Which One Doesn't Belong?: A Shapes Book

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A speech bubble out of the yellow shape appears that reads: This one is also the only even number… all of the others are odd!] A speech bubble out of the yellow shape over 2:3 appears that reads: Ok, so this one doesn’t work. Why else might 5 not belong? But I knew what the student meant, and so did the rest of the class. When I asked him to explain, he said a scalene triangle is a triangle with all three sides having different lengths. A scalene quadrilateral, therefore, is a quadrilateral with all four sides having different lengths. OK, so this one doesn't work. Why else might five not belong? What are you thinking? Ah, OK. Yes, lots of different answers. But some of you are thinking this as well. Under the starburst, a blue text box appears with text: Can you make a case for why each one doesn’t belong?] Speaker

Categorical data are expressed using characteristics. For example, to answer the question “What brand of phones do people use?” you would survey several people and their answers result in categorical data. How many students are on the roster for this class?” would produce numerical data that does not vary. There is only one value in the data set, so there is no variability. Which One Doesn't Belong? and other resources and I've always found the routine to be a good one for math learning and supporting conversations around math. I think it would also be very interesting to have the students write their own reflections. Did they find this activity interesting and why? What do they think they learned from this activity?

Below is more text: Then, ask your family, friends or your classmates about the next diagram…see if you can work together to come up with a reason for each collection.] At the conclusion of the unit, I would like to repeat the activity and see how their answers and explanations change. Will I see any growth in their vocabulary? Will they notice new differences based on the properties of the figures? Below the starbust, is a blue text box with text: Can you make a case for why each one doesn’t belong?] Oh, that's really nice. So, can I make a case now for why each one doesn't belong? Yes, we did that. The yellow round shape disappears. A blue text box appears at the top centre with text: Can you make a case for why each one doesn’t belong?]

These are examples non-statistical questions because they are answered by collecting data that does not vary: This bold-color shapes book is, as the author had hoped, “a resource that can make a meaningful contribution to geometry instruction” (p. 16) but can also reside in an elementary school library. It allows for meaningful conversations, unanswered questions, and deep dives into the subtle and complex similarities and differences between shapes. In the upper right corner of the screen, a green starburst appears with text: Which one doesn’t belong?

OK, so what about 11 then? Well, we worked out that it's odd, but so is three and five. They're both odd. What's a reason... Aha! I hear you. Makes sense, doesn’t it? But, is it mathematically correct? I don’t know. My students gave me some pretty good arguments justifying their reasoning! We decided we needed to do some research on the word scalene. Does it only apply to triangles? Mmm, what are you thinking? Mmm, so, this would be a good time to get out your paper and pencil and see if you could write down an idea for why each one of those dominoes you think...sorry, why one of those dominoes doesn't belong. And then...yes, I know. The NSW Department of Education is committed to employing the best and brightest teachers who can teach and make a difference in NSW public schools. Does the question you wrote fit best with the questions from number 1, 2, or 3? Explain your reasoning.