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Rise Run Triangles

This lesson helps students understand that through a graph and a right triangle that they are able to determine slope.  Students will determine rise over run to find slope.  Students also determine if slopes are positive or negative by the direction of the line.  Students also use fractions to show slope and show slope in the simplest fractions.

Weblink address (URL): 
Rise Run Triangles

Standards & Objectives

Learning objectives: 

Students will be able to:

  • Determine if the slope of a line is positive or negative
  • Express the slope of a line as a fraction
Essential and guiding questions: 
  • Which, if any, of the fractions did you have to simplify when you found the slope of a line? How can you avoid the need to simplify a fraction?
  • Suppose you have identified 3 slope triangles for a line to help you find the correct slope. What can you say about the relationship between these triangles?
  • Explain the difference between a line with positive slope and a line with negative slope.
  • Explain the difference between a line with slope 1/2 and a line with slope 2/1.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • Show students a given point on a coordinate grid and give them a value for the slope of a line. Ask them to draw a line that has that slope through the given point.
  • How does the slope triangle method apply to horizontal and vertical lines? What does the slope-triangle look like for a vertical line? What does the slope-triangle look like for a horizontal line? What problems arise, and how do they affect the slope?
  • How is slope formula consistent with the slope triangle method for finding the slope of a line? How does calculating y1 – y2 relate to the height of the slope triangle? How does calculating x1 – x2 relate to the length of the slope triangle?

 

Helpful Hints

Materials:

  • Counting for Slope Activity Sheet 
  • Colored pencils (optional)

References

Contributors: 
Donna Boatwright
Originator: 
Ayers Institute for Learning & Innovation