Formative Assessment 68

Assessment Problem: 

Marna and Peter are two students who are standing one meter apart.  They start walking in a straight line one behind the other.  Marna is walking behind Peter carrying a calculator and CBR to measure the distance between them.  They walk for 7 seconds.  Interpret the graph at right.

Common Responses: 

Students frequently don’t realize that both Marna and Peter are moving at the same time and that the graph is displaying the relative distance between them over the 7 seconds.
Some think that Peter has stopped when the slope is 0.
Students who recognize that both Marna and Peter are moving realize that Peter is moving faster than Marna when the slope is positive, they are moving at the same rate when the slope is 0, and that Peter is moving slower than Marna when the slope is negative.

Mathematical Issues: 

Cartesian graphs are used to describe real world phenomena and convey complex mathematical meanings. The logic of interpreting a cartesian representation of relative motion becomes apparent through discussion .

Domain: 
Analysis of Change
Theme: 
Interpreting Graphs
Common Core Standards: 
Modeling
Research References: 
Radford, L., MIranda, I., & Guzman, J. (2008). Relative motion, graphs, and the heteroglossic transformation of meanings: A semiotic analysis. Paper presented at the Joint 32nd Conference of the International Group for the Psychology of Mathematics Education and the 30th North American Chapter.