# 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 *A**dvanced Common Core Math Explorations: Ratios, Proportions, and Similarity *(p. 46–47)* *by Jerry Burkhart.

Copyright 2016, Prufrock Press: Waco, TX. Reproduced with permission.