Algebra 1 5-1 Complete Lesson: Rate of Change and Slope

5 (2 ratings)

by Matthew Richardson

| 31 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

1

2

1

10 pts

Solve It! The table shows the horizontal and vertical distances from the base of the mountain at several poles along the path of a ski lift. The poles are connected by a cable. Between which two poles is the cable's path the steepest?

Pole A

Pole B

Pole C

Pole D

2

10 pts

Solve It! How do you know?

3

3

5 pts

Problem 1 Got It?

A

B

4

4

10 pts

Problem 2 Got It?

A

B

C

D

5

5

10 pts

Problem 2 Got It?

A

B

C

D

6

6

5 pts

Problem 2 Got It?

A

B

7

10 pts

Problem 3 Got It? What is the slope of the line through the points (1, 3) and (4, -1)?

Enter only a number in fraction form.

8

10 pts

Problem 3 Got It? Reasoning: Plot the points (1, 3) and (4, -1) from the previous item and draw a line through them. Include relevant graph detail: label axes, indicate scale on both axes, add arrows to the ends of lines and axes.

9

10 pts

Problem 3 Got It? Reasoning: Does the slope of the line you drew in the previous item match the slope you calculated in the item before that? Explain.

10

10

10 pts

Problem 4 Got It?

A

B

C

D

11

11

10 pts

Problem 4 Got It?

A

B

C

D

12

12

5 pts

A

B

13

13

10 pts

A

B

C

D

14

14

10 pts

A

B

C

D

15

10 pts

Vocabulary: What characteristic of a graph represents rate of change?

The x-intercept

The slope

The y-intercept

16

10 pts

Open-Ended: Give an example of a real-world situation that you can model with a horizontal line. What is the rate of change for the situation? Explain.

17

18

17

10 pts

Error Analysis: A student calculated the slope of the line shown to be 2. What is the correct slope?

2

-2

1/2

-1/2

18

10 pts

Error Analysis: Explain the student's mistake.

19

10 pts

Review Lesson 4-7: Identify the second, fourth, and tenth terms of the sequence.

5

7

9

19

21

20

10 pts

Review Lesson 4-7: Identify the second, fourth, and tenth terms of the sequence.

-5

0

1

7

13

49

21

10 pts

Review Lesson 3-8: Use the sets below to build each union or intersection on the right of elements on the left.

- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- { }

- A ∩ B
- A ∩ C
- B ⋃ C

22

10 pts

Review Lesson 2-7: Solve the proportion.

13

3.3

6.8

7.5

23

10 pts

Review Lesson 2-7: Solve the proportion.

Enter only a number.

24

10 pts

Review Lesson 2-7: Solve the proportion.

Enter only a number.

25

10 pts

Review Lesson 2-7: Solve the proportion.

Enter only a number.

26

10 pts

Vocabulary Review: Use the terms on the left to complete the sentences on the right.

- always
- sometimes
- never
- division
- multiplication
- different
- the same

- A rate is __?__ a ratio.
- A ratio is __?__ a rate.
- A rate compares two quantities by __?__.
- A rate compares quantities in __?__ unit(s).

27

10 pts

Use Your Vocabulary: How does the slope of a road affect a person's driving?

28

10 pts

Use Your Vocabulary: What kind of ski slope would a beginning skier use.

29

29

10 pts

Concept Summary: Slopes of Lines Identify the type of slope shown by the line in each graph.

- negative slope
- positive slope
- slope of 0
- undefined slope

- Graph A
- Graph B
- Graph C
- Graph D

30

100 pts

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

31

10 pts

Reflection: Math Success

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