Lupe's Ramp Company – noticing and wondering

In this task, students use strategies of their choice to compare the steepnesses of three ramps. Before, during, and after the task, they make observations and ask questions.


Note: H and V stand for the horizontal and vertical lengths respectively.

I wonder if all three ramps have the same steepness.
I wonder if it matters whether the numbers represent feet, meters, or some other unit.
I notice that I can use pictures, tables, graphs, and calculations to explore the steepness of the ramps.
I notice that increasing H makes the ramp flatter.
i notice that increasing V makes the ramp steeper.
I wonder how it will look if I place smaller ramps inside larger ones.
I wonder what happens if I add (subtract) the same number to (from) H and V.
I wonder what happens if I multiply or divide H and V by the same number.
I wonder if I can combine V and H into a single number that describes the steepness.
I notice that V ÷ H is a unit rate.


adapted from Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity (p. 46–47) by Jerry Burkhart.
Copyright 2016, Prufrock Press:
 Waco, TX. Reproduced with permission.