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Chapter 1Variables, Function Patterns, and Graphs
Check Skills You’ll Need
Lesson 1-1
Variables, Patterns, and GraphsEstimate to find whether each answer is reasonable.1. $154.38
22.45
276.12 + 28.98
$481.93
3. 76.425 18.94 182.6
+ 54.769
232.729
4. $316.24 – 48.76
$267.48
2. 478.23 – 199.30
378.93
(For help, go to the skills handbook page 75.)
Lesson 1-1
Variables, Patterns, and Graphs
Objective 1
• Model relationships with variables
Objective 2
• Model relationships with equations
Key Concepts
Lesson 1-1
Variables, Patterns, and Graphs
A variable is
An algebraic expression is
Examples:
An equation is
An open sentence is
Lesson 1-1
Variables, Patterns, and Graphs
Write an algebraic expression for each phrase.
a. the sum of n and 8
b. six less than b
Example 1
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.”
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.
Lesson 1-1
Variables, Patterns, and Graphs
Example 4 Write an equation for the data in the table.
Gallons
Miles
4 6 8 10
80 120 160 200
Lesson Quiz
Lesson 1-1
Variables, Patterns, and Graphs
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.
Homework
Lesson 1-1
Variables, Patterns, and Graphs
Pages 6 – 8;1 – 24, 48 – 56
Check Skills You’ll Need
Lesson 1-2
Exponents and Order of Operations
(For help, go to the skills handbook page 755.)
Find the greatest common factor of each set of numbers.
1. 4 and 8 2. 12 and 15 3. 5 and 7
7. 4 and 8 8. 12 and 15 9. 5 and 7
10. 3 and 9 11. 6 and 9 12. 9 and 12
4. 8 and 12 5. 14 and 21 6. 12 and 20
Find the least common multiple of each set of numbers.
Objective 1
• Simplify and evaluate expressions and formulas
Objective 2
• Simplify and evaluate expressions containing grouping symbols
Lesson 1-2
Exponents and Order of Operations
Key Concepts
Lesson 1-2
Exponents and Order of Operations
To simplify a numerical expression,
You evaluate an algebraic expression by
Key Concepts
Lesson 1-2
Exponents and Order of Operations
An exponent is
A power has two parts, a ________ and an ___________.
Lesson 1-2
Exponents and Order of Operations
Simplify 32 + 62 – 14 • 3.Example 1
Lesson 1-2
Exponents and Order of Operations
Example 2 Evaluate 5x + 32 ÷ p for x = 2 and p = 3.
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%.
Lesson 1-2
Exponents and Order of Operations
Example 4 Simplify 3(8 + 6) ÷ (42 – 10).
Lesson 1-2
Exponents and Order of Operations
Example 5 Evaluate each expression for x = 11 and z = 16.
a. (xz)2 b. xz2
Lesson 1-2
Exponents and Order of Operations
Example 6 Simplify 4[(2 • 9) + (15 ÷ 3)2].
Lesson Quiz
Lesson 1-2
Exponents and Order of Operations
Simplify each expression.
1. 50 – 4 • 3 + 6
2. 3(6 + 22) – 5
3. 2[(1 + 5)2 – (18 ÷ 3)]
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
Homework
Lesson 1-2
Exponents and Order of Operations
Pages 12 – 132 – 58 even, 63,73
Check Skills You’ll Need
Lesson 1-3
Exploring Real Numbers(For help, go to the skills handbook page 762.)
Write each decimal as a fraction and each fraction as a decimal.
1. 0.5 2. 0.05 3. 3.25 4. 0.325
5. 6. 7. 8. 325
38
23
59
Objective 1
• Classify numbers
Objective 2
• Compare Numbers
Lesson 1-3
Exploring Real Numbers
Lesson 1-3
Exploring Real NumbersKey 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, . . .}
Lesson 1-3
Exploring Real NumbersKey Concepts
Rational numbers: any number that can be written in the
form , where a and b are integers and b ≠ 0. b
a
A rational number in decimal form is either terminating, such as 3.27 or repeating, such as 8.232323…, which can be written as .
All integers are rational numbers because you can write any integer n as .
23.8
1
n
Lesson 1-3
Exploring Real NumbersKey Concepts
Irrational numbers: any number that cannot be written in
the form , where a and b are integers. b
a
An irrational number in decimal form does not terminate or repeat.
Together, rational numbers and irrational numbers form the set of real numbers.
Lesson 1-3
Exploring Real NumbersKey Concepts
Lesson 1-3
Exploring Real NumbersExample 1 Name the set(s) of numbers to which each
number belongs.
a. –17
b. 5.46
d. 89
21 43c.
Lesson 1-3
Exploring Real NumbersExample 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
Lesson 1-3
Exploring Real NumbersExample 3 Determine whether the statement is true or false.
If it is false, give a counterexample.
All negative numbers are integers.
Lesson 1-3
Exploring Real NumbersKey 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
Lesson 1-3
Exploring Real NumbersKey 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
Lesson 1-3
Exploring Real NumbersExample 4 Write , , and , in order from
least to greatest.
4
1
3
2
16
5
Lesson 1-3
Exploring Real NumbersExample 5 Find each absolute value.
a. |–5| b. |3.2|
Name the set(s) of numbers to which each given number belongs.
1. –7.2 2. 3. 11
Use <, =, or > to compare.
4. 5. _ _
6. Find
Lesson 1-3
Exploring Real NumbersLesson Quiz
34
58
34
58
13
13
9
Lesson 1-3
Exploring Real NumbersHomework
Page 20 – 212 – 62 even
Quiz 1-1 through 1-3
Lesson 1-4
Patterns and FunctionsCheck 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
Lesson 1-4
Patterns and Functions
Objective 1
• Write a function rule
Objective 2
• Understand relationships of quantities in a function
Lesson 1-4
Patterns and FunctionsKey Concepts
A function is
A function rule such as C = p + 0.06p,
Lesson 1-4
Patterns and FunctionsKey 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.
Lesson 1-4
Patterns and FunctionsExample 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
Lesson 1-4
Patterns and FunctionsExample 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?
Lesson 1-4
Patterns and FunctionsExample 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.
Lesson 1-4
Patterns and FunctionsLesson Quiz
Copy and complete each table. Then write a function rule for each relationship.
Number of Lemons 1 2 3 4
Cups of Punch 1.5 3 4.5
Minutes in Phone Call 1 2 3 4
Cost of Call $2.15 $2.30 $2.45
1.
2.
Lesson 1-4
Patterns and FunctionsLesson Quiz
Gerald rents 2 movies for each day of the 3-day holiday weekend. Each rental costs between $2.50 and $5.
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.
3.
4.
Identify the independent and dependent quantity in each situation and find reasonable domain and range values.
Lesson 1-4
Patterns and FunctionsHomework
Pages 29 – 30 1 – 10
Quiz 1-4
Check Skills You’ll Need
Lesson 1-5
Scatter Plots(For help, go to Review Page 24.)
Graph each point on the same coordinate grid.
1. (6, 4) 2. (–5, 1) 3. 4. (0, –1)
5,2
12
Lesson 1-5
Scatter Plots
Objective
• Analyze data using scatter plots
Key Concepts
Lesson 1-5
Scatter Plots
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.
Key Concepts
Lesson 1-5
Scatter Plots
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.
Lesson 1-5
Scatter PlotsExample 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
Lesson 1-5
Scatter PlotsExample 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.
Lesson Quiz
Lesson 1-5
Scatter Plots
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.
Homework
Lesson 1-5
Scatter Plots
Practice 1 – 5
Check Skills You’ll Need
Lesson 1-6
Mean, Median, Mode, and Range(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, 1.9 2. 144, 235, 98, 72, 58, 195
3. –12, 14, –3, –8, 7, 0 4. 2 , –3 , –4 , 6 , –2 , 4
Use mental math to simplify.
5. 6.3 + 4 + 5 + 6 + 75
5 + 6 + 8 + 94
12
23
38
14
58
12
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
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
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 _____________________________.
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
sum of the data items
Meantotal number of data items
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
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
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.
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
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.
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
The range of a set of data is
• The range gives you a measure of the spread of the data.
Lesson 1-6
Mean, Median, Mode, and RangeExample 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
Lesson 1-6
Mean, Median, Mode, and RangeExample 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?
Lesson 1-6
Mean, Median, Mode, and RangeExample 3 Find the range and mean of each set of data.
Use the range to compare the spread of the
two sets of data.
45 47 34 36 38 56 35 27 47 35
Key Concepts
Lesson 1-6
Mean, Median, Mode, and Range
A stem-and-leaf plot is
To make a stem-and-leaf plot, separate each number into a stem and a leaf.
51
9
1 6
5 6
8
7
Lesson 1-6
Mean, Median, Mode, and RangeExample 4 Make a stem-and-leaf plot for the data.
75 64 53 51 61 75 77 57 68 65 63 59 76 63
Lesson 1-6
Mean, Median, Mode, and RangeExample 5 Find the mean of the city mileage and the
mean of the highway mileage for 8 new cars.
4|2 means 42
Lesson Quiz
Lesson 1-6
Mean, Median, Mode, and Range1. Find the mean, median, and mode. Which measure of central
tendency best describes the data? 49 52 53 56 62 61 55 52
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?
Homework
Lesson 1-6
Mean, Median, Mode, and Range
Pages 43-442 – 24 even
Quiz 1-5 & 1-6
Chapter 1 Test