Formative Assessment 76

Assessment Problem: 

Students are asked to interpret slope within the context of a real world situation.  Students are given a road sign from a street in Colorado that says, “7% grade ahead.”
Explain the meaning of the sign.

Common Responses: 

S1:"Like 100% might be vertical. Then 7% would be up from 0, which would be flat, horizontal."
S2: Maybe a comparison to like a normal-maybe it's like 7% upgrade or something, the angle.
S3: Maybe like a circle would be 360, or a circle would be 100. Then it would be 7% of that..
S4: I think it's the percent of the steepness of the mountain from like a flat surface.
Probably find an angle of steepness.

Mathematical Issues: 

Slope can represent real life situations such as the steepness of a hill. When dealing with physical situations of steepness, students rarely use proportional reasoning comparing the height of an object to the base of the object. Instead, students tend to focus on angles or a single attribute, such as the length of the ramp. Students are more likely to use the idea of rate or ratio when dealing with symbolic equations than in real world situations. Students are most successful calculating rate as a function of time, which in many ways is the most intuitive form of rate. If a student knows that they have traveled 200 miles in four hours they are able to identify the rate as 50 miles in one hour.

Analysis of Change
Understanding Slope
Common Core Standards: 
F-IF: Interpreting Functions
A-REI: Reasoning with Equations and Inequalities
Research References: 
Stump, S. L. (2001). High school precalculus students' understanding of slope as measure. School Science and Mathematics, 101(2), 81-89.