A previous post expanded upon the possibility of using Fraction Talk images with(in) the structure of Which One Doesn’t Belong? The feedback from this amalgam has been overwhelmingly positive, and it got me thinking about how a teacher might go about composing similar prompts.

I am going to assume that teachers build WODB prompts in two ways. (Mainly because this is how I’ve approached them).

First are those who carefully anticipate student responses when choosing the four constituents, be them pictures, numbers, shapes, or Fraction Talk images. I have used this design strategy to target specific outcomes with the conversations.

Second are those who assemble the prompts with a theme in mind (be it geometric, algebraic, or otherwise), but do not target specific justifications. I have used this design strategy to target broad conversations about a specific subject.

Regardless of which side of the spectrum you fall on, the WODB classroom structure is so rich that it often sponsors surprise. That is, a WODB opens so much space for student action that some interesting tidbit almost always emerges no matter how much you anticipate and script student thinking.

Here are two Fraction Talk WODB prompts I threw together in the second fashion–with no specific conversation in mind. I am, however, interested in triggering conversations around fractions, the pictorial model, and any connections that emerge from the students.

Then I got to thinking, what if I could design a Fraction Talk WODB in the first fashion, but with a twist: I mandate the characteristics I am specifically looking for, and the students design the images. Here is what I came up with (and would love feedback on it):

Design a Fraction Talk WODB where:

• The Top-Right doesn’t belong because you cannot shade one-half with any combination of sections.
• The Top-Left doesn’t belong because there is only one triangle with an area of one-eighth.
• The Bottom-Right doesn’t belong because it is the only one with four identical sections.
• The Bottom-Left doesn’t belong because it is the only one that has a square and a rectangle with identical areas.

I feel as though this adds a significant twist to the WODB structure while still harnessing its approachable nature. It allows a space for teachers to initiate mathematically rich conversations yet target specific understandings all at once.

Let me know what images you and your students come up with to satisfy the constraints. Tweet @FractionTalks or submit via the site submission form.