Finding the Slope of Different Staircases Using Rise and Run

Introduction

In this lesson, students will research and explore the concept of the slope formula by collecting data and evaluating.

Task

The objective for each student is to explore throughout the school, the community, or even their homes and locate three different flights of stairs. Once they have chosen their three flights of stairs, the students will estimate which flight is the steepest before making any calculations. After each student has submitted their guess to the teacher the following day, they must then measure the slope of each staircase to test their hypothesis.

Process

The student process to prove or disprove their hypothesis will include:

  • Defining the slope in relation to the change in height versus the change in distance (horizontal), or the ratio of rise to run.
  • Measuring the rise and run of all three flights of stairs.
  • Calculating the slope of each flight of stairs
  • Using the slope calculations found to determine which staircase was the steepest.

Evaluation

Criteria

 1 2 3

Project

Participation
  • Student did not participate in this project.
  • Student only participated for a portion of the project.
  • Student participated and completed their project effectively.

Student

Calculations
  • The calculations for slope were incorrect and needed many adjustments.
  • The calculations for slope were nearly all correct and only needed minor adjustments.
  • The calculations for slope were all correct and did not require any adjustments.

Group

Hypothesis (*Bonus)
  • The student did not correctly guess which staircase was the steepest. +0
  • The student was very close for their guess of which staircase was the steepest. +0.5
  • The student guessed exactly which staircase was the steepest. +1

*Students will also be graded on a final research paper explaining what they have learned throughout this lesson.

Conclusion

At the end of this lesson, derived from the equation y = mx for a line that is passing through an origin and from the equation y = mx + b for a line intercepting through the vertical axis (b), students should be able to explain how they reached their different slope (m) calculations from the different points and objects they used in this lesson. The students will be evaluated on their participation and slope calculations. They will also be given the opportunity for bonus points if they can prove their hypothesis was correct.

Students must turn in a final paper describing how they came up with their slope calculations and what steps they took in determining why their hypothesis was proven or disproven.

Credits

Teacher Page

Grades 6-8

  • CCSS.Math.Content.7.G.A.1
    Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
  • CCSS.Math.Content.8.EE.B.6
    Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
  • CCSS.Math.Content.8.F.B.4
    Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.