Math Gr4 Ch12

Chapter 12Algebra and Graphing

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Chapter 12Algebra and Graphing

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Lesson 12-1 Negative Numbers

Lesson 12-2 Find Points on a Grid

Lesson 12-3 Graph Ordered Pairs

Lesson 12-4 Problem-Solving Strategy: Use Logical Reasoning

Lesson 12-5 Functions

Lesson 12-6 Graph Functions

Lesson 12-7 Problem-Solving Investigation: Choose a Strategy

1212Algebra and Graphing



Five-Minute Check (over Chapter 11)

Main Idea and Vocabulary

California Standards

Example 1

Example 2

Example 3

12-112-1 Negative Numbers



• I will understand and use negative numbers.

• positive number

• negative number



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


Write the number that represents the situation. Then show the number on a number line. Sara owes her mom $5.


When you owe money, it is a decrease. The number is –5.



Write the number that represents the situation.The temperature is 7 below zero.

A. –7

B. 7

C. 0

D. –8



Write the number that represents the situation. Then show the number on a number line. Grant earned $7 for shoveling Mr. Lincoln’s driveway.

When you earn money, it is an increase. The number is 7 or +7.



Write the number that represents the situation. Julia deposits $25 into her bank account.

A. 0

B. 25

C. –25

D. 30



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. Answer: So, C is +4.



Write the number of each letter on the number line.

A. –5; –4; –3

B. –3; –1; 4

C. –3; –2; –1

D. –3; 1; 4



Five-Minute Check (over Lesson 12-1)



Example 1

Example 2

12-212-2 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



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).


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.




What is located at point (1, 3)?

A. red house

B. blue house

C. tan house


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)?




What letter is located at (–4, 2)?

A. Q

B. R

C. S






Key Concept: Length of Line Segments

Example 1

Example 2

12-312-3 Graph Ordered Pairs



• I will graph ordered pairs and find the lengths of line segments on a coordinate grid.

• graph



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.




Graph point P at (–2, 4).


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



Choose which graph shows point A at (1, 4).

A. B.




C. D.




C.


Find the distance between (2, 2) and (2, 6).


The line segment is vertical. Subtract the y-coordinates.

length of segment= 6 – 2= 4

Answer: The length is 4 units.



Find the distance between (1, 5) and (1, 2).

A. 2 units

B. 3 units

C. 4 units

D. 5 units




Main Idea


Example 1: Problem-Solving Strategy

12-412-4 Problem-Solving Strategy: Use Logical Reasoning



• I will solve problems using logical reasoning.



Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.



Standard 4SDAP1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.


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?



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.



Plan

You can use logical reasoning and a table to solve the problem.



Solve

Answer: So, Jill must live on Pine Street.


• 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.


Check

Look back at the problem. The answer makes sense for the facts given in the problem.

So, the answer is correct.







Example 1

Example 2

Example 3

12-512-5 Functions


12-512-5 Functions

• I will complete function tables.

• function


12-512-5 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.


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.

12-512-5 Functions

4 × 2

6 × 2

8

12


12-512-5 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.

A. 4 × 2 = 8; 6 × 2 = 12

B. 5 × 4 = 25; 5 × 6 = 35

C. 5 × 4 = 20; 5 × 6 = 30

D. 4 × 4 = 16; 6 × 6 = 36


Use the rule y = 4x to complete a function table where the input is 4, 6, 8, 10.

12-512-5 Functions

The rule y = 4x means to multiply x by 4 to get y.


12-512-5 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?

A. 10, 20, 30, 40

B. 5, 10, 15, 20

C. 7, 9, 11, 13

D. 2, 4, 6, 8


Use the rule y = 2x + 5 to complete a function table where the input is 3, 5, 7.

12-512-5 Functions

First, multiply x by 2. Then, add 5 to the product to get y.


12-512-5 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?

A. 8, 16, 24

B. 9, 17, 25

C. 2, 4, 6

D. 3, 5, 7




Main Idea


Example 1

Example 2

12-612-6 Graph Functions

Graph Functions



• I will 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).


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.


Step 1 Write the ordered pairs. Then graph.


Step 2 Extend the pattern in the graph by drawing a straight line. The straight line will help you see the pattern.


Answer: So, 6 smoothies will cost $18.



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


Graph 10 points on the graph of the function y = 3x – 1.

Complete a table to find the ordered pairs.



Then graph the ordered pairs on a coordinate plane. Connect the points with a straight line.




Choose the correct chart of ordered pairs and graph that go with the equation y = 2x + 2.

A.




B.




C.




D.




D.




Main Idea


Example 1: Problem-Solving Investigation

12-712-7 Problem-Solving Investigation: Choose a Strategy



• I will solve problems by choosing the best strategy.



Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.



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.


AIDEN: I just got a new video game system. Games cost $20. Felice has the older version of the 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.



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.



Plan

To find the answer, organize the data to show the number of games and the total amount of money spent.



Solve


Answer: Since Aiden’s games cost more, he can only buy 3, whereas Felice can buy 4.


Check

Look back at the problem. Since 20 × 3 = 60 and 15 × 4 = 60, you know that the answer is correct.





Five-Minute Checks

Graph Functions


Lesson 12-1 (over Chapter 11)

Lesson 12-2 (over Lesson 12-1)







(over Chapter 11)

Find the area of the figure.

A. 60

B. 36

C. 56

D. 48

6

4

4

6


Write the number of letter A on the number line.

A. –2

B. 3

C. –3

D. –1

(over Lesson 12-1)


Write the number of letter B on the number line.

A. 3

B. 1

C. –2

D. 2

(over Lesson 12-1)


Write the number of letter C on the number line.

A. –4

B. 4

C. 2

D. 3

(over Lesson 12-1)


Write the ordered pair that names point A.

A. (2, –2)

B. (–1, 2)

C. (–2, 2)

D. (–2, –2)

(over Lesson 12-2)


Write the ordered pair that names point B.

A. (–5, –1)

B. (5, 1)

C. (–5, 2)

D. (–5, 1)

(over Lesson 12-2)


Write the ordered pair that names point C.

A. (–4, 3)

B. (4, –3)

C. (–4, –3)

D. (4, 3)

(over Lesson 12-2)


Find the length of the horizontal or vertical line segment formed by the following set of ordered pairs: (5, 4), (1, 4).

A. 6

B. 9

C. 4

D. 5

(over Lesson 12-3)


Find the length of the horizontal or vertical line segment formed by the following set of ordered pairs: (–3, 6), (–3, 0).

A. 3

B. 6

C. 9

D. 0

(over Lesson 12-3)


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

(over Lesson 12-4)


Use the rule to complete the function table.

A. 5, 6, 7

B. 9, 18, 27

C. 6, 9, 12

D. 5, 8, 11

(over Lesson 12-5)


Choose the set of points that belong on the graph of the function y = 2x.

A. (1, 2), (3, 6), (5, 8)

B. (1, 3), (2, 4), (3, 5)

C. (2, 1), (4, 2), (6, 3)

D. (1, 2), (2, 4), (3, 6)

(over Lesson 12-6)


Choose the set of points that belong on the graph of the function 2x = y.

A. (20, 10), (18, 9), (16, 8)

B. (10, 12), (9, 11), (8, 10)

C. (10, 20), (9, 18), (8, 16)

D. (10, 20), (18, 9), (8, 16)

(over Lesson 12-6)

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Math Gr4 Ch12