Yes, I am in fact still teaching math. We only have 4 more school days, and 2 of those are booked solid. This might be my last real math class of the year, but there’s still hope for Thursday!

One day last week, I saw this on Twitter:

I really wish I had not just saved the photo and could tell you where I found it. But honestly, it was probably around 10:00 at night and I’m surprised I even remember I copied the picture. I appear not to have retweeted it because I have really searched and can’t find the original source. If you know who it is, please tell me!

Today I had a long math class (a full 90 minutes, which happens once a week. We don’t always use the whole time, but I am always glad for the extra!) so I pulled this picture up on the Apple TV.

We talked about what we saw. Then I asked, “How can this child say that 3 hexagons is equal to 11 other shapes?” I was met with blank stares, which is exactly as I had hoped it would be. I sent them back to their tables with pattern blocks to see if they could figure out what this random stranger was talking about, and if s/he was actually right.

They played around for a few minutes, and then one child showed me this:

I asked him to explain. “Well, I saw that 2 of the red were the same as the yellow, so I just tried out the others and it worked.” Good old “Guess & Check”. As soon as he explained, other people at his table gave it a try. In the meantime, on the other side of the room, another child had discovered the same thing. When I talked to him, he added, “And now (X) is copying me!” The child next to him had made the same representation. “It might seem like copying, but I think X was just learning from you. And look what (X) is doing now.” I asked her to explain, “Well, I wondered if we could make more hexagons with other shapes, not just the red, triangles and the blues.” That inspired the other children in her group to start exploring more options. Could anything be done with the square, for example.

We all gathered on the carpet and I put up a few examples of the student’s work. “Now,” I told them, “I’d like to see if you can come up with balanced equations of your own. Maybe you’ll come up with something that doesn’t even use hexagons!” and away they went. Here are some of the things they came up with:

I have to say I was pretty happy with the results! There was a lot of deductive reasoning going on as students built one shape and then reasoned that they could build other similar shapes. It was interesting and I am sorry I don’t have more pictures to share! My favourite was a long row of rhombus’ on one side of the balance, and a long row of triangles on the other, all neatly stacked in a row that equalled the length of the rhombus row.

This is my other favourite:

She built her own balance! At first I thought she had too many blocks for no reason and was very close to questioning her when I realized it was a model of the balance.

I figured out, a few weeks too late, that we need more practice with shape names. But I was happy with the spatial reasoning I saw!

So, #SorryNotSorry kids! You may have thought you were finished with the year, but, alas, you were not! And stay tuned to find out what we are doing on Thursday!

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