Assessment Problem:

Miss Dean’s moped went 48 miles on 3/8 gallon of gas. How many miles would the moped go on one gallon of gas?

Common Responses:

A typical response would be to multiply 48 by 3/8, which equals 18, rather than dividing by 3/8.

Mathematical Issues:

Students use superficial cues or irrelevant information to choose operations. (See encyclopedia entry Choosing Operations in Modeling) This problem can be used to investigate how students are choosing operations for word problems, how students conceive of operations, and student’s ability to connect operations to contextualized situations.

Domain:

Modeling & Word Problems

Theme:

Translating words to symbols

Common Core Standards:

6.EE Expressions and Equations

Research References:

Bell, A., Swan, M., & Taylor, G. (1981). Choice of operation in verbal problems with decimal numbers. Educational Studies in Mathematics, 12, 399-420. 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. Sowder, L. (1988). Children's solutions of story problems. The Journal of Mathematical Behavior, 7, 227-238. (Additional references cited on pages 227-228 of Sowder’s article)