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

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Last updated about 4 years ago
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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.

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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?

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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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.

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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.

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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.

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Problem 4 Got It?

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Problem 4 Got It?

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15.

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

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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.

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

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Error Analysis: Explain the student's mistake.

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

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

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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

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Review Lesson 2-7: Solve the proportion.

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Review Lesson 2-7: Solve the proportion.

Enter only a number.

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Review Lesson 2-7: Solve the proportion.

Enter only a number.

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Review Lesson 2-7: Solve the proportion.

Enter only a number.

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26.

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).

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

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

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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

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30.

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.

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31.

Reflection: Math Success

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Solve It! How do you know?