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

Domain: 
Analysis of Change
Theme: 
Graphing
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.