The Pet Problem: There are 280 animals signed up to be in the pet show. There are four times as many dogs as cats and there are twice as many birds as cats. How many of each animal signed up for the pet show?

Students generally used either 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.

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.