Remember last week when my kiddos were my teachers? This week it kind of happened that way again–again without my real planning it that way. And you know, sometimes those are the best kinds of warm-ups–when they happen at just the right time as just the right response to something that happened in our classroom. Here we go. 🙂 (Oh, and I think somehow we ended up with a warm-up for every morning this week! Hot dog!)
We ended last week with the beginning of our new addition/subtraction unit, so I started with a 3-digit problem. And no, it wasn’t until we sat down to talk about the solution that I realized that the answer went up and over 1,000. Oops. But hey, if you can do those hard ones, then everything else is just cake, right? No one seemed to notice. And many of them got it right, which was nice and exciting. We talked about both compensation (making the problem easier by making 620 + 541) and splitting it by place value to add.
Ok…so Tuesday’s warm-up didn’t end up the way I thought it would. (Man is there a theme here lately?) I wrote this problem BEFORE school, knowing that it would tie into our place value work, as well as remind them of work we had done previously with this topic. And then I had some AMAZING professional development work in math with Kara Imm (an amazing teacher from Mathematics in the City out of NYC) and the rest of my 2nd grade team that afternoon.
(Sorry, she’s so amazing I have to stop and introduce you to her for a second. 🙂 )
During our planning we decided that we were working to launch a new investigation called The T-Shirt Factory, which is based in the context of a family who starts a t-shirt factory. Nicholas, the son in the story, works with rolls and loose shirts to organize and keep inventory, and the kiddos work alongside and within this context to solve similar problems to the ones he encounters.
Anyhow, after I had written this problem, we planned our lesson and I soon realized that my warm-up didn’t really fit in the pacing and sequence we’d decided upon. It wouldn’t make sense further on down the line if we discussed it on that day. So instead of fulling working it out and digging into how and why and what their strategies were, we just shared our initial thoughts. And then, like a happy accident, I figured another way I could use this debrief and the results I got to help plan my next lesson–just not in the way I thought I would originally.
When we met on the rug to talk about this problem, I started with questions. They were to listen for the number of 10s they had marked on their post-it and then stand in a certain place in the room. I called all combinations that kiddos could have said (9, 2, 5, 52, 29, 20, 500), and we ended up with two groups: 52 and 2. This was not surprising, based on two common understandings of what I mean when I say “tens” and how numbers are “inside” other numbers. Next, instead of sharing out how and why 52 was the correct answer or why one group only said 2, each group talked to a partner in their SAME group to share why they had decided upon 52. The focus was on communicating how they knew; this is something that is tricky for many of my friends to whom mathematics comes easily. The “2” group did the same thing within their ranks. Then, I paired them up with someone from the opposite group and they had to then work to convince their new partner why their number made more sense. And then we stopped, knowing we’d pick up that same conversation again on a later day during our t-shirt factory work.
Remember the theme of unexpected results? Here’s another example of that. Usually when it’s time to talk about the math warm-up, we meet together on the rug and talk about the problem. We don’t necessarily refer to specific post-its, these just serve as the kiddos’ opportunity to think about it prior to our conversation. On Wednesday I was out of the classroom during our normal debriefing time (because of more math conversations with Kara and the team), so I only had their morning work to look at. I gathered info about who knew what to do with these 3-digit numbers and who still showed that they needed to continue to practice (it was about 50/50 I’d say). It gave me an idea, then, for the next day’s problem, building on the solutions I saw given here with this one.
First of all, I have to giggle as I remember when Ja’Mia asked me today if this story was true. Of course, my friend’s son volunteered to help us with our math lesson! (wink, wink!). But really, I did see my friend’s son that day, so there’s something. 🙂
Ok, this one taught me something I had forgotten about 2nd graders: 1) they haven’t yet done a problem like this one where I’d asked them to analyze someone else’s thinking, and 2) they answered ONLY the question I ask.
See? The question (which I crossed off today during our conversation as we talked about what the problem really wanted us to think about) could simply be answered with a quick and simple “yes” and so most of them did that. They probably thought I had lost my mind by giving them a question like that!
I did have a couple who did get to the thinking I was looking for (but who knows how since I asked the question in the TOTAL wrong way!). For example, I wanted kiddos to notice that rather than just taking jumps by place value (200 + 70 + 5), the tiny jump of 3 made sense next because it got us to a 10, which is easier to work with. That resulting 570 also creates an easy double to add mentally (570 + 70, like 7 + 7), leaving a quick +2 to finish up. Here’s Khalani’s answer example:
The whole “my friend’s son” thing got me to ask my real son for some help and he was more than willing to do so (plus it meant that if he was helping me with my homework that he didn’t have to work on his own!). I gave him the problem 519 + 365 and asked him to solve it using a number line to model his thinking since that’s what we’ve been working on. He did not do it on purpose, but we realized after he finished that he had left out a part, and we actually decided that was a great thing to have happen; my kiddos might have more to talk about if they weren’t just reviewing their own work and saying “yep, it matches.” Having a different answer and having to figure out why it is different was a new kind of thinking for them.
We didn’t have time to completely finish the debrief, but we were able to talk about how he started, like why he put 519 first as well as why his first jump was just 1 rather than 300, which would have been a typical “place value” jump. They talked through what he had done and noticed that he misrecorded his +30 jump as only a +3, and that his answer seemed too small; most figured he had forgotten to add on the last 300.
This week’s warm-ups took on a new role. Our thinking was really deepened, and we dug into how and why in a way we haven’t done in a while. Plus it was great to be able to have 5 in a row!!
What do you think about our thinking? What had you tried with analyzing others’ mathematical thinking? Do you have any problems you can share with us? We’d love to hear from you!!