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

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 – 199.30 22.45 276.12 378.93 + 28.98 $481.93 4. $316.24 3. 76.425 – 48.76 18.94 182.6 $267.48 + 54.769 232.729

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

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

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

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.”

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.

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 4 6 8 10 80 120 160 200

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.

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

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 8 2. 12 and 15 3. 5 and 7 4. 8 and 12 5. 14 and 21 6. 12 and 20 Find the least common multiple of each set of numbers. 7. 4 and 8 8. 12 and 15 9. 5 and 7 10. 3 and 9 11. 6 and 9 12. 9 and 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

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

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

Lesson 1-2 Exponents and Order of Operations Example 1 Simplify 32 + 62 – 14 • 3.

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 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. 1. 50 – 4 • 3 + 6 2. 3(6 + 22) – 5 3. 2[(1 + 5)2 – (18 ÷ 3)]

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

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. 0.5 2. 0.05 3. 3.25 4. 0.325 5. 6. 7. 8. 3 2 5 3 8 2 3 5 9

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

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, . . .}

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 8.232323…, which can be written as . All integers are rational numbers because you can write any integer n as .

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.

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

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

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

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.

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

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

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

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

Lesson 1-3 Exploring Real Numbers Lesson Quiz 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 3 4 5 8 3 4 5 8

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

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

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 Functions Key Concepts A function is A function rule such as C = p + 0.06p,

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.

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

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?

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.

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.

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.

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

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) 3. 4. (0, –1)

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

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.

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.

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

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.

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.

Lesson 1-5 Scatter Plots Homework Practice 1 – 5

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, 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 + 7 5 5 + 6 + 8 + 9 4 1 2 3 8

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

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 _____________________________.

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

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.

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.

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.

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

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?

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. 45 47 34 36 38 56 35 27 47 35

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

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

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

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? 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?

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