As part of an upcoming “TNIFHS” post, I wanted to include *one* example of what Christopher Danielson’s approach to a better shapes book might look like in a high school math class. [Update: Christopher’s *Which One Doesn’t Belong?* is available from Stenhouse; from Pembroke for Canadians.] But then I had some fun with this and created a few more. In each set, a reason can be given for each of the four options being the odd one out. I’ve done this type of thing with numbers and equations before. Worthwhile, but not what I’m going for here. Each set below is pictorial. Also, I went naked; I stripped the graphs of grid lines and ordered pairs. More noticing properties, less determining equations. Aside from graphs, where else in secondary mathematics might this fit? The last two images below are my attempts at answering this question.

Download the pdf.

Update: Mary Bourassa created a website.

Update (10/04/17):

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Wow. This is great. We are totally going to use these with our teachers. Should be some interesting conversations. The one initial concern I have is that some of these don’t neatly fit into a single course under Common Core (obviously not your concern). For example it would be interesting to have four lines where some have common slopes, common y-intercepts, common x-intercepts, etc.

Thanks for sharing.

Thanks Robert. Let me know how it goes. I did consider the single course thing. For example, linear and quadratic inequalities both appear in Math 11 here. But previously, linear inequalities were introduced in Math 10, quadratic inequalities in Math 11. Too lazy to look it up, I wondered if this was true in CCSSM (or, single course or not, whether it was more worthwhile to compare nothing but linear inequalities). So, I included an alternate version of this one in the pdf; I replaced y > (x – 2)^2 – 1 with x > 2. Is the absolute value function in the first set another concern? I tried your slope and x- and y-intercept idea but end up painting myself into a corner with the one distinguishing property restriction. A more forgiving question here (from the writing side) is “Which two of these are most alike?” These are much easier to create (e.g., y = 2x + 3, y = 2x – 3, y = -2x + 3, y = -2x – 3).

I consider WODB as a tool to work on the SMPs of reasoning, constructing arguments, and attend to precision. They are great as a formative assessment tool so that you can see what students pay attention to and the language that is used to describe.

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I love the purple algebra tile one. I will definitely be using it soon. Thinking about why top right doesn’t belong. These are quite creative.

Thanks Martin. Think factors/side lengths. There’s another algebra tile one in the pdf. Let me know how it goes.

I would like to use Shape 13 at the http://wodb.ca/index.html site for our PSESD August Math Newsletter problem of the month. May I have permission to do so? Thanks!

Absolutely!

Thank you!

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I love this site! I wanted to see if you knew or have seen of any graphic organizers that people are using to help incorporate this in their class. Thanks!

Hi Crystal. Thanks! I don’t know of any graphic organizers here. Can you tell me a bit more about what you’re looking for?

Searching #wodb on Twitter will help with how teachers are using this routine in their classrooms. I have always done this as a whole class discussion. I project the set of images directly on the whiteboard and then record students reasons (maybe some turn-and-talk first) around the borders of each of the four images. In classrooms without projectors, I’ve printed them and glued/taped them on chart paper. Again, I record student reasons around the border (or have students place–and explain–sticky notes).

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