Splash Screen Chapter 12 Algebra and Graphing Click the mouse or press the space bar to continue. Chapter 12 Algebra and Graphing Click the mouse or press the space bar to continue.

Chapter Menu Lesson 12-1Lesson 12-1Negative Numbers Lesson 12-2Lesson 12-2Find Points on a Grid Lesson 12-3Lesson 12-3Graph Ordered Pairs Lesson 12-4Lesson 12-4Problem-Solving Strategy: Use Logical Reasoning Lesson 12-5Lesson 12-5Functions Lesson 12-6Lesson 12-6Graph Functions Lesson 12-7Lesson 12-7Problem-Solving Investigation: Choose a Strategy 12 Algebra and Graphing

Lesson 1 Menu Five-Minute Check (over Chapter 11) Main Idea and Vocabulary California Standards Example 1: Write Negative Numbers Example 2: Write Negative Numbers Example 3: Identify Numbers 12-1 Negative Numbers

Lesson 1 MI/Vocab 12-1 Negative Numbers I will understand and use negative numbers. positive number negative number

Lesson 1 Standard Negative Numbers Standard 4NS1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, and in “owing”).

Lesson 1 Ex1 Write the number that represents the situation. Sara owes her mom $ Negative Numbers When you owe money, it is a decrease. Answer: The number is –5.

Lesson 1 CYP Negative Numbers Write the number that represents the situation. The temperature is 7 below zero. A.–7 B.7 C.0 D.–8

Lesson 1 Ex Negative Numbers Write the number that represents the situation. Grant earned $7 for shoveling Mr. Lincoln’s driveway. When you earn money, it is an increase. Answer: The number is 7 or +7.

Lesson 1 CYP Negative Numbers Write the number that represents the situation. Julia deposits $25 into her bank account. A.0 B.25 C.–25 D.30

Lesson 1 Ex Negative Numbers Write the number of each letter on the number line. A is between –4 and –2. So, A is –3. B is between –2 and 0. So, B is –1. C is the same distance from zero as +4. So, C is +4. Answer: A is –3, B is –1, and C is +4.

Lesson 1 CYP Negative Numbers Write the number of each letter on the number line. A. A: –5; B: –4; C: –3 B. A: –3; B: –1; C: 4 C. A: –3; B: –2; C: –1 D. A: –3; B: 1; C: 4

End of Lesson 1

Lesson 2 Menu Five-Minute Check (over Lesson 12-1) Main Idea and Vocabulary California Standards Example 1: Find Ordered Pairs Example 2: Find Ordered Pairs 12-2 Find Points on a Grid

Lesson 2 MI/Vocab 12-2 Find Points on a Grid I will use ordered pairs to find and name points on a grid. coordinate plane origin x-axis y-axis ordered pair coordinates

Lesson 2 Standard 12-2 Find Points on a Grid Preparation for Standard 4MG2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line).

Lesson 2 Ex1 What is located at point (2, 5)? To find (2, 5), start at (0, 0). Move right 2 units. Then, move up 5 units. Answer: The ordered pair (2, 5) locates the post office Find Points on a Grid

Lesson 2 CYP Find Points on a Grid What is located at point (1, 3)? A.red house B.blue house C.tan house

Lesson 2 Ex2 To find (–3, 5), start at (0, 0). The –3 tells you to move 3 units to the left. The 5 tells you to move 5 units up. Answer: The ordered pair (–3, 5) locates the letter C. What letter is located at (–3, 5)? 12-2 Find Points on a Grid

Lesson 2 CYP Find Points on a Grid What letter is located at (–4, 2)? A.Q B.R C.S

End of Lesson 2

Lesson 3 Menu Five-Minute Check (over Lesson 12-2) Main Idea and Vocabulary California Standards Key Concept: Length of Line Segments Example 1: Graph Ordered Pairs Example 2: Length of Line Segments Example 3: Length of Line Segments 12-3 Graph Ordered Pairs

Lesson 3 MI/Vocab 12-3 Graph Ordered Pairs I will graph ordered pairs and find the lengths of line segments on a coordinate grid. graph

Lesson 3 Standard Graph Ordered Pairs Standard 4MG2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates. Standard 4MG2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates.

Lesson 3 Key Concept Graph Ordered Pairs

Lesson 3 Ex1 Graph point P at (–2, 4) Graph Ordered Pairs Step 1 Start at (0, 0). Step 2 The x-coordinate is –2. So, move 2 units to the left. Step 3 The y-coordinate is 4. So, move 4 units up. Step 4 Graph a point at (–2, 4). Label it P. P

Lesson 3 CYP Graph Ordered Pairs Choose which graph shows point A at (1, 4). A.B.

Lesson 3 CYP Graph Ordered Pairs C.D.

Lesson 3 CYP Graph Ordered Pairs Answer: C.

Lesson 3 Ex2 Find the distance between (2, 2) and (2, 6) Graph Ordered Pairs The line segment is vertical. Subtract the y-coordinates. 6 – 2 or 4 Answer: The length is 4 units.

Lesson 3 CYP Graph Ordered Pairs Find the distance between (1, 5) and (1, 2). A.2 units B.3 units C.4 units D.5 units

Lesson 3 Ex Graph Ordered Pairs Find the length of the line segment between (3, –2) and (1, –2). The line segment is horizontal. Subtract the x-coordinates. 3 – 1 or 2 Answer: The length is 2 units.

Lesson 3 CYP Graph Ordered Pairs Find the length of the line segment between (4, 1) and (7, 1). A.11 units B.3 units C.4 units D.7 units

End of Lesson 3

Lesson 4 Menu Five-Minute Check (over Lesson 12-3) Main Idea California Standards Example 1: Problem-Solving Strategy 12-4 Problem-Solving Strategy: Use Logical Reasoning

Lesson 4 MI/Vocab 12-4 Problem-Solving Strategy: Use Logical Reasoning I will solve problems using logical reasoning.

Lesson 4 Standard Problem-Solving Strategy: Use Logical Reasoning Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Lesson 4 Standard Problem-Solving Strategy: Use Logical Reasoning Standard 4SDAP1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.

Lesson 4 Ex1 Bella, Devan, Carl, and Jill live on Ash, Pine, Maple, and Oak Streets. Bella lives on Ash. Devan does not live on Pine. Carl lives on Maple. What street does Jill live on? 12-4 Problem-Solving Strategy: Use Logical Reasoning

Lesson 4 Ex1 Understand What facts do you know? The four students live on Ash, Pine, Maple, and Oak Streets. Bella lives on Ash Street. Devan does not live on Pine Street. Carl lives on Maple Street. What do you need to find? Find what street Jill lives on Problem-Solving Strategy: Use Logical Reasoning

Lesson 4 Ex1 Plan You can use logical reasoning and a table to solve the problem Problem-Solving Strategy: Use Logical Reasoning

Lesson 4 Ex1 Solve Answer: So, Jill must live on Pine Street Problem-Solving Strategy: Use Logical Reasoning Bella lives on Ash and Carl lives on Maple. So Jill cannot live on either of these streets. Devan does not live on Pine Street. He must live on Oak Street. xxx xxx xxx xxx

Lesson 4 Ex1 Check Look back at the problem. The answer makes sense for the facts given in the problem. So, the answer is correct Problem-Solving Strategy: Use Logical Reasoning

End of Lesson 4

Lesson 5 Menu Five-Minute Check (over Lesson 12-4) Main Idea and Vocabulary California Standards Example 1: Complete a Function Table Example 2: Complete a Function Table Example 3: Complete a Function Table 12-5 Functions

Lesson 5 MI/Vocab 12-5 Functions I will complete function tables.

Lesson 5 MI/Vocab 12-5 Functions function variable

Lesson 5 Standard Functions Standard 4AF1.5 Understand that an equation, such as y = 3x + 5, is a prescription for determining a second number when a first number is given.

Lesson 5 Ex1 Jake makes a $2 profit for each magazine subscription he sells. Complete the function table to show the profits earned for the number of subscriptions sold. Make a table to find how much money Jake will make for the number of subscriptions sold. Multiply each input by 2 to find each output Functions 4 × 2 6 ×

Lesson 5 CYP Functions Anita makes $5 for every yard she rakes leaves for. Complete the function table to show the profits earned for the number of yards raked.

Lesson 5 CYP Functions A. B.

Lesson 5 CYP Functions C. D.

Lesson 5 CYP Functions Answer: B.

4 × 416 Lesson 5 Ex2 Use the rule y = 4x to complete a function table where the input is 4, 6, 8, Functions The rule y = 4x means to multiply x by 4 to get y. 4 × × × 1040

Lesson 5 CYP Functions Use the rule y = 5x to complete a function table where the input is 2, 4, 6, 8. What is the output for each input?

Lesson 5 CYP Functions B. A.

Lesson 5 CYP Functions C. D.

Lesson 5 CYP Functions Answer: C.

Lesson 5 Ex3 Use the rule y = 2x + 5 to complete a function table where the input is 3, 5, Functions First, multiply x by 2. Then, add 5 to the product to get y

Lesson 5 CYP Functions Use the rule y = 4x + 1 to complete a function table where the input is 2, 4, 6. What is the output for each input?

Lesson 5 CYP Functions A. B. C. D.

End of Lesson 5

Lesson 6 Menu Five-Minute Check (over Lesson 12-5) Main Idea California Standards Example 1: Graph a Function Example 2: Graph a Function 12-6 Graph Functions

Lesson 6 MI/Vocab 12-6 Graph Functions I will graph functions.

Lesson 6 Standard 12-6 Graph Functions Standard 4MG2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line).

Lesson 6 Ex1 Each smoothie at the bakery costs $3. The function table shows how much it will cost if you buy 1, 2, 3, or 4 smoothies. Write the ordered pairs and graph the function y = 3x. Then use the graph to find how much 6 smoothies will cost Graph Functions Step 1 Write the ordered pairs. Then graph. (1, 3) (2, 6) (3, 9) (4, 12)

Lesson 6 Ex1 Step 2 Extend the pattern in the graph by drawing a straight line. The straight line will help you see the pattern Graph Functions Answer: So, 6 smoothies will cost $18.

Lesson 6 CYP Graph Functions Noah gets $11 a week for allowance. Find ordered pairs and graph y = 11x to find how much money Noah will have after 8 weeks. A.$70 B.$75 C.$80 D.$88

Lesson 6 Ex2 Graph 10 points on the graph of the function y = 3x – 1. Complete a table to find the ordered pairs Graph Functions

Lesson 6 Ex2 Then graph the ordered pairs on a coordinate plane. Connect the points with a straight line Graph Functions

Lesson 6 CYP Graph Functions Choose the correct chart and graph that represent the equation y = 2x + 2. A.

Lesson 6 CYP Graph Functions B.

Lesson 6 CYP Graph Functions C.

Lesson 6 CYP Graph Functions D.

Lesson 6 CYP Graph Functions Answer: D.

End of Lesson 6

Lesson 7 Menu Five-Minute Check (over Lesson 12-6) Main Idea California Standards Example 1: Problem-Solving Investigation 12-7 Problem-Solving Investigation: Choose a Strategy

Lesson 7 MI/Vocab 12-7 Problem-Solving Investigation: Choose a Strategy I will solve problems by choosing the best strategy.

Lesson 7 Standard Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Lesson 7 Standard Problem-Solving Investigation: Choose a Strategy Standard 4AF1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.

Lesson 7 Ex1 AIDEN: I have a video game system. Games cost $20. Felice has a different video game system. Her games cost $15. How many video games can we each buy if we each have $60? YOUR MISSION: Find out how many games each person can buy Problem-Solving Investigation: Choose a Strategy

Lesson 7 Ex1 Understand What facts do you know? Games for Aiden’s game system cost $20. Games for Felice’s game system cost $15. Each has $60 to spend on video games. What do you need to find? Find how many games each person can buy Problem-Solving Investigation: Choose a Strategy

Lesson 7 Ex1 Plan 12-7 Problem-Solving Investigation: Choose a Strategy To find the answer, organize the data in a table to show the number of games and the total amount of money spent.

Lesson 7 Ex1 Solve 12-7 Problem-Solving Investigation: Choose a Strategy Answer: Since Aiden’s games cost more, he can only buy 3, but Felice can buy 4.

Lesson 7 Ex1 Check 12-7 Problem-Solving Investigation: Choose a Strategy Look back at the problem. Since 20 × 3 = 60 and 15 × 4 = 60, you know that the answer is correct.

End of Lesson 7

12 Algebra and Graphing 12 Algebra and Graphing CR Menu Five-Minute Checks Math Tool Chest Image Bank Graph Functions

12 Algebra and Graphing IB Instructions To use the images that are on the following four 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.

12 Algebra and Graphing IB 1

12 Algebra and Graphing IB 2

12 Algebra and Graphing IB 3

12 Algebra and Graphing IB 4

12 Algebra and Graphing 12 Algebra and Graphing 5Min Menu Lesson 12-1Lesson 12-1(over Chapter 11) Lesson 12-2Lesson 12-2(over Lesson 12-1) Lesson 12-3Lesson 12-3(over Lesson 12-2) Lesson 12-4Lesson 12-4(over Lesson 12-3) Lesson 12-5Lesson 12-5(over Lesson 12-4) Lesson 12-6Lesson 12-6(over Lesson 12-5) Lesson 12-7Lesson 12-7(over Lesson 12-6)

12 Algebra and Graphing 5Min 1-1 (over Chapter 11) Find the area of the figure. A.60 square units B.36 square units C.56 square units D.68 square units

12 Algebra and Graphing 5Min 2-1 Write the number of letter A on the number line. A.–2 B.3 C.–3 D.–1 (over Lesson 12-1)

12 Algebra and Graphing 5Min 2-2 Write the number of letter B on the number line. A.3 B.1 C.–2 D.2 (over Lesson 12-1)

12 Algebra and Graphing 5Min 2-3 Write the number of letter C on the number line. A.–4 B.4 C.2 D.3 (over Lesson 12-1)

12 Algebra and Graphing 5Min 3-1 Write the ordered pair that names point A. A.(2, –2) B.(–1, 2) C.(–2, 2) D.(–2, –2) (over Lesson 12-2)

12 Algebra and Graphing 5Min 3-2 Write the ordered pair that names point B. A.(–5, –1) B.(5, 1) C.(–5, 2) D.(–5, 1) (over Lesson 12-2)

12 Algebra and Graphing 5Min 3-3 Write the ordered pair that names point C. A.(–4, 3) B.(4, –3) C.(–4, –3) D.(4, 3) (over Lesson 12-2)

12 Algebra and Graphing 5Min 4-1 (over Lesson 12-3) Graph and label A(4, 3) on a grid. A.B.

12 Algebra and Graphing 5Min 4-1 (over Lesson 12-3) C.D.

12 Algebra and Graphing 5Min 4-1 (over Lesson 12-3) Answer: A.

12 Algebra and Graphing 5Min 4-2 (over Lesson 12-3) Graph and label Q(–3, 3) on a grid. A.B.

12 Algebra and Graphing 5Min 4-2 (over Lesson 12-3) C.D.

12 Algebra and Graphing 5Min 4-2 (over Lesson 12-3) Answer: A.

12 Algebra and Graphing 5Min 4-3 (over Lesson 12-3) Find the length of the horizontal or vertical line segment formed by (5, 4) and (1, 4). A.6 units B.9 units C.4 units D.5 units

12 Algebra and Graphing 5Min 4-4 (over Lesson 12-3) Find the length of the horizontal or vertical line segment formed by (–3, 6) and (–3, 0). A.3 units B.6 units C.9 units D.0 units

12 Algebra and Graphing 5Min 5-1 (over Lesson 12-4) Hugo has horses and ducks on his farm. He has 3 times as many horses as he does ducks. Together, the animals have 14 legs. How many horses and ducks does Hugo have? A.1 horse, 3 ducks B.2 horses, 3 ducks C.1 horse, 5 ducks D.3 horses, 1 duck

12 Algebra and Graphing 5Min 6-1 Use the rule and function table to find the missing outputs. A.5, 6, 7 B.9, 18, 27 C.6, 9, 12 D.5, 8, 11 (over Lesson 12-5)

12 Algebra and Graphing 5Min 7-1 Choose the set of points that belong on the graph of the function y = 2x. (over Lesson 12-6) A.B.

12 Algebra and Graphing 5Min 7-1 (over Lesson 12-6) C.D.

12 Algebra and Graphing 5Min 7-1 (over Lesson 12-6) Answer: B.

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