1. Variables, Function Patterns, and Graphs
Chapter 1
Variables, Function Patterns, and Graphs

2. Lesson 1-1 Variables, Patterns, and Graphs
Check Skills You’ll Need
(For help, go to the skills handbook page 75.)
Estimate to find whether each answer is reasonable. 1.
$154.38 2.
478.23 –
22.45
276.12
378.93
$481.93 4.
$316.24 3.
76.425 –
18.94
182.6
$267.48

3. Lesson 1-1 Variables, Patterns, and Graphs
Objective 1
Model relationships with variables
Objective 2
Model relationships with equations

4. Lesson 1-1 Variables, Patterns, and Graphs
Key Concepts
A variable is
An algebraic expression is
Examples:
An equation is
An open sentence is

5. Write an algebraic expression for each phrase.
Lesson 1-1 Variables, Patterns, and Graphs
Example 1
Write an algebraic expression for each phrase.
a. the sum of n and 8
b. six less than b

6. Define a variable and write an algebraic expression for each phrase.
Lesson 1-1 Variables, Patterns, and Graphs
Example 2
Define a variable and write an algebraic expression for each phrase.
a. “ten more than twice a number.”
b. “three times a number minus six.”

7. Lesson 1-1 Variables, Patterns, and Graphs
Example 3
Write an equation to show the total income from selling tickets to a school play for $5 each.

8. Write an equation for the data in the table.
Lesson 1-1 Variables, Patterns, and Graphs
Example 4
Write an equation for the data in the table.
Gallons
Miles

9. Lesson 1-1 Variables, Patterns, and Graphs
Lesson Quiz
Write an algebraic expression for each phrase.
1. 7 less than 9
2. the product of 8 and p
3. 4 more than twice c
Define variables and write an equation to model each situation.
4. The total cost is the number of sandwiches times $3.50.
5. The perimeter of a regular hexagon is 6 times the length of one side.

10. Lesson 1-1 Variables, Patterns, and Graphs
Homework
Pages 6 – 8;
1 – 24, 48 – 56

11. Lesson 1-2 Exponents and Order of Operations
Check Skills You’ll Need
(For help, go to the skills handbook page 755.)
Find the greatest common factor of each set of numbers.
1. 4 and and and 7
4. 8 and and and 20
Find the least common multiple of each set of numbers.
7. 4 and and and 7
10. 3 and and and 12

12. Lesson 1-2 Exponents and Order of Operations
Objective 1
Simplify and evaluate expressions and formulas
Objective 2
Simplify and evaluate expressions containing grouping symbols

13. Lesson 1-2 Exponents and Order of Operations
Key Concepts
To simplify a numerical expression,
You evaluate an algebraic expression by

14. Lesson 1-2 Exponents and Order of Operations
Key Concepts
An exponent is
A power has two parts, a ________ and an ___________.

15. Lesson 1-2 Exponents and Order of Operations
Example 1
Simplify – 14 • 3.

16. Lesson 1-2 Exponents and Order of Operations
Example 2
Evaluate 5x + 32 ÷ p for x = 2 and p = 3.

17. Lesson 1-2 Exponents and Order of Operations
Example 3
Find the total cost of a pair of jeans if the price is $32 and the sales tax rate is 8%.

18. Lesson 1-2 Exponents and Order of Operations
Example 4
Simplify 3(8 + 6) ÷ (42 – 10).

19. Lesson 1-2 Exponents and Order of Operations
Example 5
Evaluate each expression for x = 11 and z = 16.
a. (xz)2
b. xz2

20. Lesson 1-2 Exponents and Order of Operations
Example 6
Simplify 4[(2 • 9) + (15 ÷ 3)2].

21. Lesson 1-2 Exponents and Order of Operations
Lesson Quiz
Evaluate each expression.
4. 4x + 3y for x = 2 and y = 4
5. 2 • p2 + 3s for p = 3 and s = 11
6. xy2 + z for x = 3, y = 6 and z = 4
Simplify each expression.
– 4 • 3 + 6
2. 3(6 + 22) – 5
3. 2[(1 + 5)2 – (18 ÷ 3)]

22. Lesson 1-2 Exponents and Order of Operations
Homework
Pages 12 – 13
2 – 58 even, 63,73

23. Lesson 1-3 Exploring Real Numbers
Check Skills You’ll Need
(For help, go to the skills handbook page 762.)
Write each decimal as a fraction and each fraction
as a decimal. 2 5 3 8 2 3 5 9

24. Lesson 1-3 Exploring Real Numbers
Objective 1
Classify numbers
Objective 2
Compare Numbers

25. Lesson 1-3 Exploring Real Numbers
Key Concepts
Natural numbers: Counting numbers
{1, 2, 3, . . .}
Whole numbers: Natural numbers and zero
{0, 1, 2, 3, . . .}
Integers: Negative numbers, zero, positive numbers
{. . . , -2, -1, 0, 1, 2, . . .}

26. Lesson 1-3 Exploring Real Numbers
Key Concepts
Rational numbers: any number that can be written in the form , where a and b are integers and b ≠ 0.
A rational number in decimal form is either terminating, such as 3.27 or repeating, such as …, which can be written as
All integers are rational numbers because you can write any integer n as .

27. Lesson 1-3 Exploring Real Numbers
Key Concepts
Irrational numbers: any number that cannot be written in the form , where a and b are integers.
An irrational number in decimal form does not terminate or repeat.

28. Lesson 1-3 Exploring Real Numbers
Key Concepts
Together, rational numbers and irrational numbers form the set of real numbers.

29. Lesson 1-3 Exploring Real Numbers
Example 1
Name the set(s) of numbers to which each number belongs.
a. –17
b. 5.46
 21 43 c.
d. 89

30. Lesson 1-3 Exploring Real Numbers
Example 2
Which set of numbers is most reasonable for each situation?
a. the number of available tables at a restaurant
b. the length of a dollar bill
c. the outdoor temperature

31. Lesson 1-3 Exploring Real Numbers
Example 3
Determine whether the statement is true or false. If it is false, give a counterexample.
All negative numbers are integers.

32. Lesson 1-3 Exploring Real Numbers
Key Concepts
An inequality is a
When you compare two real numbers, only one of these can be true:
a < b a = b a > b
is less than is equal to is greater than
There are three other symbols that compare two values.
a ≤ b a ≠ b a ≥ b
is less than is not equal to is greater than
or equal to or equal to

33. Lesson 1-3 Exploring Real Numbers
Key Concepts
Two numbers that are the same distance from zero on a number line but lie in opposite directions are opposites.
The absolute value of a number is

34. Lesson 1-3 Exploring Real Numbers
Example 4
Write , , and , in order from least to greatest.

35. Lesson 1-3 Exploring Real Numbers
Example 5
Find each absolute value.
a. |–5|
b. |3.2|

36. Lesson 1-3 Exploring Real Numbers
Lesson Quiz
Name the set(s) of numbers to which each given number belongs.
1. –
Use <, =, or > to compare.
4. 5. _ _
6. Find 3 4 5 8 3 4 5 8

37. Lesson 1-3 Exploring Real Numbers
Homework
Page 20 – 21
2 – 62 even
Quiz 1-1 through 1-3

38. Lesson 1-4 Patterns and Functions
Check Skills You’ll Need
(For help, go to Lesson 1-1.)
Write an algebraic expression for each phrase.
1. 10 more than twice a number
2. a number divided by 4
3. 8 minus six times a number
4. twice a number subtracted from 7

39. Lesson 1-4 Patterns and Functions
Objective 1
Write a function rule
Objective 2
Understand relationships of quantities in a function

40. Lesson 1-4 Patterns and Functions
Key Concepts
A function is
A function rule such as C = p p,

41. Lesson 1-4 Patterns and Functions
Key Concepts
The value of the dependent variable depends on the value of the independent variable.
The possible values for the input, or independent variable, of a function are the __________ of the function.
The possible values of the output, or the dependent variable, of a function are the __________ of the function.

42. Lesson 1-4 Patterns and Functions
Example 1
Suppose you are buying apples from a vending machine. Use the table to write a function rule.
Number of Apples 1 2 3 4
Cost
$0.35
$0.70
$1.05
$1.40

43. Lesson 1-4 Patterns and Functions
Example 2
Suppose you want to find out how much gas a trip will take, in a car that uses one gallon of gas to go about 18 miles. What are the independent quantity and the dependent quantity for this situation?

44. Lesson 1-4 Patterns and Functions
Example 3
Ken burns 425 calories per hour when he bikes. He bikes from 3 to 7 hours each weekend. Identify the independent and dependent quantities for this situation and find reasonable domain and range values.

45. Lesson 1-4 Patterns and Functions
Lesson Quiz
Copy and complete each table. Then write a function rule for each relationship. 1.
Number of Lemons 1 2 3 4
Cups of Punch
1.5
4.5
Minutes in Phone Call 1 2 3 4
Cost of Call
$2.15
$2.30
$2.45 2.

46. Lesson 1-4 Patterns and Functions
Lesson Quiz
Identify the independent and dependent quantity in each situation and find reasonable domain and range values. 3.
Gerald rents 2 movies for each day of the 3-day holiday weekend. Each rental costs between $2.50 and $5. 4.
The weight of each kitten in the litter of 5 is between 10 and 12 ounces. Jill chooses a basket that can support the total weight of the litter.

47. Lesson 1-4 Patterns and Functions
Homework
Pages 29 – 30
1 – 10
Quiz 1-4

48. Graph each point on the same coordinate grid.
Lesson 1-5 Scatter Plots
Check Skills You’ll Need
(For help, go to Review Page 24.)
Graph each point on the same coordinate grid.
1. (6, 4) 2. (–5, 1) (0, –1)

49. Lesson 1-5 Scatter Plots
Objective
Analyze data using scatter plots

50. To make a scatter plot, plot the two groups of data as ordered pairs.
Lesson 1-5 Scatter Plots
Key Concepts
A scatter plot is
To make a scatter plot, plot the two groups of data as ordered pairs.
Most scatter plots are in the first quadrant of a coordinate plane, because the data are usually positive numbers.

51. Lesson 1-5 Scatter Plots
Key Concepts
You can use scatter plots to find trends in data. The scatter plots below show the four types of relationships two sets of data may have.

52. Lesson 1-5 Scatter Plots
Example 1
The table shows the number of hours worked and the amount of money each person earned. Make a scatter plot of the data.
Name
Hours worked
Amount earned
Janel 6
$25.00
Roscoe 12
$51.00
Victoria 11
$46.75
Alex 9
$38.25
Jordan 15
$63.75
Jennifer 10
$42.50

53. Lesson 1-5 Scatter Plots
Example 2
Use the scatter plot in your answer for Example 1 to answer the following question: Is there a positive correlation, negative correlation, or no correlation between the number of hours worked and the amount earned? Explain.

54. Lesson 1-5 Scatter Plots
Lesson Quiz
Use the graph for 1 – 6.
Name the coordinates of each point.
1. A 2. D 3. F 4. G
5. In which quadrant is point E? 6. Describe the trend.

55. Lesson 1-5 Scatter Plots
Homework
Practice 1 – 5

56. Lesson 1-6 Mean, Median, Mode, and Range
Check Skills You’ll Need
(For help, go to Lesson 1-2 and 1-3.)
Write the numbers in each group in order from least to greatest.
1. 2.4, 9.8, 3.6, 7.5, , 235, 98, 72, 58, 195
3. –12, 14, –3, –8, 7, , –3 , –4 , 6 , –2 , 4
Use mental math to simplify. 5 4 1 2 3 8

57. Lesson 1-6 Mean, Median, Mode, and Range
Objective 1
Find mean, median, mode, and range
Objective 2
Make and use stem-and-leaf plots

58. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
To understand a set of data, you need to organize and summarize the data using a measure of central tendency. Mean, median, and mode are all _____________________________.

59. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
The _______ is often referred to as the average.
Use the mean to describe the middle of a set of data that does not have an outlier.
An outlier is

60. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
The median is
For a set containing an even number of data items, the median is the mean of the two middle data values.
Use the median to describe the middle of a set of data that does have an outlier.

61. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
The mode is
It is possible for a set of data to have no mode, one mode, or more than one mode.
Use the mode when the data are nonnumeric or when choosing the most popular item.

62. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
The range of a set of data is
The range gives you a measure of the spread of the data.

63. Lesson 1-6 Mean, Median, Mode, and Range
Example 1
Find the mean, median, and mode of the data below. Determine which measure of central tendency best describes the data.
14   10   2   13   16   3   12   11

64. Lesson 1-6 Mean, Median, Mode, and Range
Example 2
Suppose your grades on three science exams are 82, 94, and 89. What grade do you need on your next exam to have an average of 90?

65. Lesson 1-6 Mean, Median, Mode, and Range
Example 3
Find the range and mean of each set of data. Use the range to compare the spread of the two sets of data.

66. Lesson 1-6 Mean, Median, Mode, and Range
Key Concepts
A stem-and-leaf plot is
To make a stem-and-leaf plot, separate each number into a stem and a leaf. 9 1 6 8 5 6 7 51

67. Lesson 1-6 Mean, Median, Mode, and Range
Example 4
Make a stem-and-leaf plot for the data.
75  64  53  51  61  75  77  57  68  65  63  59  76  63

68. Lesson 1-6 Mean, Median, Mode, and Range
Example 5
Find the mean of the city mileage and the mean of the highway mileage for 8 new cars.
4|2 means 42

69. Lesson 1-6 Mean, Median, Mode, and Range
Lesson Quiz
1. Find the mean, median, and mode. Which measure of central tendency best describes the data?
2. Make a stem-and-leaf plot for the data above.
3. Your test grades are 83, 94, 86, and 91. What grade do you need to earn on your next test to have an average of 90?

70. Lesson 1-6 Mean, Median, Mode, and Range
Homework
Pages 43-44
2 – 24 even
Quiz 1-5 & 1-6
Chapter 1 Test