5 Practices for Orchestrating Productive Mathematics Discussions

Chapter 2: Setting goals and selecting tasks

If I want my seventh graders to have a meaningful mathematical discussion I have to raise the level of thinking in the learning target. But it’s not over yet. I also need to select an appropriate task to support the learning goal.

As I wrote last week, I’m really enamored with this number puzzle.

Choose any number. Add the number that is 1 more than your original number. Add 11. Divide by 2. Subtract your original number. What is your answer? Do the puzzle again for other numbers. Why do you get the answers that you get? Will this always work?

This puzzle fits nicely with our 7^{th} grade expressions and equations unit and has the potential to be an anchor problem. Let’s look at how I can modify the learning target to raise the level of thinking and mathematical discussion.

Original target: Students will translate verbal phrases into an expression or equation.

I know my students can handle a more robust learning target. The number puzzle can certainly support it. This is still a work in progress, but here’s my revised target:

Revised target: After translating a verbal phrase into an equation, students will discover how grouping symbols and order of operations provide clarity.

When I gave the puzzle to the students, their first inclination was to simply follow the directions. Based on their work, their equation would look something like this:

This lesson now has a much better chance for meaningful mathematical discussion by focusing on grouping symbols, order of operations and how their use provides clarity. I could begin by saying, “Take out the equals sign and question mark. Make equivalent expressions using parentheses, brackets, fraction bars, etc.” We could then have a discussion as to which equations best represent the puzzle.

As I mentioned this is still a work in progress. If you have insights, please share.

Other bloggers discussing Chapter 2 can be found at the link below.