Formative Assessment 66

Assessment Problem: 

Consider the starburst pattern on the right.  Using a graphing utility (such as grapher or a graphing calculator), recreate the starburst pattern.

Common Responses: 

Although most students will recognize that the pattern can be formed by graphing lines of the equation y=mx, finding the correct values for m to yield the picture is difficult.  Many students will select integer values of m, but that does not result in the graphic with evenly spaced lines.  Students need to select non-integer values at non-evenly spaced increments to form the starburst pattern.

Mathematical Issues: 

This activity helps students to think about slope. Using a graphing utility, students able to discover the relationship between algebraic representations of linear functions and the graphical representation. See also Module Connecting Graphs to Algebraic Representations

Analysis of Change
Common Core Standards: 
F-BF: Building Functions
Research References: 
Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. A. Romberg, E. Fennema & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 69-100). Hillsdale, NJ: Lawrence Erlbaum Associates Publishers.