Recently in a Gr 5-6 classroom the teacher gave this question (see photo) to his students to solve in pairs. Some students had different numbers to work with. This is an example of a thinking type question found yearly on EQAO. These questions are the most difficult for students to solve and the most challenging for teachers to teach. They involve multiple steps and several calculations. Just knowing where to begin is the struggle for many students. It is so important to build confidence and risk-taking while developing the understanding of math concepts.

When I have students work through these types of problems I begin by asking them to solve the problem in a way that makes sense to them. This step is important because my explicit teaching begins after this and now they have an experience to refer to. I want the students to understand that there are many different ways to solve these problems. The way they choose to begin determines the type of calculation they use and their next steps.

This is an example of a problem where using proportional reasoning simplifies a complex process. Students who did not think of this are exposed to this kind of thinking through my connections to the student work generated, the questions I ask and the conversation I facilitate.

The next day’s lesson will be the same problem with different numbers and students will practice using proportional reasoning to arrive at their solutions. I will scaffold this for them by providing the steps I want them to follow. I would not do this without them having first experience solving the problem in their own way. This is an important connection between shared math and guided math.

Calculate the cost for 1 hour.

Calculate the cost for 1 day.

Calculate the cost for 1 work week.

- A key learning for me over the years is that the problem scenario is important to provide the context for the math to emerge, but we do not have to keep changing the context daily. Keep the problem the same and change the numbers as appropriate for each student. Build in opportunities for independent practice. This allows the student and teacher to focus on the mathematics and the appropriate differentiation for the students in front of them. Think about how this will simplify your planning and allow you to focus on observing and documenting student learning to inform your next steps. Think about how this will impact both student confidence and perseverance with solving problems!