## Friday, January 9, 2015

### 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.

................................................

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.

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!

1. Really interesting notes. I am tempted to try something similar w/ 1st and 2nd grade classes when I have them for an hour each to play math games or do explorations. I am afraid language deficiency will be an issue (I teach in a language that isn't my native one).

I don't fully understand what you are developing with the poetry writing, and I'm fascinated to see more examples. I wonder if it relates somehow to the idea of elegance in mathematical proof and analysis? Some of Paul Lockhart's comments really made an impression in this regard and I've had many interesting discussions asking kids their opinion of a mathematical argument: is it beautiful?

Almost always, they are stunned initially because they've never heard that question in a math class.

2. Thanks for your comments Joshua! I didn't put it here, but I was really clear w/ the kids that there was more than one answer to any one set of shapes. I think that working with ordinary language descriptions is really all you need to do in the primary grades -- the focus here I think is to simply get them talking. You might do one image as a big group to give them a chance to practice and a chance for you to see where they're starting from.

Also, where I'm going with the poetry project is detailed in the pdf I liked at the start and end of this post. Basically, the first math/poetry activity is about comparisons and you can read some examples of the kinds of poetry I was thinking about when you go to the doc. I'm thinking about the next math/poetry project being about composing/decomposing shapes, but it really depends on whether I can find a useful activity to provoke thinking on this topic.

1. re: the pdf in the second paragraph, I mean *linked* not liked!