Formative Assessment 127

Assessment Problem: 

372 people are working in a large store. There are 4 times as many stock people as checkers, and 18 more checkers than managers. How many stock people are in the company? How many checkers? How many managers?

Common Responses: 

1) Example of “algebraic” solution:
M + S + C = 372
4C = S
M +18 = C
(C – 18) + 4C + C = 372
=>6C -18 = 372
=>6C = 390
=>C = 65
4(65) = S
=>260 = S
M + 18 = 65
=>M = 47
(This problem could be solved arithmetically with a guess and check method)
2) Example of “arithmetic” solution:
F = 120 + 30 = 150
B = 150 / 2 = 75
(Guess and check would also serve as a arithmetic solution strategy for this problem)
Example of “algebraic” solution:
120 + B + F = 345
2B = F
F – 30 = 120
120 + B + 2B = 345
=>3B = 225
=>B = 75
 

Mathematical Issues: 

When solving word problems, some students automatically apply algebraic methods that are unnecessarily cumbersome. Other students refuse to use algebraic methods (relying solely on arithmetic calculations) because they do not see the utility of using algebra. These problems help assess student’s ability to flexibly apply arithmetic and algebraic solution strategies.

Domain: 
Modeling & Word Problems
Theme: 
Algebraic Solutions
Common Core Standards: 
6.EE Expressions and Equations
Research References: 
Khng, K. H., & Lee, K. (2009). Inhibiting interference from prior knowledge: Arithmetic intrusions in algebra word problem solving. Learning and Individual Differences, 19, 161-268. MacGregor, M., & Stacey, K. (1996). Using Algebra to Solve Problems: Selecting,Symbolising, and Integrating Information. Paper presented at the 19th Annual Mathematics Education Research Group of Australasia Conference. MacGregor, M., & Stacey, K. (1998). Cognitive models underlying algebraic and non-algebraic solution to unequal partition problems Mathematics Education Research Journal 10(2), 46-60. Reed (1999). Word Problems Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems.Journal of Mathematical Behavior, 18(2), 149-167. Van Dooren, W., Verschaffel, L., & Onghena, P. (2003). Pre-service Teacher's Preferred Strategies for Solving Arithmetic and Algebra