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Understand slope as the steepness of a line.

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Walking Up Flights of Stairs
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Real World Applications – Algebra I


Measuring Slope with Stairs

Student Exploration

Students will calculate the slope and compare the slopes of different flights of stairs.

What You Need:

  1. Two separate flights of stairs that are different
  2. A measuring tool (such as a ruler) that can measure height and length of each stair


  1. How are the two flights of stairs you chose the same? How are they different?
  2. For each flight of stairs, answer the following:
    1. What can you say about the steepness of each flight of stairs?
    2. What is the height of each stair? What is the length?
    3. Which measurement is the change of \begin{align*}y (\Delta y)\end{align*}? Which is the change of \begin{align*}x (\Delta x)\end{align*}? (Which is the horizontal change and which is the vertical change?)
    4. What’s the slope of each flight of stairs? Explain your process.
    5. Compare your calculations to your observations. Now, what can you say about the steepness of each flight of stairs?

Extension Investigation

  1. If \begin{align*}y = mx + b\end{align*}, what is the equation for each flight of stairs?

Connections to other CK-12 Subject Areas

  • Geometry (Pythagorean Theorem)
  • Algebra I (Linear Equations)
  • Earth Science (topography)

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