## Real World Applications – Algebra I

### Topic

Measuring Slope with Stairs

### Student Exploration

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

What You Need:

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

Process:

- How are the two flights of stairs you chose the same? How are they different?
- For each flight of stairs, answer the following:
- What can you say about the steepness of each flight of stairs?
- What is the height of each stair? What is the length?
- 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?)
- What’s the slope of each flight of stairs? Explain your process.
- Compare your calculations to your observations. Now, what can you say about the steepness of each flight of stairs?

### Extension Investigation

- 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)