Using a Pattern Table To Solve Contextualized Proportion Problems

Students in a sixth-grade classroom we visited were celebrating a classmate's birthday and enjoying fun-sized bags of Peanut M&M's candies. We overheard them discussing their curiosity at the small number of blue M&M's each of them had received in their small bags. Because the students were occupied in an informal, party atmosphere, we were pleasantly surprised to hear one student, Rickea, comment on a related mathematical issue. She speculated that the teacher's class-sized bag would have relatively few blue M&M's, as well. What a wonderful teaching opportunity for ratios and proportions Rickea's casual comment posed! In this article, we describe (1) how we built a week-long, problem-based unit around Rickea's original proportion question and (2) the effectiveness of using problem solving to help Rickea and her classmates construct knowledge about ratio and proportional thinking.