Formative Assessment 73

Assessment Problem: 

The Smith family's whole holiday is shown on the graph at right. The vertical axis shows the distance (in kilometers) away from home and the horizontal axis shows the time (in days) since the start of their trip.
1) During which days did the Smith family travel fastest? How can you tell?
2) They stayed with friends for a few days. Which days?
3) On average, how fast (measured in kilometers per day) did the Smith family travel to get to their destination?

Common Responses: 

Correct Answers:
i) Day 10 because they traveled 600K that day, more than any other OR because the line is steepest that day
ii) Days 7, 8, and 9 when they did not travel anywhere
iii) 1200 K / 10 days = 120K/day  OR they might add up each day individually (getting 1200K) and divide by the number of days (10) to get 120K/day.
Common Incorrect Responses:
i) Days 1 & 2 because they are the steepest (student sees a steep upslope and does not see a steep downslope).
ii) Days 3, 4, 5, 6 because they are the flattest (student doesn’t count the horizontal line).
iii) Student cannot determine an average from the graph.

Mathematical Issues: 

Students may struggle first in interpreting this graph as an example of rate of change. They may also struggle with question iii, determining a rate of change from the graph.

Analysis of Change
Rate of Change
Learning Progressions: 
Linear Equations
Common Core Standards: 
F-IF: Interpreting Functions
Research References: 
Herbert, S., & Pierce, R. (2008). An ‘Emergent Model’ for Rate of Change. International Journal of Computers for Mathematical Learning, 13(3), 231-249. P. 140