This activity comes from Fawn Nguyen, complete with write up and student handouts. The activity has students put 6 different staircases in order of steepness, first without measuring anything, relying on whatever strategies they come up with. So right off the bat, students need to define steepness. After coming up with an order, they share their order with a few other students, discuss their rankings and they can either stick with their original order or change their ranking. Finally they can measure the staircases with whatever tools they need, including rulers. Then the final step is for students to figure out the correct ranking and which calculations support their ranking, essentially discovering how to determine steepness.

This activity would be great after students did Unit 2: Three Views of a Function (Rule, Table, Graph) and Unit 3: Rate of Change and Starting Amount.