In this week’s gift-themed Pre-Algebra Problem of the Week, students had to figure out an original cost given some percentages of the original cost. Specifically, they knew that five children contributed to pay for one big gift for their mother. Two of the (relatively broke) children paid $75 each. Of the remaining three, one paid 20% of the cost, one paid 25% of the cost, and the last paid 1/3 of the cost. Then the question was, how much did the whole thing cost? (A more realistic question might have been, “if the whole thing cost $692.31, did the last person to pay really contribute 1/3 of the cost like she planned to?” but it’s more algebraic reasoning this way).
Anyway, for me, the one reading the student solutions to the problem, the interesting challenge was to figure out what went wrong when students got answers other than $692.31. Were there conceptual struggles? Problems thinking up methods to get to the answer? Or problems executing the chosen paths? I always look for common wrong answers, because those usually show me conceptual struggles. This week, the common wrong answer was $681.82 (or sometimes just $680, or $681). I thought, “huh, I wonder why students are getting that answer…” Why do you think they might be? Read More→