. The review covers key concepts like the relationship between multiplication/division and addition/subtraction, order of operations, properties of operations, and using formulas to find geometric measures.

1. Name _________________________________________Date _____________________
Mrs. Labuski / Mrs. Portsmore Per ________ Mod 4 Lessons 1-8 Review
Lesson 1
Using your knowledge of identities, fill in each of the blanks.
1. 7 + 3 - _____ = 7 Answer: 3
2. 35 - _____ + 20 = 35 Answer: 20
3. 84 – 17 + 17 = _____ Answer: 84
4. c + d - ____ = c Answer: d
5. e – f + f = _____ Answer: e
Lesson 2
Fill in each blank.
1. 620 ÷ 5 x 5 = ________ Answer: 620
2. 654 x ____ ÷ 63 = 654 Answer: 63
3. _____ ÷ 30 x 30 = 390 Answer: 390
4. How are the relationships of multiplication and division similar to addition and
subtraction?
Answer: Both relationships create identities.
Fill in the blank to make each number sentence true.
5. a x b ÷ b = _____ Answer: a
6. _____ ÷ d x d = c Answer: c
Lesson 3
Write an equivalent expression to show the relationship of multiplication and addition.
1. 5 x 9 9 + 9 + 9 + 9 + 9
2. 7 + 7 + 7 3 x 7
3. g + g + g + g 4g
4. f + f + f + s + s 3f + 2s
5. 4y y + y + y + y
6. 2a + 4b + 3c a + a + b + b + b + b + c + c + c

2. 7. Write the addition sentence and the multiplication sentence that describes the model.
8. Angelina is not familiar with tape diagrams and she believes that she can show the
relationship of multiplication and addition on a number line. Help Angelina demonstrate that
the expression 4 x 3 is equivalent to 3 + 3 + 3 + 3 on a number line.
4 x 3 = four groups of 3:
3 + 3 + 3 + 3 = counting up by threes:
Since both number lines start at zero and end at 12, the expressions are equivalent
Lesson 4
NOTES:
Division
Equation
Divisor Indicates the
Size of the Unit
Tape Diagram
What is
𝒙, 𝒚, 𝒛?
𝟏𝟐 ÷ 𝒙 = 𝟒 𝟏𝟐 − 𝒙 − 𝒙 − 𝒙 − 𝒙 = 𝟎 𝒙 = 𝟑
𝟏𝟓 ÷ 𝒙 = 𝟑 𝟏𝟓 − 𝒙 − 𝒙 − 𝒙 = 𝟎
15 – 5 – 5 – 5 = 0; x = 5 units in each group
x = 5
Division
Equation
Divisor Indicates the
Number of Units
Tape Diagram
What is
𝒙, 𝒚, 𝒛?
𝟏𝟐 ÷ 𝒙 = 𝟒 𝟏𝟐 − 𝟒 − 𝟒 − 𝟒 = 𝟎 𝒙 = 𝟑
𝟏𝟓 ÷ 𝒙 = 𝟑 15–3–3–3- 3–3 = 0
15 – 3 – 3 – 3 -3 -3 = 0; x = 5 group
x = 5
4 + 4 + 4 and 3 x 4

3. 1. If 24 ÷ x = 4, how many times would x have to be subtracted from 24 in order for the answer
to be zero?
24 – 4 – 4 – 4 – 4 – 4 – 4 = 0
six; x = 6
2. 48 – c – c – c – c = 0. Write a division sentence for this repeated subtraction sentence. What
is the value of c?
48 ÷ c = 4 ; c = 12
3. If 42 ÷ t = 7, which number is being subtracted seven times in order for the answer to be
zero?
6
4. Represent 63 ÷ 9 = 7 using subtraction.
63 – 7 -7 -7 -7 -7 -7 -7 -7 – 7 = 0
Lesson 5
1. Complete the table by filling in the blank cells.
Exponential
Form
Written as a Series of Products
(repeated factors)
Standard Form
4 5 4 x 4 x 4 x 4 x 4 1,024
23
2 × 2 × 2 8
3. 7 3 3.7 x 3.7 x 3.7 50.653
(
1
3
)
4 𝟏
𝟑
𝒙
𝟏
𝟑
𝒙
𝟏
𝟑
𝒙
𝟏
𝟑
𝟏
𝟖𝟏
2. Write an equivalent expression for 𝑦 × 𝑎 using only addition.
(𝒂 + 𝒂 + ⋯ 𝒂)⏟
𝒚 𝒕𝒊𝒎𝒆𝒔
3. Write an equivalent expression for 𝑦 𝑏
using only multiplication.
𝒚 𝒃
= (𝒚 ∙ 𝒚 ⋯ 𝒚)⏟
𝒃 𝒕𝒊𝒎𝒆𝒔
a. Explain what 𝑦 is in this new expression.
y is the factor that will be repeatedly multiplied by itself.
b. Explain what 𝑏 is in this new expression.
b is the number of times y will be multiplied.
4. What is the difference between 3𝑥 and 𝑥3
? Evaluate both of these expressions when 𝑥 = 2.
3x = x + x + x or 3 times x x3 =
x • x • x
3(2) = 2 + 2 + 2 or 3 • 2 23
= 2 • 2 • 2
6 8

4. Lesson 6
1. 6 + 82
÷ 4 × 2 − 2
What operation is evaluated first? exponent
What operations are evaluated next? division then multiplication (from left to right)
What operations are always evaluated last? addition and subtraction (from left to right)
What is the final answer?
6 + 82
÷ 4 • 2 - 2
6 + 64 ÷ 4 • 2 – 2
6 + 16 • 2 - 2
6 + 32 – 2
38 – 2
36
2. Evaluate each of the following.
a. 22 + (12 – 5)2
b. 6 • (23 + 5 – 24÷ (8 + 4))
22 + (12 – 5)2
6 • (23 + 5 – 24 ÷ (8 + 4))
22 + (7)2
6 • (23 + 5 – 24 ÷ 12)
22 + 49 6 • (23 + 5 –2)
71 6 • (28 –2)
6 • 26
156
c. ( (2 x 2)2
+ (4 x 32
) ) ÷ 4 d. Write an expression to represent the model
( (4)2
+ (4 x 32
) ) ÷ 4
( 16 + (4 x 32
) ) ÷ 4 3 + (4 x 2)
( 16 + (4 x 9) ) ÷ 4
( 16 + 36 ) ÷ 4
52 ÷ 4
13
3. Mrs. Labuski and her daughter ran a 5K on Saturday. The registration fee was $30 for each
of them. Mrs. Labuski decided to also buy raffled tickets to support the fundraiser. Mrs.
Labuski purchased 5 raffle tickets for $3 each. Write an expression to represent what Mrs.
Labuski paid for the 5K.
((2 x 30) + ( 5 x 3))

5. Lesson 7
1. In the drawing, what does the s represent? side
a. What does s+s+s+s represent? perimeter
b. what does s · s (s2
) represent? area
c. Use the information s=3 to evaluate for the expressions in part a and b.
P = s + s + s + s A = s2
P = 3 + 3 = 3 = 3 A = 32
Perimeter = 12 units Area=9 units squared or 6 un2
2. Complete the table for the given figure (not to scale)
3. Find the volume of the given figure.
Lesson 8
1. Write the property for the given expression
a. r + p= p + r Commutative Property of Addition
b. t · q = q · t Commutative Property of Multiplication
c. p+0=p Additive identity property of zero
d. w · 1= w Multiplicative identity property of one
2. Demonstrate the property listed in the first column by filling in the third column.
Commutative Property of Addition 47 + q = q + 47
Commutative Property of Multiplication s · n= n • s
Additive Property of Zero h + 0= h
Multiplicative Identity Property of One k · 1 = k
Vocabulary Review
In the expression 34
, the “3” is the base and the “4” is the power or exponent
In the term 7b, the “7” is the coefficient and the “b” is the variable
Multiplication is repeated addition
Exponents are repeated multipilcation
Length of
Rectangle
Width of
Rectangle
Rectangle’s Area written
as an expression
Rectangle’s Area Written
as a Number
47 32 47 in x 32 in 1504 in2
S
32 in
47 in
4mm
6.2 mm
9.3mm
V = l x w x h
V = 9.3 x 6.2 x 4
V = 230.64 mm3

6. Name _________________________________________Date _____________________
Mrs. Labuski / Mrs. Portsmore Per ________ Mod 4 Lessons 1-8 Review
Lesson 1
Using your knowledge of identities, fill in each of the blanks.
1. 7 + 3 - _____ = 7
2. 35 - _____ + 20 = 35
3. 84 – 17 + 17 = _____
4. c + d - ____ = c
5. e – f + f = _____
Lesson 2
Fill in each blank.
1. 620 ÷ 5 x 5 = ________
2. 654 x ____ ÷ 63 = 654
3. _____ ÷ 30 x 30 = 390
4. How are the relationships of multiplication and division similar to addition and
subtraction?
Fill in the blank to make each number sentence true.
5. a x b ÷ b = _____
6. _____ ÷ d x d = c
Lesson 3
Write an equivalent expression to show the relationship of multiplication and addition.
1. 5 x 9 ___________________________________
2. 7 + 7 + 7 ________________________________
3. g + g + g + g __________________________
4. f + f + f + s + s ___________________________
5. 4y _____________________________________
6. 2a + 4b + 3c _____________________________

7. 7. Write the addition sentence and the multiplication sentence that describes the model.
____________________________
8. Angelina is not familiar with tape diagrams and she believes that she can show the
relationship of multiplication and addition on a number line. Help Angelina demonstrate that
the expression 4 x 3 is equivalent to 3 + 3 + 3 + 3 on a number line.
Lesson 4
Answer each question using what you have learned about the relationship of division and
subtraction. Complete the tables:
Division
Equation
Divisor Indicates the
Size of the Unit
Tape Diagram
What is
𝒙, 𝒚, 𝒛?
𝟏𝟐 ÷ 𝒙 = 𝟒 𝟏𝟐 − 𝒙 − 𝒙 − 𝒙 − 𝒙 = 𝟎 𝒙 = 𝟑
𝟏𝟓 ÷ 𝒙 = 𝟑
Division
Equation
Divisor Indicates the
Number of Units
Tape Diagram
What is
𝒙, 𝒚, 𝒛?
𝟏𝟐 ÷ 𝒙 = 𝟒 𝟏𝟐 − 𝟒 − 𝟒 − 𝟒 = 𝟎 𝒙 = 𝟑
𝟏𝟓 ÷ 𝒙 = 𝟑

8. 1. If 24 ÷ x = 4, how many times would x have to be subtracted from 24 in order for the answer
to be zero?
2. 48 – c – c – c – c = 0. Write a division sentence for this repeated subtraction sentence. What
is the value of c?
3. If 42 ÷ t = 7, which number is being subtracted seven times in order for the answer to be
zero?
4. Represent 63 ÷ 9 = 7 using subtraction.
Lesson 5
1. Complete the table by filling in the blank cells.
Exponential
Form
Written as a Series of
Products (repeated factors)
Standard Form
4 5
2 × 2 × 2
3. 7 3
(
1
3
)
4
2. Write an equivalent expression for 𝑦 × 𝑎 using only addition.
3. Write an equivalent expression for 𝑦 𝑏
using only multiplication.
a. Explain what 𝑦 is in this new expression.
b. Explain what 𝑏 is in this new expression.
4. What is the difference between 3𝑥 and 𝑥3
? Evaluate both of these expressions when 𝑥 = 2.

9. Lesson 6
1. 6 + 82
÷ 4 × 2 − 2
What operation is evaluated first? _______________________________________________
What operations are evaluated next? _____________________________________________
What operations are always evaluated last? ________________________________________
What is the final answer?
2. Evaluate each of the following.
a. 22 + (12 – 5)2
b. 6 • (23 + 5 – 24÷ (8 + 4))
c. ( (2 x 2)2
+ (4 x 32
) ) ÷ 4 d. Write an expression to represent the model
__________________
3. Mrs. Labuski and her daughter ran a 5K on Saturday. The registration fee was $30 for each
of them. Mrs. Labuski decided to also buy raffled tickets to support the fundraiser. Mrs.
Labuski purchased 5 raffle tickets for $3 each. Write an expression to represent what Mrs.
Labuski paid for the 5K.

10. Lesson 7
1. In the drawing, what does the s represent? ___________________
a. What does s + s + s + s represent? ___________________
b. What does s · s (s2
) represent? ___________________
c. Use the information s=3 to evaluate for the expressions in parts a and b.
Area = _____________________ Perimeter = __________________
2. Complete the table for the given figure (not to scale)
Length of
Rectangle
Width of
Rectangle
Rectangle’s Area written
as an expression
Rectangle’s Area Written
as a Number
s
32 in
47 in

11. 3. Find the volume of the given figure.
Lesson 8
1. Write the property for the given expression
a. r + p = p + r ____________________
b. t · q = q · t ____________________
c. p + 0 = p _____________________
d. w · 1= w__________________
2. Demonstrate the property listed in the first column by filling in the third column of the table
with an equivalent expression.
Commutative Property of Addition 47 + q =
Commutative Property of
Multiplication
s · n=
Additive Property of Zero h + 0=
Multiplicative Identity Property of One k · 1 =
Vocabulary Review
In the expression 34
, the “3” is the __________ and the “4” is the __________ or ___________
In the term 7b, the “7” is the __________________ and the “b” is the _______________
Multiplication is repeated _____________________________
Exponents are repeated __________________________________
4mm
6.2 mm
9.3mm
Show all computations and steps here