Lesson Plan: What Is Slope?

Lesson Objectives

  • Define slope
  • Understand slope as a measure of steepness
  • Interpret slope in real-world contexts

TEKS Standards

  • 8.4B: Graph proportional relationships, interpreting unit rate as slope.
  • 8.4C: Use data to determine rate of change or slope and y-intercept.
  • 8.5I: Write linear equations using various representations.

Warm-up Activity (5 minutes)

  1. Display these images showing steepness and incline. Ask students which stairs look easier to climb than others. What makes one set of stairs easier to climb than others?
    https://www.media4math.com/library/75324/asset-preview
  2. Mention that today's lesson will rely on an understanding of ratios. Provide a brief review of ratios:
    A ratio compares two quantities by division. For example, the ratio of 3 to 6 is 3/6 or 1/2. Use these definitions as needed:

Introduction (10 minutes)

Key Vocabulary

Concept Development

Show students the following video on slope. This video uses staircases as the context for introducing slope. It connects slopes to ratios and calculates slope as the rise over the run. This is a precursor to introducing the slope formula in subsequent lessons.

https://www.media4math.com/library/75378/asset-preview

Math Examples

Show the following examples for calculating the slope of different staircases using the values for the rist and the run.

https://www.media4math.com/library/75376/asset-preview

For each of these examples, point out to students that a calculation for the slope was made with a single step. Ask what assumptions are made about the calculated slope. (All steps have the same rise over run.)

Go back to each of the examples and calculate the total Rise and Run based on the measurements given for the individual stair. Point out to students that the slope calculations are identical. Ask them why this is the case. (The ratios are proportional.)

Use this set of images to have different students calculate the slopes for different staircases and compare their results:

https://www.media4math.com/library/75377/asset-preview

Ask students why their results are the same, even though different numbers were used in the slope calculations.

Review (5 minutes)

Review these key points:

  • Slope is a ratio.
  • Slope is the ratio of the change in vertical distance over the change in horizontal distance.
  • Slope is also called the rise over the run.
  • Slope is a measure of steepness.
  • You can compare the steepness of, for example, staircases, by measuring the slope.

Assessment (10 minutes)

Review the lesson with this quiz.

Quiz

  1. What is a ratio? 

     
  2. Is slope a ratio? 

     
  3. If so, how is slope a ratio? 

     
  4. What is the rise over the run? 

     
  5. In a staircase, for every 2 feet you move horizontally you rise 3 feet vertically. What is the slope of this staircase?

     

Answer Key

  1. A ratio compares two quantities by division.
  2. Yes, slope is a ratio.
  3. Slope is the ratio of the vertical change (rise) to the horizontal change (run).
  4. The rise is the vertical change, the run is the horizontal change. Slope = rise/run.
  5. With a rise of 3 feet for every 2 feet run, the slope is 3/2 or 1.5.

 

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