Formative Assessment 125

Assessment Problem: 

Candy Bar Problem: There were three kinds of candy bars being sold at the concession stand during the Friday dance. There were 22 more Peanut bars sold than Wafer bars and there were 32 more Peanut Butter Bars sold than Wafer bars. There were 306 candy bars sold in all. How many of each kind of candy bar was sold?

Common Responses: 

Students generally used a guess and check strategy to choose the individual quantities and check the total.  They developed algorithmic strategies to hone their responses until they reached a solution.
Students using the unwind strategy began with the total and worked back toward individual quantities in the relationship.

Mathematical Issues: 

Students were hampered by computational errors, time constraints, and confusion about the difference between additive and multiplicative relationships. (See encyclopedia entry on Choosing Operations in Modeling) These two problems (used in conjunction) can be used to assess students’ ability to recognize multiplicative and additive relationships.

Modeling & Word Problems
Guess and check
Common Core Standards: 
7.EE: Expressions and Equations
Research References: 
Johanning, D. I. (2004). Supporting the development of algebraic thinking in middle school: A closer look at students’ informal strategies. Journal of Mathematical Behavior, 23, 371-388.