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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
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.
1. A
2. B
3. C
4. D
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
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?
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?
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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
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?
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?
Answer: The pack of six cans is the better buy.
The answer makes sense based on the facts given in the problem.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 3
B. 4
C. 5
D. 6
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?
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
Answer: So, Des Moines has about 10,854 more radios than Windsor has.
Check Based on the information given in the problem, the answer seems to be reasonable.
• factors
• exponent• base• powers• squared
• Use powers and exponents.
• cubed• evaluate• standard form• exponential form
16 = 2 · 2 · 2 · 2 = 24
The centered dots indicate multiplication
Common factors
The exponent tells how many times the base is used as a factor.
The base is the common factor.
Powers Words52 Five to the second power or five
squared.
43 Four to the third power or four
cubed.
24 Two to the fourth power.
Numbers written without exponents are in
standard form.
Example: 2 · 2 · 2 · 2 = 16
Numbers written with exponents are in exponential form.
Example: 2 · 2 · 2 · 2 = 24
Standard form
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
A. A
B. B
C. C
D. D
A. 3 ● 6
B. 6 ● 3
C. 6 ● 6 ● 6
D. 3 ● 3 ● 3 ● 3 ● 3 ● 3
Write 36 as a product of the same factor.
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
1. A
2. B
3. C
4. D
A. 7 ● 3
B. 3 ● 7
C. 7 ● 7 ● 7
D. 3 ● 3 ● 3 ● 3 ● 3 ● 3 ● 3
Write 73 as a product of the same factor.
Write Powers in Standard Form
Evaluate the expression 83.
83 = 8 ● 8 ● 8 8 is used as a factor 3 times.
= 512 Multiply.
Answer: 512
Evaluate the expression 64.
64 = 6 ● 6 ● 6 ● 6 6 is used as a factor 4 times.
= 1,296 Multiply.
Answer: 1,296
Write Powers in Standard Form
A. A
B. B
C. C
D. D
A. 10
B. 25
C. 3,125
D. 5,500
Evaluate the expression 55.
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 Powers in Exponential Form
A. A
B. B
C. C
D. D
A. 35
B. 53
C. 3 ● 5
D. 243
Write 3 ● 3 ● 3 ● 3 ● 3 in exponential form.
• square
• perfect squares• square root• radical sign
• Find squares of numbers and square roots of perfect squares.
A. A
B. B
C. C
D. D
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 are called square roots. A radical sign () indicates a square root.Example:
Find Squares of Numbers
Find the square of 5.
5 ● 5 = 25 Multiply 5 by itself.
Answer: 25
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.
Answer: 361
19 ENTER=x2 361
Find Square Roots
Answer: 6
Find
6 ● 6 = 36, so = 6. What number times itself is 36?
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.
Answer: So, a checkerboard measures 35 centimeters by 35 centimeters.
Use a calculator.[x2] 1225 ENTER=2nd 35
A. A
B. B
C. C
D. D
A. 42 ft × 25 ft
B. 65 ft × 65 ft
C. 100 ft × 100 ft
D. 210 ft × 210 ft
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?
• numerical expression
• order of operations
• Evaluate expressions using the order of operations.
Use Order of Operations
Evaluate 27 – (18 + 2).
27 – (18 + 2)
20
= 27 – 20
Answer: 7
Use Order of Operations
Evaluate 15 + 5 ● 3 – 2.
Answer: 28
15 + 5 ● 3 – 2
15
= 15 + 15 – 2
= 30 – 2
Use Order of Operations
Evaluate 12 ● 3 – 22.
Answer: 32
12 ● 3 – 22
4
= 12 ● 3 – 4
= 36 – 4
Evaluate 28 ÷ (3 – 1)2.
Answer: 7
Use Order of Operations
28 ÷ (3 – 1)2
22
= 28 ÷ 22
= 28 ÷ 4
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 of gamestations
cost of gamestation
number ofcontrollers
number of
gamescost
of gamecost of
controller+ × + ×
2 $180 5 10 $35$24× + × + ×
= 360 + 120 + 350 Multiply from left to right.
= 830 Add.
Answer: So, the total cost $830.
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.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. $240.94
B. $301.88
C. $495.74
D. $545.64
Use the table shown below. Suzanne is buying a video game station, four extra controllers, and six games. What is the total cost?
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) = $14.00This guess is too low.
Answer: 48 cookies and 55 lemonades
Guess and Check
50 cookies, 57 lemonades 0.25(50) + 0.50(57) = $41.00This guess is too high.48 cookies, 55 lemonades 0.25(48) + 0.50(55) = $39.50Check 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.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 51 adults and 71 children
B. 71 adults and 51 children
C. 58 adults and 64 children
D. 64 adults and 58 children
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?
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
• variable
• algebra• algebraic expression• coefficient
• Evaluate simple algebraic expressions.
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
• x – 7
• p ÷ 123
• 2 · y
• y · 2
• 2y
Evaluate an Algebraic Expression
Evaluate t – 4 if t = 6.
Answer: 2
t – 4 = 6 – 4 Replace t with 6.
= 2
Evaluate Expressions
Evaluate 5x + 3y if x = 7 and y = 9.
5x + 3y = 5(7) + 3(9)
= 35 + 27
= 62
Answer: 62
1. A
2. B
3. C
4. D
A. 2
B. 5
C. 24
D. 72
Evaluate 4a – 2b if a = 9 and b = 6.
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
A. A
B. B
C. C
D. D
A. $4.25
B. $7.75
C. $9.25
D. $12.75
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.
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
• equation
• solution• solving an equation• defining the variable
• Write and solve equations using mental math.
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 14 · 2 = 28 n – 5 = 3
8 + 4 = 12 27 ÷ 3 = 9 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 n + 2=
5
Solve an Equation Mentally
Answer: So, p = 19. The solution is 19.
p – 14 = 5 Write the equation.
19 – 14 = 5 You know that 19 – 14 is 5.
5 = 5 Simplify.
Solve p – 14 = 5 mentally.
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 ItemSolve 2x = 18 to find how many pounds the pumpkin can weigh.
Solve the Item
2x = 18 Write the equation.
2 ● 9 = 18 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 pumpkins for $2 per pound. Paul has $18. Use the equation 2x = 18 to find how large a pumpkin Paul can buy with $18.
1. A
2. B
3. C
4. D
A. 4
B. 5
C. 6
D. 7
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.
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
a + 11 = 18.50 Write the equation.
7.50 + 11 = 18.50 Replace a with 7.50 to make the equation true.
18.50 = 18.50 Simplify.
Answer: The number 7.50 is the solution of the equation. So, the cost of an adult movie ticket is $7.50.
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?
1. A
2. B
3. C
4. D
A. $2.10
B. $2.80
C. $3.20
D. $15.80
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.
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
• equivalent expressions
• properties
• Use Commutative, Associative, Identity, and Distributive properties to solve problems.
• 7 + 8 = 8 + 7• a + 9 = 9 + a• z + 3 = 3 + z
The order in which two numbers are added does not change their sum.
• 7 + 0 = 7• a + 0 = a• c + 0 = c
The sum of a number and 0 is the number.
• 5 ● 1 = 5• b ● 1 = b• w ● 1 = w
The product of a factor and 1 is the factor.
7 ● 8 ● 9
7 ● 8 ● 9
7 ● 8 ● 9
The way in which three numbers are grouped when they are multiplied or added does not change their sum or product.
= ( (
))=
7 + 8 + 9 7 + 8 + 9 7 + 8 + 9
= ( ()
)=
= 504= 504
= 504
= 24
= 24
= 24
Write Sentences as Equations
Use the Distributive Property to evaluate the expression 8(5 + 7).
Answer: 96
8(5 + 7) = 8(5) + 8(7)
= 40 + 56
= 96
A. A
B. B
C. C
D. D
A. 9
B. 12
C. 27
D. 36
Use the Distributive Property to evaluate the expression 4(6 + 3).
Write Sentences as Equations
Use the Distributive Property to evaluate the expression 6(9) + 6(2).
Answer: 66
6(9) + 6(2) = 6(9 + 2)
= 6(11)
= 66
6(9) + 6(2) = 54 + 12
= 66
1. A
2. B
3. C
4. D
A. 8
B. 26
C. 56
D. 105
Use the Distributive Property to evaluate the expression (5 + 3)7.
1. A
2. B
3. C
4. D
A. $2.50
B. $62.50
C. $150
D. $162.50
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?
Find 5 ● 13 ● 20 mentally. Justify each step.
Answer: 1,300
Use Properties to Evaluate Expressions
5 ● 13 ● 20 = 5 ● 13 ● 20 Commutative Property of Multiplication
= (5 ● 20) ● 13 Associative Property of Multiplication
= 100 ● 13 or 1,300 Multiply 100 and 13 mentally.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. Associative Property of Addition
B. Commutative Property of Addition
C. Identity Property of Addition
D. A and B
Name the property shown by the statement 4 + (6 + 2) = (4 + 6) + 2.
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
• sequence
• term• arithmetic sequence
• Describe the relationships and extend terms in arithmetic sequences.
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
Pencil / Eraser HomeworkQuiz P. 60 - 61Marker 7 -19 ODDHW 37 – 47 ODDRed Pen
A. A
B. B
C. C
D. D
0% 0%0%0%
A. add 9; 55, 64, 53
B. add 11; 57, 68, 79
C. add 13; 59, 72, 85
D. add 15; 61, 76, 91
Describe the relationship between the terms in the arithmetic sequence 13, 24, 35, 46, … Then write the next three terms in the sequence.
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.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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
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.
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.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 8n; 120 seats
B. 8 + n; 23 seats
C. 15n; 120 seats
D. 15 + n; 23 seats
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?
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
• function
• function rule• function table• domain• range
• Make function tables and write equations.
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 = nn = 45
Pencil / Eraser HomeworkRed Pen P. 65 - 67Marker 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 = 99n = 27
Pencil / Eraser HomeworkWhite board P. 65 - 67Marker 7 -13 ODD
29 – 39 ODD
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)
Pencil / Eraser HomeworkHW Quiz (TUE): 1-6 to 1-10 Red pen P. 75Marker 1 - 25 ALL
Function RuleInput Output
2 + 5 2 + 5 = 7
● 3 2 ● 3 = 62
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
1. A
2. B
3. C
4. D
A. m = 55 + h
B. m = 55h
C. m = 55 – h
D. mh = 55
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.
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
1. A
2. B
3. C
4. D
A. 9.16 miles
B. 61 miles
C. 49 miles
D. 330 miles
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.
Pencil / Eraser HomeworkHW Quiz (TUE): 1-6 to 1-10 Red pen
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.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 1,299
B. 1,929
C. 2,199
D. 2,919
Subtract 5,678 – 3,479.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 523
B. 513
C. 503
D. 493
Divide 29,811 ÷ 57.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 300
B. 275
C. 250
D. 225
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. A
B. B
C. C
D. D
0% 0%0%0%
A. 8($2.95 + $4.95 + $5.95 + $1.89) = x; x = $125.92
B. 2($2.95 + $4.95 + $5.95 + $1.89) = x; x = $28.42
C. (2 × $2.95) + $4.95 + (2 × $5.95) + (3 × $1.89) = x; x = $28.42
D. $2.95 + $4.95 + $5.95 + $1.89 = x; x = $15.74
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.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. $21.58
B. $21.82
C. $25.18
D. $28.42
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?
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 55%
B. 65%
C. 75%
D. 85%
A. A
B. B
C. C
D. D0% 0%0%0%
A. 1 gallon
B. 2 gallons
C. 3 gallons
D. 4 gallons
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.
(over Lesson 1-1)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 15 coupon books
B. 16 coupon books
C. 26 coupon books
D. 27 coupon books
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.
(over Lesson 1-1)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. March
B. April
C. May
D. June
(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?
A. A
B. B
C. C
D. D0% 0%0%0%
A. 18
B. 36
C. 38
D. 72
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?
(over Lesson 1-1)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 5 ● 3
B. 5 ● 5 ● 5
C. 3 ● 3 ● 3 ● 3 ● 3
D. 5 ● 5 ● 5 ● 5 ● 5
(over Lesson 1-2)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 2 ● 6
B. 6 ● 6
C. 2 ● 2 ● 2 ● 2 ● 2 ● 2
D. 6 ● 6 ● 6 ● 6 ● 6 ● 6
(over Lesson 1-2)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 512
B. 312
C. 64
D. 24
(over Lesson 1-2)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 10
B. 25
C. 32
D. 64
(over Lesson 1-2)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 303 per hour
B. 103 per hour
C. 33 per hour
D. 13 per hour
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.
(over Lesson 1-2)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. seven times eight
B. eight times seven
C. eight to the seventh power
D. seven to the eight power
Write 87 in words.
(over Lesson 1-2)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 2.6
B. 3.5
C. 14
D. 49
Find the square of 7.
(over Lesson 1-3)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 144
B. 124
C. 24
D. 6
Find the square of 12.
(over Lesson 1-3)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 3.6
B. 6.5
C. 159
D. 169
Find the square of 13.
(over Lesson 1-3)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 9
B. 40.5
C. 162
D. 6,561
(over Lesson 1-3)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 392
B. 98
C. 16
D. 14
(over Lesson 1-3)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. –128
B. 28
C. 96
D. 136
(over Lesson 1-3)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 44
B. 64
C. 120
D. 140
Evaluate the expression 7 ● 4 + (21 – 5).
(over Lesson 1-4)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 371
B. 307
C. 59
D. 43
Evaluate the expression (7 – 4)3 + 32.
(over Lesson 1-4)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 9
B. 11
C. 12
D. 27
(over Lesson 1-4)
Evaluate the expression 16 ÷ 4 + 63 ÷ 9.
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 30
B. 90
C. 3,000
D. 9,000
Evaluate the expression 3 × 103.
(over Lesson 1-4)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 12
B. 4
C. 2.25
D. 1.12
(over Lesson 1-4)
Evaluate the expression 144 ÷ (2)6.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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
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.
(over Lesson 1-4)
A. A
B. B
C. C
D. D
0% 0%0%0%
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
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)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 8
B. 6
C. 5
D. 7
A number is multiplied by 8. Then 5 is subtracted from the product. The result is 43. What is the number?
(over Lesson 1-5)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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
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?
(over Lesson 1-5)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 3, 9, 27, 81, 243, ...
B. 1, 8, 27, 64, 125, ...
C. 3, 6, 9, 12, 15, ...
D. 1, 4, 7, 10, 13, ...
Which sequence follows the rule 3n, where n represents the position of a term in the sequence?
(over Lesson 1-5)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 1
B. 2
C. 4
D. 8
(over Lesson 1-6)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 12
B. 22
C. 32
D. 42
Evaluate 7r – 3p for r = 7 and p = 9.
(over Lesson 1-6)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 96
B. 58
C. 47
D. 33
Evaluate (p – m) + 5(2n) for m = 2, n = 4, and p = 9.
(over Lesson 1-6)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 3
B. 1
C. 0.50
D. 0.25
(over Lesson 1-6)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 0.08
B. 1.33
C. 2.25
D. 6.75
(over Lesson 1-6)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 145e + 59p
B. 145p + 59e
C. (145 + 59) + pe
D. p(145 – 59) + e
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?
(over Lesson 1-6)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 82
B. 72
C. 32
D. 28
Solve the equation 27 + n = 55 mentally.
(over Lesson 1-7)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 3
B. 4
C. 5
D. 6
Solve the equation 9y = 45 mentally.
(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.
(over Lesson 1-7)
1. A
2. B
3. C
0%0%0%
A B C
A. 1.6
B. 2.8
C. 3.1
Name the number from the list {2.3, 3.5, 4.6} that is the solution of the equation 18m = 63.
(over Lesson 1-7)
1. A
2. B
3. C
A. 2.3
B. 3.5
C. 4.6
0%0%0%
A B C
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. $8.50
B. $8.75
C. $9.50
D. $9.75
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.
(over Lesson 1-7)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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?
(over Lesson 1-7)
A. 32 + t = 26
B. 32 ÷ t = 26
C. 26 – 32 = t
D. 26 + t = 32
A. A
B. B
C. C
D. D
0% 0%0%0%
A. 3 ● 4 + 8; 20
B. 3 + 3 ● 8; 27
C. 3 ● 4 + 3 ● 8; 36
D. 3 ● 8 + 4 ● 8; 56
Using the Distributive Property, write the expression 3(4 + 8) as an equivalent expression and then evaluate it.
(over Lesson 1-8)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 9 ● 4 – 8; 28
B. 9 ● 8 – 9 ● 4; 36
C. 9 ● 8 – 4 ● 8; 40
D. 9 ● 8 – 4; 68
Using the Distributive Property, write the expression 9(8 – 4) as an equivalent expression and then evaluate it.
(over Lesson 1-8)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. Associative Property of Addition
B. Commutative Property of Addition
C. Distributive Property of Addition
D. Identity Property of Addition
Name the property shown by the statement x + y = y + x.
(over Lesson 1-8)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. Associative Property of Multiplication
B. Commutative Property of Multiplication
C. Distributive Property of Multiplication
D. Identity Property of Multiplication
Name the property shown by the statement 31 × 1 = 31.
(over Lesson 1-8)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. Associative Property of Multiplication
B. Commutative Property of Multiplication
C. Distributive Property of Multiplication
D. Identity Property of Multiplication
Name the property shown by the statement (m × n) × p = m × (n × p).
(over Lesson 1-8)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. a × (c × b)
B. c × ( a × b)
C. (b × c) × a
D. (a × b) × c
Rewrite a × (b × c) using the Associative Property of Multiplication.
(over Lesson 1-8)
A. A
B. B
C. C
D. D
0% 0%0%0%
A. × 8; arithmetic
B. × 8; geometric
C. × 4; arithmetic
D. × 4; geometric
Describe the pattern in the sequence 2, 16, 128, 1,024, … and identify it as arithmetic or geometric.
(over Lesson 1-9)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. + 3.2; arithmetic
B. + 3.2; geometric
C. + 8.8; arithmetic
D. + 8.8; geometric
Describe the pattern in the sequence 2.8, 6, 9.2, 12.4, … and identify it as arithmetic or geometric.
(over Lesson 1-9)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 36, 12, 4
B. 216, 648, 1,944
C. 316, 948, 2,844
D. 324, 972, 2,916
Write the next three terms of the sequence 4, 12, 36, 108, … .
(over Lesson 1-9)
A. A
B. B
C. C
D. D
0% 0%0%0%
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
Write the next three terms of the sequence 2.1, 2.8, 3.5, 4.2, … .
(over Lesson 1-9)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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
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?
(over Lesson 1-9)
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 723.5
B. 819.2
C. 845.2
D. 901.1
Find the next term in the sequence 3.2, 12.8, 51.2, 204.8, … .
(over Lesson 1-9)
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