Explicit teaching must take place in the consolidation part of the shared math lesson when working with EQAO type thinking questions. To be most effective, teachers need to know the learning goal. As Dr Marian Small says the learning goal should be connected to understanding and less about doing. When we understand the important mathematics we want to highlight in a lesson, then our selection of student work, the questions we ask or any of the instructional moves we make push this learning forward. Does this mean that with this one lesson all students will understand or be at the same place? No, but now we have important information about our students to inform where we will go next (assessment for learning). I want students to experience solving a problem in a way that makes sense to them and from this information I determine how I will move towards greater precision in service of the important mathematics. With this problem (see below), I want students to understand that working with bigger units is easier because the numbers stay smaller. When we work with smaller numbers there is less room for calculation errors and the work is much more manageable. I want educators to understand that this learning goal focuses on unitizing a key concept of proportional reasoning. A focus on unitizing will help students move from additive to multiplicative thinking.

Recently, I gave the following problem to a Grade 6 class. This may look familiar as I adapted this problem from one I talked about in a previous post called, EQAO Thinking Type Questions.

*A pencil company packages 5 pencils in each pencil box. The company packages 350 pencils in one hour. The company operates 7 hours a day, 5 days a week. How many boxes of pencils does the company package in one week? Show your work and annotate your numbers.*

I explain to students that annotate means label. This forces them to think about what the numbers in the problem represent and brings meaning to the calculations they choose to use to solve the multi steps within problems like this. For students who do this for the first time this can be challenging so I do explicit teaching in the consolidation (the end of the day’s lesson) by facilitating a discussion and strategically using student work. I want the learning goal to emerge here and it will be prominently displayed the next day.

I want students to move from saying:

I divided 350 by 5

to explaining

I found the number of pencils packaged in an hour. Then I …..

This is a subtle shift but one that I believe will impact their problem solving skills, their confidence and their understanding of the multi steps within problems such as these EQAO Thinking type questions.