Assessment Problem:

A carpenter has a board 200 inches long and 12 inches wide. He makes 4 identical shelves and still has a piece of board 36 inches long leftover. How long is each shelf?

Common Responses:

There is not a common response, rather students tend to try multiple methods and generally become lost in the process.

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)