How might we use a Math Talk to help students connect fractions and a host of two-dimensional geometry concepts? How might this same Math Talk take learners into “a broad mathematical terrain of interconnected concepts, procedures, representations, and explanations”? (Kazemi & Hintz, 2014) How might an **Open Strategy Share** discussion structure overlaid on this Math Talk help students see a range of possibilities within this interconnected landscape? Let’s explore these ideas further…!

Consider the following Math Talk:

Take a few minutes (say, time yourself for 3 minutes) and sketch squares where ¼ of each square is shaded in a different way. One ground rule first… Let’s say that the following two depictions represent the same “way” to shade ¼ of a square. Instead of sketching different iterations of the same “type” of ¼…can you shade ¼ in a different way? How many different ways? Set your timer and see where your brain takes you…!

Where did your brain take you? How many different ways of shading ¼ of a square did you generate?

After working on this task individually for 2-3 minutes, learners share their thinking with their tablemates. In so doing, they consider and discuss *Did we all approach this task the same way?* and *What additional approaches did my peers use?* and *What additional ideas do we now have as a group because of discussing each other’s work?*

We have led this Math Talk with multiple groups of adult learners. Here is a sample of the collective work that has come out of this individual think time followed by small group discussion time:

What would you do with this work? What is the benefit of orchestrating an

Open Strategy ShareMath Talk over some of these examples?

Kazemi & Hintz (2014) suggest:

“Open strategy sharing is typically the first way to get mathematical discussions going in classrooms. It’s like having a good, basic recipe for a soup from which you can make all kinds of variations. Open strategy sharing allows you to nurture the norms needed for a productive math-talk community. And you can use this discussion structure to model how students should talk with one another.” (p. 17)

I particularly like how the Open Strategy Share discussion structure provides an initial access point for teachers looking to introduce or enhance math talk in their classrooms. Also, as Kazemi & Hintz discuss, these structures provide wonderful opportunities for students to learn *how to talk about mathematics*.

But, if this is the “basic recipe for soup,” what would your *variation* be? What would you choose to highlight or spin off from for a follow-up Math Talk at some later time? Where else *instructionally* might this Math Talk go?

Check out Part 2 of this blog post to see a sample follow-up Math Talk that utilizes the **Why? Let’s Justify** discussion structure.

(See Elham Kazemi & Allison Hintz’s book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions for more information on the

Open Strategy Sharediscussion structure.)

[…] [Part 1 of this blog post discussed the original Math Talk and an Open Strategy Share discussion structure.] […]

[…] another Math Talk from this session in the post Math Talk: 1/4 of a Square (Part 1). This post also explores the Open Strategy Share discussion […]

When I used to meet my geometry students on their registration day, I had them explore how many ways they could trisect a square.