Math Poetry Project: "Which one doesn't belong?" [Part 1b]

This is the second part of the activity I did using Christopher Danielson's new book project "Which one doesn't belong?" It's the math provocation/experience in a new math poetry project I'm developing. 

If you haven't already, make sure you read the first conversation I had with this 3/4 class here. You're gonna' want to because you will get to see me exert considerable energy helping the kids develop a concept of sameness and then nudging them on to similarity. This post is gravy compared the first 20 minutes of class!

I debated whether or not to summarize these conversations, but as I was transcribing my recordings I found the progression of ideas really interesting (including my own struggles to figure out what the kids were saying and what they meant!)  That's all to say: here's another transcript! Enjoy!

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Me: Let’s make a list. I think, from going around the groups, I think everyone had similar reasons but let’s just make sure. Who had the blue background? It’s the blue with green shapes. And it’s interesting that we had talked about color being a way to sort out differences but that’s not an option here, so you had to think about it a little differently.  If you didn’t have this card, I’m going to put it here on the board so you can get a sense of what we’re talking about.  Who wants to start?

Kid 1: Well, three of them have six sides and one of them had five.

Me: Great. Who else wants to share another way they sorted out one that didn’t belong.

Kid 2, pointing to the three hexagons: Well, these are all diagonalish, and the other one is not.

Me: So I’m going to write on the board “three are diagonalish’  Aweseome. Who else has something to share.

Kid 3: Three of them were made out of original shapes.

Me: Can you tell us about that? What do you mean?

Kid 3: Like pentagon, hexagon and the other one is made out of squares. 

Me: Oh, so looking at this (pointing to the fourth shape)…

Kid 3: That’s NOT a shape.

Me: So if I write…I’m going to bracket this because that doesn’t include three of them, you’re not excluding one. These and these you recognize as shapes.

Kid 3: Yeah, that’s made out of squares…and that isn’t.

Me: Oh I see!

Teacher: It’s not like an identifiable shape.

Me: Made out of squares….okay I’m going to un-bracket that, now I understand! Thank you! What else.

Kid 4: One has an odd number of sides, the others have an even number of sides.

[And typing this out, I realize that in this second half of class as I recorded their findings that I was writing down the three that make the inclusive group, not the shape that was excluded. I wonder why?]

Me: Who else had this picture? Does anyone else want to add some more?

Kid 5: One will never, no matter what you do, whether you add or take away parts, will never be a standard shape.  [We talked about this a little, but it really was just a reiteration of the earlier conversation. I left it in because this kid was so emphatic and expressive about his belief!]

Kid 6: Another one is that three have obtuse angles.

Me: And what do you mean by obtuse? [I asked this because I’m pretty sure most of the other kids didn’t know but it was also good to hear her thinking about this as well.]

Kid 6: What I mean is that on the paper, only the one with the squares have right angles that are kind of like perfect almost. The rest of them are more open and obtuse. 

Me: Do you guys understand this? We could do that with our hands really quick. If you have  a right angle [making one with my hands] they’re like all around us, they’re what makes our walls stand up straight, and so I think what she’s saying is that they’re actually wider than that [opening my hands up wider]. Does that make sense when you look at that picture? Now we have this one…

Kid 7: One of the rectangles is the only one with an outline.

Me: So the other three are…

Kid 7: solid.

Me: What’s another category for this one?

Kid 8: Three of them have right angles, one of them does not.

Me: What else?

Kid 9: These three are not like this one.

Me: Okay, I want to take a minute to talk about this because I think a couple groups mentioned this. There are three are not like the square, but when you look at the three? Can you see why they’re putting them into that group?

Kid 1: Well they’re all longer.

Me: Oh, longer is an interesting reason. What were you guys saying about it?

Kid 10: Well…

Me: Did you basically tell me, although it took me a long time to understand what you were saying, is that they are not squares. So that the thing they have in common is that they’re a negative. They are not squares.  Anything  else?

Kid 11: Okay, so, one has three sides and the others have 4.

Kid 12: One is red and the rest are blue. 

I am so impressed with your thinking! This was SO fun! Here’s what’s going to happen …next time we’re going to take this idea of sameness and difference and we’re going to write some poems [pdf of project description here].  And do you remember the c rods we used to make our faces? We’re also going to use those to design our poems.  

Math Poetry Project: "Which one doesn't belong?" [Part 1a]

I'm working informally but collaboratively with some math teacher friends to develop a math poetry project. My goal is to provide K-6 kids with authentic experiences with both mathematical ideas/thinking and poetry composition. I want the math activities to inspire rich and generative conversation. The poetry should extend those mathematical ideas and thinking into the larger world of interests, thoughts and actions of each individual child.

The first project is about comparison (the pdf of full lesson is here). Comparing one thing to another to find similarities and differences is at the heart of mathematical reasoning and equivalence relations. One thing can be described many ways depending on what you choose to focus on. In this first activity, we will focus on sets of shapes with many different and interesting properties. This activity uses the visual provocations from the new book Which one doesn't belong? by Christopher Danielson (you can download the free (for now) pdf here).

I did this activty with my daughter's grade 3/4 class today; 24 kids grouped into small groups of 4. Initially I thought I could tell the whole story in one post but after transcribing the rich (and quite fascinating) conversation we had around the first (warm-up) image, I realized I needed more than one post to tell the story.

Part 1b of this lesson is here.

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I love hearing what kids think and why. What was fascinating to me was that although I was clear that the goal was to find "the one that doesn't belong" out of the four shapes on the page this didn't seem to make much sense to them, at least initially. Their small group reasoning showed me that they were thinking of only one general property/attribute: the shape.

But the most fascinating thing of all was that they were, initially, only finding differences and very little in the way of sameness.  I know that was the question, but in fact, more than one group was convinced that NONE of the shapes were the same as each other. As one girl said: "They are all unique in some way." It seemed that by focusing on difference kept them from grouping the rest into a set. In this introductory portion of the lesson I spent considerable energy supporting them toward a concept of sameness and then a final little nudge toward similarity.

Like I said -- fascinating.

I gave all groups the same image for the first half of the activity. Here's how it played out:

After about 5-7 minutes of letting the small groups look at and talk about what they were noticing and letting them get started with figuring out "which one doesn't belong" I said:

Me:  So I have walked around the groups and it’s very interesting. There are a bunch of groups that are saying that none of those little shapes belongs in a group.  I will tell you, if there are four shapes, the question is which one doesn't belong to that group? And there will be more than one answer. We’re thinking of them as a whole group, not as individual shapes. There are different ways to look at this. It’s not just the shape. What other things tell you something about them?

Kid 1: The color.

Me: So what is one thing that three shapes have in common but one shape doesn't?  Let’s make a list of the kinds of groups of three you made. What was the first thing you noticed that three of those shapes had in common?

Kid 2: They’re all squares in different sizes and shapes.

Me: She’s saying three are squares and one is not? What’s another way you could group those shapes together?

Kid 3: All of them have four edges.

Me: So that’s a way of saying that they all belong, because they all have four edges. We’re going to start a different category over here. What else?

Kid 4: One of them is at a different angle.

Me: [Because a LOT of kids were calling the turned square a diamond I pressed the point a little further using their language.] I’m wondering what you think about that little blue shape. Is it a square or is it a diamond? Can you look at that blue diamond-y square. What would happen if you tried to put it right on top of that red square? 

Kid 5: It depends on the way you turn it.

Me: So your definition of a diamond is that it depends on the way it’s turned.  But what if you turn the page? Does it look like a square? Can it be both a square or a diamond?

Kid 6: Or a rhombus!

Me: Oh, hmmm. A rhombus (drawing one on the board). Who think this looks more like a diamond. [kids exclaim: yeah!] So if you can turn that little blue thing and it looks like a square when you turn it so the bottom edge is toward you, is it a square or a diamond do you think? [kids agree, it's a square]

Me: What other ways can you look at that picture and say ‘these things definitely belong together and this one doesn’t’?

Kid 7: So, the rectangle…all of these can make a square or a diamond, but this one [the rectangle] doesn't

Me: Okay. Is there any other property...

Teacher: Remember last year we were talking about attributes...?

Me: Yeah, the things we can use to describe something. We can describe them by their shape but how else can we describe them?

Kid: Color?

Me: So which one doesn't belong if we’re looking at color?

Kid 8: the little red one.

Me: Right now we have color and we have shape as the categories. Are there any other categories that helped you make your decision?

Kid 9: Um, size?

Me: Tell me more about that.

Kid 9: Three are small but one is huge.

Me: Any other way to think about this?

Kid 10: Well I already said that one of them was at a different angle. It will ALWAYS be at a different angle than the others b/c you cannot turn that shape without turning the whole paper!!!

Me: Got it! So we will say the word “position."  So we will say that ‘three are parallel to the edge of the paper’. Does that make sense to you? [class says yes]. Is there anything you want to add to this list?

Kid 7: I don’t think any of them belong together. Because they’re all different.  They all have something special about them.

Me: So you’re saying they’re all different from each other in some way. Can you give me some examples?

Kid 7: Well, one is red and all the others are blue. One is a different shape from all of them.

Me: Can you give me one example of how they’re all different, like how is that red square different from the blue one?  Compare them to each other? [Kid 7 starts moving counter clockwise around the page, comparing one shape to the next, the second shape to the third...]

Kid 7: This one is smaller than that one, and that one is angled differently…[fades off]

Me: And how does the angled differently one compare to the one at the bottom?  How many people understands her reasons? [lots of kids raise their hands]

At this point I knew they were at a good enough place to take this introductory experience and move on to  more challenging images. I need to listen to the audio to decide if I'll report on the second half of this class, but I know that this first 20-25 minutes supported the forward movement of their reasoning in the next section with new images. I definitely heard a lot more descriptive language, both formal and informal, and they seemed more certain in their analysis. Best of all, with some small exceptions, the kids' energy was really strong for the entire hour and they were really listening during our group discussions.

Next week I'm moving on to the poetry portion. You can look at the lesson plan here, but imagine writing poems around topics like:

Vanilla OR chocolate?
Endermen OR Slimes?
Circles AND Spirals

You get my drift? My hope is that our work in the shape comparison portion will inspire some really interesting writing. Cheers.

Part 1b of this lesson is here!