Inspired by what I had read about a grade 6 math class at the Calgary Science School, I recently assigned my math class a “big problem”. I asked students, how much of the world’s oxygen need is met by Canada’s forests? All I gave them was the question. I didn’t give them any statistics and I didn’t break the problem into steps. Instead, I asked students to brainstorm what information they would need in order to find an answer and then had them do some online research.
Students quickly figured out that the world’s population is constantly changing, that there are all kinds of different estimates of how many trees are in a square kilometer of forest, the amount of oxygen produced per tree depends on the type of tree and the amount of forest in Canada is changing too… They realized that the problem was more complex than they initially thought and that every choice they made about estimating and rounding the data would have an impact on the accuracy of their final answer. This was, in fact, my hope when I assigned the problem.
Before doing this problem, whenever I asked students to reflect on the reasonableness of their answer, I rarely got more than, “I know my answer is reasonable because I checked.” Now, students know that a reasonable answer requires a lot more than accurate calculations and they know to comment on the data used in the calculations as well as choices they make when it comes to rounding and estimating.
This exercise also had some additional spin-off benefits, the most significant of which was the level of engagement in the class. Both during the research phase and in the actual calculations, all students stayed on-task throughout each 40-minute class period. There were a lot of calculations to do, and the calculations themselves were challenging – more challenging than what students would have found in the textbook problems. I told students that they could use calculators for any calculations that had numbers that were more than 5 digits long. However, I often found students doing long-hand calculations, including a group of girls doing long division of a 17-digit number. I have never seen textbook word problems elicit that level of effort or keep all the students in the class engaged.
Throughout the week during which we worked on this I did have a nagging concern that students weren’t getting enough practice and feedback with the basics of addition, subtraction, multiplication and division, but the test results later in the unit indicated that that wasn’t the case. In fact, because the students were actually interested in solving the “big problem”, they were more willing to ask for help and check their work than when they work on practice problems from the textbook. Rather than rushing through the work to move on to the next activity, students were willing to persist and revise in order to produce work that meant something.