Lesson 1-1
A Plan for Problem Solving
Lesson 1-2
Powers and Exponents
Lesson 1-3
Squares and Square Roots
Lesson 1-4
Order of Operations
Lesson 1-5
Problem-Solving Investigation: Guess and
Check
Lesson 1-6
Algebra: Variables and Expressions
Lesson 1-7
Algebra: Equations
Lesson 1-8
Algebra: Properties
Lesson 1-9
Algebra: Arithmetic Sequences
Lesson 1-10
Algebra: Equations and Functions
• Solve problems using THE FOUR-STEP PLAN.
In Mathematics, there is four-step plan you can use to
help you solve any problem.
1. Explore: Knowing the problem.
2. Plan: Finding a way to solve the problem.
3. Solve: Solving the problem.
4. Check: Checking to make sure you solved the
problem correctly.
In Mathematics, there is four-step plan you can use to
help you solve any problem.
1. Explore
•
Read the problem carefully.
•
What information in given?
•
What do you want to find out?
•
Is enough information given?
•
Is there any information that you don’t need?
2. Plan
•
How do the facts relate to each other?
•
Select a strategy for solving the problem. There
may be more than one way to solve the problem.
•
Estimate the answer.
In Mathematics, there is four-step plan you can use to
help you solve any problem.
3. Solve
•
Use your plan to solve the problem.
•
If your plan does not work, revise it or make a new
plan.
4. Check
•
Does your answer fit the facts given in the
problem?
•
Is your answer reasonable compared to your
estimate?
•
If not, make a new plan and start again.
READING Ben borrows a 500-page book from the
library. On the first day, he reads 24 pages. On the
second day, he reads 39 pages and on the third day
he reads 54 pages. If Ben follows the same pattern
of number of pages read for seven days, will he
have finished the book at the end of the week?
A. No, he will have only read
483 pages.
B. No, he will have only read
492 pages.
C. yes
D. not enough information
given to answer
1.
2.
3.
4.
A
B
C
D
FOUR-STEP PLAN.
1. Explore: Knowing the problem.
2. Plan: Finding a way to solve the problem.
3. Solve: Solving the problem.
4. Check: Checking to make sure you solved the
problem correctly.
Ben borrows a 500-page book from the library. On the
first day, he reads 24 pages. On the second day, he
reads 39 pages and on the third day he reads 54
pages. If Ben follows the same pattern of number of
pages read for seven days, will he have finished the
book at the end of the week?
READING Ben borrows a 500-page book from the
library. On the first day, he reads 24 pages. On the
second day, he reads 39 pages and on the third day
he reads 54 pages. If Ben follows the same pattern
of number of pages read for seven days, will he
have finished the book at the end of the week?
A. No, he will have only read
483 pages.
B. No, he will have only read
492 pages.
C. yes
1.
2.
3.
4.
A
B
C
D
A
D. not enough information
given to answer
0%
B
C
D
Use the Four-Step Plan
SPENDING A can of soda holds 12 fluid ounces. A
2-liter bottle holds about 67 fluid ounces. If a pack of
six cans costs the same as a 2-liter bottle, which is
the better buy?
Explore What are you trying to find?
You are trying to find the number of fluid ounces
of soda in a pack of six cans. This number can
then be compared to the number of fluid ounces
in a 2-liter bottle to determine which is the better
buy.
What information do you need to solve the
problem?
You need to know the number of fluid ounces in
each can of soda.
Use the Four-Step Plan
Plan
You can find the number of fluid ounces of
soda in a pack of six cans by multiplying the
number of fluid ounces in one can by six.
Solve
12 × 6 = 72
There are 72 fluid ounces of soda in a pack
of six cans. The number of fluid ounces of
soda in a 2-liter bottle is about 67. Therefore,
the pack of six cans is the better buy
because you get more soda for the same
price.
Use the Four-Step Plan
Check
Is your answer reasonable?
The answer makes sense based on the facts
given in the problem.
Answer: The pack of six cans is the better buy.
FIELD TRIP The sixth grade class at Meadow Middle
School is taking a field trip to the local zoo. There will
be 142 students plus 12 adults going on the trip. If
each school bus can hold 48 people, how many
buses will be needed for the field trip?
A. 3
B. 4
0%
D
A
0%
A
B
0%
C
D
C
D. 6
A.
B.
0%
C.
D.
B
C. 5
Use a Strategy in the Four-Step Plan
POPULATION For every 100,000 people in the
United States, there are 5,750 radios. For every
100,000 people in Canada, there are 323 radios.
Suppose Sheamus lives in Des Moines, Iowa and
Alex lives in Windsor, Ontario. Both cities have
about 200,000 residents. About how many more
radios are there in Sheamus’s city than in Alex’s
city?
Explore
You know the approximate number of radios
per 100,000 people in both Sheamus’s city
and Alex’s city.
Use a Strategy in the Four-Step Plan
Plan
You can find the approximate number of
radios in each city by multiplying the estimate
per 100,000 people by two to get an estimate
per 200,000 people. Then, subtract to find how
many more radios there are in Des Moines
than in Windsor.
Solve
Des Moines: 5,750  2 = 11,500
Windsor: 323  2 = 646
11,500 – 646 = 10,854
So, Des Moines has about 10,854 more
radios than Windsor has.
Use a Strategy in the Four-Step Plan
Check
Based on the information given in the problem,
the answer seems to be reasonable.
Answer: So, Des Moines has about 10,854 more radios
than Windsor has.
• Use powers and exponents.
• factors
• cubed
• exponent
• evaluate
• base
• standard form
• powers
• exponential form
• squared
The centered dots
indicate multiplication
The exponent tells how
many times the base is
used as a factor.
16 = 2 · 2 · 2 · 2 = 24
Common factors
The base is the
common factor.
Powers
Words
2
5
Five to the second power or five
3
4
Four to the third power or four
4
2
Two to the fourth power.
squared.
cubed.
Numbers written without exponents are in
standard form.
Example: 2 · 2 · 2 · 2 = 16
Standard form
Numbers written with exponents are in
exponential form.
Example: 2 · 2 · 2 · 2 = 24
Exponential form
Write Powers as Products
Write 84 as a product of the same factor.
Eight is used as a factor four times.
Answer: 84 = 8 ● 8 ● 8 ● 8
Write 36 as a product of the same factor.
A. 3 ● 6
B. 6 ● 3
C. 6 ● 6 ● 6
D. 3 ● 3 ● 3 ● 3 ● 3 ● 3
A.
B.
C.
D.
A
B
C
D
Write Powers as Products
Write 46 as a product of the same factor.
Four is used as a factor 6 times.
Answer: 46 = 4 ● 4 ● 4 ● 4 ● 4 ● 4
Write 73 as a product of the same factor.
A.
7●3
B.
3●7
C. 7 ● 7 ● 7
D. 3 ● 3 ● 3 ● 3 ● 3 ● 3 ● 3
1.
2.
3.
4.
A
B
C
D
Write Powers in Standard Form
Evaluate the expression 83.
83 = 8 ● 8 ● 8
= 512
Answer: 512
8 is used as a factor 3 times.
Multiply.
Evaluate the expression 44.
A. 8
B. 16
C. 44
D. 256
1.
2.
3.
4.
A
B
C
D
Write Powers in Standard Form
Evaluate the expression 64.
64 = 6 ● 6 ● 6 ● 6
= 1,296
Answer: 1,296
6 is used as a factor 4 times.
Multiply.
Evaluate the expression 55.
A. 10
B. 25
C. 3,125
D. 5,500
A.
B.
C.
D.
A
B
C
D
Write Powers in Exponential Form
Write 9 ● 9 ● 9 ● 9 ● 9 ● 9 in exponential form.
9 is the base. It is used as a factor 6 times. So, the
exponent is 6.
Answer: 9 ● 9 ● 9 ● 9 ● 9 ● 9 = 96
Write 3 ● 3 ● 3 ● 3 ● 3 in exponential form.
A. 35
B. 53
C. 3 ● 5
D. 243
A.
B.
C.
D.
A
B
C
D
• Find squares of numbers and square roots of
perfect squares.
• square
• perfect squares
• square root
• radical sign
The product of a number and itself is the square of that
number.
Example: The square of 5 is 5 ∙ 5 = 52 = 25.
Numbers that are multiplied to form perfect squares
A. Aa
are called square roots. A radical sign (√) indicates
square root.
B. B
C. C
Example: 𝟏𝟔 = 𝟒 𝒃𝒆𝒄𝒂𝒖𝒔𝒆 𝟒 ∙ 𝟒 = 𝟏𝟔
D.
D
Find Squares of Numbers
Find the square of 5.
5 ● 5 = 25
Answer: 25
Multiply 5 by itself.
Find the square of 7.
A. 2.65
B. 14
C. 49
D. 343
A.
B.
C.
D.
A
B
C
D
Find Squares of Numbers
Find the square of 19.
Method 1
Use paper and pencil.
19 ● 19 = 361
Multiply 19 by itself.
Method 2
Use a calculator.
19
x2
ENTER
=
Answer: 361
361
Find the square of 21.
A. 4.58
B. 42
C. 121
D. 441
1.
2.
3.
4.
A
B
C
D
Find Square Roots
Find
6 ● 6 = 36, so
Answer: 6
= 6. What number times itself is 36?
Find
A. 8
B. 32
C. 640
D. 4,096
1.
2.
3.
4.
A
B
C
D
Find Square Roots
Find
2nd
[x2] 676
Answer:
ENTER
=
26
Use a calculator.
Find
A. 16
B. 23
C. 529
D. 279,841
A.
B.
C.
D.
A
B
C
D
GAMES A checkerboard is a square with an area of
1,225 square centimeters. What are the dimensions
of the checkerboard?
The checkerboard is a square. By finding the square
root of the area, 1,225, you find the length of one side
of the board.
2nd
[x2] 1225
ENTER
=
35
Use a calculator.
Answer: So, a checkerboard measures 35 centimeters
by 35 centimeters.
GARDENING Kyle is planting a new garden that is a
square with an area of 4,225 square feet. What are
the dimensions of Kyle’s garden?
A. 42 ft × 25 ft
B. 65 ft × 65 ft
C. 100 ft × 100 ft
D. 210 ft × 210 ft
A.
B.
C.
D.
A
B
C
D
• Evaluate expressions using the order of operations.
• numerical expression
• order of operations
1. 15 – 5 ● 2 + 7
2. 5 ● 32 – 7
3. 2 + (23 ● 3) + 6 – 1
Use Order of Operations
Evaluate 27 – (18 + 2).
27 – (18 + 2)
20
= 27 –
20
Answer: 7
Evaluate 45 – (26 + 3).
A. 16
B. 22
C. 42
D. 74
A.
B.
C.
D.
A
B
C
D
Use Order of Operations
Evaluate 15 + 5 ● 3 – 2.
15 + 5 ● 3 – 2
15
= 15 + 15
=
–2
30 – 2
Answer: 28
Evaluate 32 – 3 ● 7 + 4.
A. –1
B. 15
C. 125
D. 207
1.
2.
3.
4.
A
B
C
D
Use Order of Operations
Evaluate 12 ● 3 – 22.
12 ● 3 – 22
4
= 12 ● 3 – 4
=
36 – 4
Answer: 32
Evaluate 9 × 5 + 32.
A. 51
B. 54
C. 126
D. 514
1.
2.
3.
4.
A
B
C
D
Use Order of Operations
Evaluate 28 ÷ (3 – 1)2.
28 ÷ (3 – 1)2
22
= 28 ÷
22
= 28 ÷
4
Answer: 7
Evaluate 36 ÷ (14 – 11)2.
A. 3
B. 4
C. 6
D. 9
A.
B.
C.
D.
A
B
C
D
VIDEO GAMES Use the table shown below. Taylor
is buying two video game stations, five extra
controllers, and ten games. What is the total cost?
number
number
cost of
cost of
cost
number of
of
of game
game
× station + controllers × controller + games × of game
stations
2
×
$180 +
5
×
$24
+
10
×
= 360 + 120 + 350
Multiply from left to right.
= 830
Add.
$35
Check
Check the reasonableness of the
answer by estimating. The cost is about
(2 × 200) + (5 × 25) + (10 × 40) = 400 +
125 + 400, or about $925. The solution
is reasonable.
Answer: So, the total cost $830.
Use the table shown below. Suzanne is buying
a video game station, four extra controllers,
and six games. What is the total cost?
D. $545.64
0%
D
A
C. $495.74
0%
A
B
0%
C
D
C
B. $301.88
A.
B.
0%
C.
D.
B
A. $240.94
• Solve problems using the guess and check
strategy.
Guess and Check
CONCESSIONS The concession stand at the
school play sold lemonade for $0.50 and cookies
for $0.25. They sold 7 more lemonades than
cookies and they made a total of $39.50. How many
lemonades and cookies were sold?
Explore
You know the cost of each lemonade and
cookies. You know the total amount made
and that they sold 7 more lemonades than
cookies. You need to know how many
lemonades and cookies were sold.
Plan
Make a guess and check it. Adjust the guess
until you get the correct answer.
Guess and Check
Solve
Make a guess.
14 cookies, 21 lemonades 0.25(14) + 0.50(21) = $14.00
This guess is too low.
50 cookies, 57 lemonades 0.25(50) + 0.50(57) = $41.00
This guess is too high.
48 cookies, 55 lemonades 0.25(48) + 0.50(55) = $39.50
Check
48 cookies cost $12, and 55 lemonades
cost $27.50. Since $12 + $27.50 = $39.50
and 55 is 7 more than 48, the guess is
correct.
Answer: 48 cookies and 55 lemonades
ZOO A total of 122 adults and children went to the
zoo. Adult tickets cost $6.50 and children’s tickets
cost $3.75. If the total cost of the tickets was $597.75,
how many adults and children went to the zoo?
A. 51 adults and 71 children
B. 71 adults and 51 children
0%
D
A
0%
A
B
0%
C
D
C
D. 64 adults and 58 children
A.
B.
0%
C.
D.
B
C. 58 adults and 64 children
Five-Minute Check (over Lesson 1-5)
Main Idea and Vocabulary
California Standards
Example 1: Evaluate an Algebraic Expression
Example 2: Evaluate Expressions
Example 3: Evaluate Expressions
Example 4: Real-World Example
• Evaluate simple algebraic expressions.
• variable
• algebra
• algebraic expression
• coefficient
A VARIABLE is a letter that
stands for a number. The number
is unknown. A variable can use
any letter of the alphabet.
• n+5
•2·y
• x–7
•y·2
• p ÷ 123
• 2y
Evaluate an Algebraic Expression
Evaluate t – 4 if t = 6.
t–4=6–4
=2
Answer: 2
Replace t with 6.
Evaluate 7 + m if m = 4.
A. 3
B. 7
C. 11
D. 28
A.
B.
C.
D.
A
B
C
D
Evaluate Expressions
Evaluate 5x + 3y if x = 7 and y = 9.
5x + 3y = 5(7) + 3(9)
= 35 + 27
= 62
Answer: 62
Evaluate 4a – 2b if a = 9 and b = 6.
A. 2
B. 5
C. 24
D. 72
1.
2.
3.
4.
A
B
C
D
Evaluate Expressions
Evaluate 5 + a2 if a = 5.
5 + a2 = 5 + 52
Replace a with 5.
= 5 + 25
Evaluate the power.
= 30
Add.
Answer: 30
Evaluate 24 – s2 if s = 3.
A. 15
B. 18
C. 164
D. 441
1.
2.
3.
4.
A
B
C
D
BOWLING David is going bowling with a group of
friends. His cost for bowling can be described by the
formula 1.75 + 2.5g, where g is the number of games
David bowls. Find the total cost of bowling if David
bowls 3 games.
A. $4.25
B. $7.75
C. $9.25
D. $12.75
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 1-6)
Main Idea and Vocabulary
California Standards
Example 1: Solve an Equation Mentally
Example 2: Standards Example
Example 3: Real-World Example
• Write and solve equations using mental math.
• equation
• solution
• solving an equation
• defining the variable
An EQUATION is a mathematical
sentence that says, two
expressions are equal.
EQUAL SIGN (=) means that the
amount is the same on both sides.
12 – 3 = 9
8 + 4 = 12
14 · 2 = 28
27 ÷ 3 = 9
n–5=3
12 ÷ y = 2
An Equation is like a balance scale.
Everything must be equal on both
sides.
=
10
5+5
An Equation is like a balance scale.
Everything must be equal on both
sides.
=
12
6+6
An Equation is like a balance scale.
Everything must be equal on both
sides.
=
7
n+2
An Equation is like a balance scale.
Everything must be equal on both
sides.
=
7
5n + 2
Solve an Equation Mentally
Solve p – 14 = 5 mentally.
p – 14 = 5
19 – 14 = 5
5=5
Write the equation.
You know that 19 – 14 is 5.
Simplify.
Answer: So, p = 19. The solution is 19.
Solve p – 6 = 11 mentally.
A. 5
B. 17
C. 23
D. 66
A.
B.
C.
D.
A
B
C
D
A store sells pumpkins for $2 per pound. Paul has
$18. Use the equation 2x = 18 to find how large a
pumpkin Paul can buy with $18.
A 6 lb
B 7 lb
C 8 lb
D 9 lb
Read the Item
Solve 2x = 18 to find how many pounds the pumpkin can
weigh.
A store sells pumpkins for $2 per pound. Paul has
$18. Use the equation 2x = 18 to find how large a
pumpkin Paul can buy with $18.
Solve the Item
2x = 18
2 ● 9 = 18
Write the equation.
You know that 2 ● 9 is 18.
Answer: Paul can buy a pumpkin as large as 9 pounds.
The answer is D.
A store sells notebooks for $3 each. Stephanie has
$15. Use the equation 3x = 15 to find how many
notebooks Stephanie can buy with $15.
A. 4
B. 5
C. 6
D. 7
1.
2.
3.
4.
A
B
C
D
ENTERTAINMENT An adult paid $18.50 for herself
and two students to see a movie. If the two student
tickets cost $11 together, what is the cost of an
adult ticket?
Words
The cost of one adult ticket and two
student tickets is $18.50.
Variable
Let a represent the cost of an adult movie
ticket.
Equation a + 11 = 18.50
ENTERTAINMENT An adult paid $18.50 for herself
and two students to see a movie. If the two student
tickets cost $11 together, what is the cost of an
adult ticket?
a + 11 = 18.50 Write the equation.
7.50 + 11 = 18.50
18.50 = 18.50
Replace a with 7.50 to make the
equation true.
Simplify.
Answer: The number 7.50 is the solution of the
equation. So, the cost of an adult movie ticket
is $7.50.
ICE CREAM Julie spends $9.50 at the ice cream
parlor. She buys a hot fudge sundae for herself and
ice cream cones for each of the three friends who
are with her. Find the cost of Julie’s sundae if the
three ice cream cones together cost $6.30.
A. $2.10
B. $2.80
C. $3.20
D. $15.80
1.
2.
3.
4.
A
B
C
D
Five-Minute Check (over Lesson 1-7)
Main Idea and Vocabulary
California Standards
Key Concept: Distributive Property
Example 1: Write Sentences as Equations
Example 2: Write Sentences as Equations
Example 3: Real-World Example
Concept Summary: Real Number Properties
Example 4: Use Properties to Evaluate Expressions
• Use Commutative, Associative, Identity, and
Distributive properties to solve problems.
• equivalent expressions
• properties
The order in which two
numbers are added does not
change their sum.
•7+8=8+7
•a+9=9+a
•z+3=3+z
The sum of a number and 0 is
the number.
•7+0=7
•a+0=a
•c+0=c
The product of a factor and 1 is
the factor.
•5●1=5
•b●1=b
•w●1=w
The way in which three numbers are grouped when
they are multiplied or added does not change their
sum or product.
7 ● 8 ● 9 = 504
= ( 7 ● 8) ● 9 = 504
= 7 ● (8 ● 9) = 504
= 24
7+8+9
= ( 7 + 8) + 9 = 24
= 7 + (8 + 9) = 24
Write Sentences as Equations
Use the Distributive Property to evaluate the
expression 8(5 + 7).
8(5 + 7) = 8(5) + 8(7)
= 40 + 56
= 96
Answer: 96
Use the Distributive Property to evaluate the
expression 4(6 + 3).
A. 9
B. 12
C. 27
D. 36
A.
B.
C.
D.
A
B
C
D
Write Sentences as Equations
Use the Distributive Property to evaluate the
expression 6(9) + 6(2).
6(9) + 6(2) = 54 + 12
= 66
6(9) + 6(2) = 6(9 + 2)
= 6(11)
= 66
Answer: 66
Use the Distributive Property to evaluate the
expression (5 + 3)7.
A. 8
B. 26
C. 56
D. 105
1.
2.
3.
4.
A
B
C
D
COOKIES Heidi sold cookies for $2.50 per box for a
fundraiser. If she sold 60 boxes of cookies, how
much money did she raise?
A. $2.50
B. $62.50
C. $150
D. $162.50
1.
2.
3.
4.
A
B
C
D
Use Properties to Evaluate Expressions
Find 5 ● 13 ● 20 mentally. Justify each step.
5 ● 13 ● 20 = 5 ● 13 ● 20
= (5 ● 20) ● 13
Commutative Property
of Multiplication
Associative Property
of Multiplication
= 100 ● 13 or 1,300 Multiply 100 and
13 mentally.
Answer: 1,300
Name the property shown by the statement
4 + (6 + 2) = (4 + 6) + 2.
A. Associative Property of
Addition
B. Commutative Property of
Addition
C. Identity Property of
Addition
D. A and B
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 1-8)
Main Idea and Vocabulary
California Standards
Example 1: Describe and Extend Sequences
Example 2: Describe and Extend Sequences
Example 3: Real-World Example
• Describe the relationships and extend terms in
arithmetic sequences.
• sequence
• term
• arithmetic sequence
Pencil / Eraser
Quiz
Marker
HW
Red Pen
Homework
P. 60 - 61
7 -19 ODD
37 – 47 ODD
Describe the relationship between the terms in the
arithmetic sequence 7, 11, 15, 19, … Then write the
next three terms in the sequence.
Each term is found by adding 4 to the previous
term.
19 + 4 = 23
23 + 4 = 27
27 + 4 = 31
Describe the relationship between the terms in the
arithmetic sequence 13, 24, 35, 46, … Then write the
next three terms in the sequence.
A. add 9; 55, 64, 53
B. add 11; 57, 68, 79
C. add 13; 59, 72, 85
D. add 15; 61, 76, 91
A
B0%
C
D
D
C
B
A
0%
A.
0% B.0%
C.
D.
Describe and Extend Sequences
Describe the relationship between the terms in the
arithmetic sequence 0.1, 0.5, 0.9, 1.3, … Then write
the next three terms in the sequence.
Each term is found by adding 0.4 to the previous
term.
1.3 + 0.4 = 1.7
1.7 + 0.4 = 2.1
2.1 + 0.4 = 2.5
The next three terms are 1.7, 2.1, 2.5.
Describe the relationship between the terms in the
arithmetic sequence 0.6, 1.5, 2.4, 3.3, … Then write
the next three terms in the sequence.
A. add 0.3; 3.6, 3.9, 4.2
B. add 0.5; 3.8, 4.3, 4.8
C. add 0.8; 4.1, 4.9, 5.7
D. add 0.9; 4.2, 5.1, 6.0
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
EXERCISE Mehmet started a new exercise routine.
The first day, he did 2 sit-ups. Each day after that,
he did 2 more sit-ups than the previous day. If he
continues this pattern, how many sit-ups will he do
on the tenth day?
Make a table to display the sequence.
Each term is 2 times its position number. So, the
expression is 2n.
2n
Write the expression.
2(10) = 20
Replace n with 10.
Answer: So, on the tenth day, Mehmet will do 20
sit-ups.
CONCERTS The first row of a theater has 8 seats.
Each additional row has eight more seats than the
previous row. If this pattern continues, what
algebraic expression can be used to find the number
of seats in the 15th row? How many seats will be in
the 15th row?
0%
A. 8n; 120 seats
B. 8 + n; 23 seats
C. 15n; 120 seats
1.
2.
3.
4.
A
B
C
D
A
D. 15 + n; 23 seats
B
C
D
Five-Minute Check (over Lesson 1-9)
Main Idea and Vocabulary
California Standards
Example 1: Make a Function Table
Example 2: Real-World Example
Example 3: Real-World Example
• Make function tables and write equations.
• function
• function rule
• function table
• domain
• range
Pencil / Eraser
Red Pen
Marker
Homework
P. 65 - 67
7 -13 ODD
29 – 39 ODD
Jasmin runs 15 minutes before school and
30 minutes after school. How many minutes
total does Jasmin run in a day? Write an
equation with a variable, and then solve.
15 + 30 = n
n = 45
Pencil / Eraser
White board
Marker
Homework
P. 65 - 67
7 -13 ODD
29 – 39 ODD
Timothy got 72 right on his timed test in July.
He got 99 right on this same test in
November. How many more right answers
did he get on his second test? Write an
equation with a variable, and then solve.
72 + n = 99
n = 27
Pencil / Eraser
HW
Red pen
Marker
Homework
Quiz (TUE): 1-6 to 1-10
P. 75
1 - 25 ALL
One marble costs 25 cents. Issak bought 4.
How much did he spend? Write an equation
with a variable, and then solve.
4 ● 25 = n
n = 100 cents or 1 dollar ($1)
Input
Function Rule
Output
2
+5
2+5=7
2
●3
2●3=6
14
÷7
14 ÷ 7 = 2
Another word for Input is Domain.
Another word for Output is Range.
Make a Function Table
WORK Asha makes $6.00 an hour working at a
grocery store. Make a function table that shows
Asha’s total earnings for working 1, 2, 3, and 4 hours.
Interactive Lab:
Function Machines
MOVIE RENTAL Dave goes to the video store to rent
a movie. The cost per movie is $3.50. Make a function
table that shows the amount Dave would pay for
renting 1, 2, 3, and 4 movies.
Answer:
READING Melanie read 14 pages of a detective
novel each hour. Write an equation using two
variables to show how many pages p she read in h
hours.
Make a table to display the sequence.
Variable
Let p represent the number of pages read.
Let h represent the number of hours.
Equation p = 14 ● h
Equation p = 14 h
TRAVEL Derrick drove 55 miles per hour to visit his
grandmother. Write an equation using two variables
to show how many miles m he drove in h hours.
A. m = 55 + h
B. m = 55h
C. m = 55 – h
D. mh = 55
1.
2.
3.
4.
A
B
C
D
COST Derrick drove 55 miles per hour to visit his
grandmother. Write an equation using two variables
to show how many miles m he drove in h hours.
Add some problems that they
have to make the equation
itself. The tests have these
kinds of problems.
READING Melanie read 14 pages of a detective
novel each hour. Use the equation p = 14h (p is how
many pages she reads in h hours). Find how many
pages Melanie read in 7 hours.
p = 14h
Write the equation.
p = 14(7) Replace h with 7.
p = 98
Multiply.
Answer: 98 pages
Pencil / Eraser
HW
Red pen
Homework
Quiz (TUE): 1-6 to 1-10
TRAVEL Derrick drove 55 miles per hour to visit his
grandmother. Using the equation m = 55h, find how
many miles Derrick drove in 6 hours.
A. 9.16 miles
B. 61 miles
C. 49 miles
D. 330 miles
1.
2.
3.
4.
A
B
C
D
Five-Minute Checks
Image Bank
Math Tools
Arithmetic Sequences
Modeling Algebraic Expressions
Function Machines
Lesson 1-1
Lesson 1-2 (over Lesson 1-1)
Lesson 1-3 (over Lesson 1-2)
Lesson 1-4 (over Lesson 1-3)
Lesson 1-5 (over Lesson 1-4)
Lesson 1-6 (over Lesson 1-5)
Lesson 1-7 (over Lesson 1-6)
Lesson 1-8 (over Lesson 1-7)
Lesson 1-9 (over Lesson 1-8)
Lesson 1-10 (over Lesson 1-9)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
Subtract 5,678 – 3,479.
A. 1,299
B. 1,929
C. 2,199
D. 2,919
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Divide 29,811 ÷ 57.
A. 523
B. 513
C. 503
D. 493
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Each classroom in a school has 30 student desks.
If the average class size is 25 students, and there
are 55 classrooms occupied by classes, about how
many unused desks are there?
A. 300
0%
1.
2.
3.
4.
B. 275
C. 250
D. 225
A
B
C
D
A
B
C
D
Katrina’s family wants to order
Chinese food for dinner. Using the
table, write and solve an equation
to find how much money Katrina’s
family needs to pay for their order.
0%
D
D.
0%
A
B
0%
C
D
C
C.
A.
B.
0%
C.
D.
B
B.
8($2.95 + $4.95 + $5.95 + $1.89) = x;
x = $125.92
2($2.95 + $4.95 + $5.95 + $1.89) = x;
x = $28.42
(2 × $2.95) + $4.95 + (2 × $5.95) +
(3 × $1.89) = x; x = $28.42
$2.95 + $4.95 + $5.95 + $1.89 = x;
x = $15.74
A
A.
Katrina’s family wants to order
Chinese food for dinner. How much
change should Katrina’s father
receive if he pays for the Chinese
food with a fifty-dollar bill?
A.
$21.58
1.
2.
3.
4.
0%
B.
$21.82
C.
$25.18
D.
$28.42
A
B
C
D
A
B
C
D
A. 55%
0%
B. 65%
1.
2.
3.
4.
C. 75%
D. 85%
A
B
A
B
C
D
C
D
(over Lesson 1-1)
Ryan’s living room is 10 feet wide, 12 feet long, and
10 feet high. If one gallon of paint covers 400 square
feet of surface area, how many gallons of paints
would Ryan need to paint all four walls and the
ceiling? Use the four-step plan to solve the problem.
A. 1 gallon
B. 2 gallons
C. 3 gallons
0%
D
0%
C
0%
B
D. 4 gallons
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-1)
Nolan is selling coupon books to raise money for a
class trip. The cost of the trip is $400, and the profit
from each book is $15. How many coupon books does
Nolan need to sell to earn enough money to go on the
class trip? Use the four-step plan to solve the problem.
A. 15 coupon books
1.
2.
3.
4.
0%
B. 16 coupon books
C. 26 coupon books
D. 27 coupon books
A
B
C
D
A
B
C
D
(over Lesson 1-1)
Cangialosi’s Café made a $6,000 profit during January. Mr.
Cangialosi expects profits to increase $500 per month. In what
month can Mr. Cangialosi expect his profit to be
greater than
his January profit?
0%
A.
March
B.
April
C.
May
D.
June
A
B
1.
2.
3.
4.
C
D
A
B
C
D
(over Lesson 1-1)
A comic book store took in $2,700 in sales of first
editions during November. December sales of first
editions are expected to be double that amount. If
the first editions are sold for $75 each, how many
first editions are expected to be sold in December?
A. 18
B. 36
C. 38
0%
D
0%
C
0%
B
D. 72
A
0%
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-2)
A. 5 ● 3
B. 5 ● 5 ● 5
C. 3 ● 3 ● 3 ● 3 ● 3
D. 5 ● 5 ● 5 ● 5 ● 5
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-2)
A. 2 ● 6
B. 6 ● 6
C. 2 ● 2 ● 2 ● 2 ● 2 ● 2
D. 6 ● 6 ● 6 ● 6 ● 6 ● 6
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-2)
A. 512
0%
B. 312
1.
2.
3.
4.
C. 64
D. 24
A
B
A
B
C
D
C
D
(over Lesson 1-2)
A. 10
B. 25
D. 64
A
0%
B
C
D
D
0%
B
A
0%
A.
0%
B.
C.
D.
C
C. 32
(over Lesson 1-2)
A certain type of bacteria reproduces at a rate of
10 ● 10 ● 10 per hour. Write the rate at which this
bacteria reproduces in exponential form.
A. 303 per hour
0%
B. 103 per hour
C. 33 per hour
1.
2.
3.
4.
A
B
C
D
A
D. 13 per hour
B
C
D
(over Lesson 1-2)
Write 87 in words.
A. seven times eight
B. eight times seven
C. eight to the seventh power
D. seven to the eight power
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
(over Lesson 1-3)
Find the square of 7.
A. 2.6
B. 3.5
C. 14
D. 49
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-3)
Find the square of 12.
A. 144
B. 124
C. 24
D. 6
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-3)
Find the square of 13.
A. 3.6
0%
B. 6.5
1.
2.
3.
4.
C. 159
D. 169
A
B
A
B
C
D
C
D
(over Lesson 1-3)
A. 9
B. 40.5
C. 162
D. 6,561
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-3)
A. 392
B. 98
C. 16
D. 14
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-3)
A. –128
0%
B. 28
1.
2.
3.
4.
C. 96
D. 136
A
B
A
B
C
D
C
D
(over Lesson 1-4)
Evaluate the expression 7 ● 4 + (21 – 5).
A. 44
B. 64
C. 120
D. 140
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-4)
Evaluate the expression (7 – 4)3 + 32.
A. 371
B. 307
C. 59
D. 43
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-4)
Evaluate the expression 16 ÷ 4 + 63 ÷ 9.
A. 9
0%
B. 11
1.
2.
3.
4.
C. 12
D. 27
A
B
A
B
C
D
C
D
(over Lesson 1-4)
Evaluate the expression 3 × 103.
A. 30
B. 90
C. 3,000
D. 9,000
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-4)
Evaluate the expression 144 ÷ (2)6.
A. 12
B. 4
C. 2.25
D. 1.12
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-4)
On Mondays, Wednesdays, and Fridays, Adrian runs five
miles a day. On Tuesdays, Thursdays, and Saturdays, he
runs two miles. On Sunday, Adrian runs 10 miles. Write a
numerical expression to find how many miles Adrian
runs in a week. Then evaluate the expression.
A. (3 ● 5) + (2 ● 2) + 10 = x; x = 31
B. (3 ● 5) + (2 ● 2) + 10 = x; x = 29
C. (3 ● 5) + (3 ● 2) + 10 = x; x = 31
D. (3 ● 5) + (3 ● 2) + 10 = x; x = 29
1.
2.
3.
4.
0%
A
B
C
D
A
B
C
D
(over Lesson 1-5)
0%
D
A
B
0%
C
D
C
A.
0% B.0%
C.
D.
B
A. 5 packages of hot dog buns
and 4 packages of hot dogs
B. 3 packages of hot dog buns
and 5 packages of hot dogs
C. 4 packages of hot dog buns
and 5 packages of hot dogs
D. 5 packages of hot dog buns
and 3 packages of hot dogs
A
Hot dogs come in packages of 10. Hot dog buns come in
packages of 8. How many packages of hot dogs and hot
dog buns would you need to buy to have enough buns
for every hot dog? Solve using the guess and check
strategy.
(over Lesson 1-5)
A number is multiplied by 8. Then 5 is subtracted
from the product. The result is 43. What is the
number?
A. 8
0%
B. 6
C. 5
1.
2.
3.
4.
A
B
C
D
A
D. 7
B
C
D
(over Lesson 1-5)
The school carnival made $420 from ticket sales. Adult
tickets cost $5 and student tickets cost $3. Also, three
times as many students bought tickets as adults. How
many adult and student tickets were sold?
A. 20 student tickets
and 60 adult tickets
B. 90 adult tickets
and 30 student tickets
C. 60 adult tickets
and 20 student tickets
D. 90 student tickets
and 30 adult tickets
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
(over Lesson 1-5)
Which sequence follows the rule 3n, where n
represents the position of a term in the sequence?
A. 3, 9, 27, 81, 243, ...
B. 1, 8, 27, 64, 125, ...
C. 3, 6, 9, 12, 15, ...
D. 1, 4, 7, 10, 13, ...
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-6)
A. 1
B. 2
C. 4
D. 8
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-6)
Evaluate 7r – 3p for r = 7 and p = 9.
A. 12
B. 22
C. 32
D. 42
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-6)
Evaluate (p – m) + 5(2n) for m = 2, n = 4, and p = 9.
A. 96
0%
B. 58
1.
2.
3.
4.
C. 47
D. 33
A
B
A
B
C
D
C
D
(over Lesson 1-6)
A. 3
B. 1
C. 0.50
D. 0.25
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-6)
A. 0.08
B. 1.33
C. 2.25
D. 6.75
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-6)
Kerrie works at an art supply store. Which expression
could Kerrie use to find the cost of buying p cases of
paintbrushes at $145 each and e easels at $59 each?
A. 145e + 59p
B. 145p + 59e
C. (145 + 59) + pe
0%
1.
2.
3.
4.
A
D. p(145 – 59) + e
A
B
C
D
B
C
D
(over Lesson 1-7)
Solve the equation 27 + n = 55 mentally.
A. 82
B. 72
C. 32
D. 28
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-7)
Solve the equation 9y = 45 mentally.
A. 3
B. 4
C. 5
D. 6
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-7)
Name the number from the list {1.6, 2.8, 3.1} that is
the solution of the equation 2.4 + a = 4.
A. 1.6
0%
B. 2.8
1.
2.
3.
C. 3.1
A
B
A
B
C
C
(over Lesson 1-7)
Name the number from the list {2.3, 3.5, 4.6} that is
the solution of the equation 18m = 63.
A. 2.3
0%
B. 3.5
1.
2.
3.
C. 4.6
A
A
B
C
B
C
(over Lesson 1-7)
Kieran worked for 9.5 hours and earned $80.75. How
much does she get paid per hour? Use the equation
9.5w = 80.75, where w is Kieran’s hourly wage.
A. $8.50
0%
B. $8.75
C. $9.50
1.
2.
3.
4.
A
B
C
D
A
D. $9.75
B
C
D
(over Lesson 1-7)
Warren had 26 bobbleheads in his collection. After he
bought some more bobbleheads at an auction, he
had a total of 32 bobbleheads. Which equation could
be used to find how many bobbleheads he bought at
the auction?
1.
2.
3.
4.
0%
A. 32 + t = 26
B. 32 ÷ t = 26
C. 26 – 32 = t
D. 26 + t = 32
A
B
C
D
A
B
C
D
(over Lesson 1-8)
Using the Distributive Property, write the expression
3(4 + 8) as an equivalent expression and then
evaluate it.
A. 3 ● 4 + 8; 20
B. 3 + 3 ● 8; 27
D. 3 ● 8 + 4 ● 8; 56
A
B0%
C
D
D
C
A
0%
B
C. 3 ● 4 + 3 ● 8; 36
A.
0% B. 0%
C.
D.
(over Lesson 1-8)
Using the Distributive Property, write the expression
9(8 – 4) as an equivalent expression and then
evaluate it.
A. 9 ● 4 – 8; 28
0%
B. 9 ● 8 – 9 ● 4; 36
C. 9 ● 8 – 4 ● 8; 40
1.
2.
3.
4.
A
B
C
D
A
D. 9 ● 8 – 4; 68
B
C
D
(over Lesson 1-8)
Name the property shown by the statement
x + y = y + x.
A. Associative Property
of Addition
0%
B. Commutative Property
of Addition
1.
2.
3.
4.
C. Distributive Property
of Addition
D. Identity Property
of Addition
A
B
A
B
C
D
C
D
(over Lesson 1-8)
Name the property shown by the statement
31 × 1 = 31.
A. Associative Property
of Multiplication
B. Commutative Property
of Multiplication
A
B 0%
C
D
D
C
A
D. Identity Property
of Multiplication
0%
A.
0% B. 0%
C.
D.
B
C. Distributive Property
of Multiplication
(over Lesson 1-8)
Name the property shown by the statement
(m × n) × p = m × (n × p).
A. Associative Property
of Multiplication
B. Commutative Property
of Multiplication
C. Distributive Property
of Multiplication
D. Identity Property
of Multiplication
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-8)
Rewrite a × (b × c) using the Associative Property of
Multiplication.
A. a × (c × b)
0%
1.
2.
3.
4.
B. c × ( a × b)
C. (b × c) × a
D. (a × b) × c
A
B
A
B
C
D
C
D
(over Lesson 1-9)
Describe the pattern in the sequence 2, 16, 128,
1,024, … and identify it as arithmetic or geometric.
A. × 8; arithmetic
B. × 8; geometric
C. × 4; arithmetic
D. × 4; geometric
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-9)
Describe the pattern in the sequence 2.8, 6, 9.2,
12.4, … and identify it as arithmetic or geometric.
A. + 3.2; arithmetic
0%
B. + 3.2; geometric
C. + 8.8; arithmetic
D. + 8.8; geometric
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-9)
Write the next three terms of the sequence 4, 12, 36,
108, … .
A. 36, 12, 4
0%
B. 216, 648, 1,944
1.
2.
3.
4.
C. 316, 948, 2,844
A
D. 324, 972, 2,916
B
A
B
C
D
C
D
(over Lesson 1-9)
Write the next three terms of the sequence 2.1, 2.8,
3.5, 4.2, … .
A. 4.8, 5.5, 6.2
B. 4.9, 5.6, 6.3
C. 4.9, 5.5, 6.2
D. 5.6, 6.3, 7.0
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-9)
Every 18 months, National Surveys conducts a
population survey of the United States. If they
conducted a survey in September of 2003, when
will they conduct the next four surveys?
A. March 2005, September 2006,
March 2008, September 2009
B. March 2005, September 2006,
March 2007, September 2008
C. February 2005, August 2006,
March 2008, September 2008
D. February 2005, September 2006,
March 2008, September 2009
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-9)
Find the next term in the sequence 3.2, 12.8, 51.2,
204.8, … .
A. 723.5
0%
B. 819.2
1.
2.
3.
4.
C. 845.2
D. 901.1
A
B
A
B
C
D
C
D
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