Category Archives: Addition and Subtraction

Crystal Capture

This weekend I made something fun and wanted to share it in case it provides fun for anyone else.

My daughter has a board game called Unicorn Glitterluck.

It’s super cute, but not the most engrossing game. She and I especially like the purple cloud crystals, so this weekend I started brainstorming a math game I could make for us to play together. I know number combinations is an important idea she’ll be working on in 1st grade, so I thought about how to build a game around that while also incorporating the crystals.

Introducing…Crystal Capture!

Knowing that certain totals have greater probabilities of appearing than others, I created a game board that takes advantage of this. Totals like 6, 7, and 8 get rolled fairly frequently, so those spaces only get 1 crystal each. Totals like 2, 3, 11, and 12, on the other hand, have less chance of being rolled, so I only put 1 space above each of these numbers, but that space has 3 crystals.

I mocked up a game board and we did a little play testing. I quickly learned a few things:

Play-Test

I originally thought we would play until the board was cleared. Everything was going so well until all we had left was the one space above 12. We spent a good 15 minutes rolling and re-rolling. We just couldn’t roll a 12!! That was getting boring fast which led me to introduce a special move when you roll a double. That at least gave us something to do while we waited to finally roll a 12.

That evening I made a fancier game board in Powerpoint and we played the game again this morning:

Since clearing the board can potentially take a long time, which sucks the life out of the game, I changed the end condition. Now, if all nine of the spaces above 6, 7, and 8 are empty, the game ends. Since these numbers get rolled more frequently, the game has a much greater chance of ending without dragging on too long.

I did keep the special move when you roll doubles though. This adds a little strategic element. When you roll a double, you can replenish the crystals in any one space on the board. Will you refill a space above 6, 7, or 8 to keep the game going just a little bit longer? Or will you replenish one of the three-crystal spaces in hopes of rolling that number and claiming the crystals for yourself?

All in all, my daughter and I had a good time playing the game, and I learned a lot about where she’s at in her thinking about number combinations. Some observations:

  • She is very comfortable using her fingers to find totals.
  • Even though she knows each hand has 5 fingers, she’ll still count all 5 fingers one-at-a-time about 75% of the time.
  • She is pretty comfortable with most of her doubles. She knows double 5 is 10, for example. She gets confused whether double 3 or double 4 is 8. We rarely rolled double 6, so I have no idea what she knows about that one.
  • In the context of this game at least, she is not thinking about counting on from the larger number…yet. She doesn’t have a repertoire of strategies to help her even if she did stop and analyze the two dice. If she sees 1 and 5, she’ll put 1 finger up on one hand and 5 on the other, then she’ll count all.
  • I did see hints of some combinations slowly sinking in. That’s one benefit to dice games like this. As students continue to roll the same combinations over and over, they’ll start to internalize them.

Several folks on Twitter expressed interest in the game, so I wanted to write up this post and share the materials in case anyone out there wants to play it with their own children or students.

You’ll have to scrounge up your own crystals to put in the spaces, but even if you don’t have fancy purple ones like we do, small objects like buttons, along with a little imagination, work just as well. Oh, and if you can get your hands on sparkly dice, that helps, too. My daughter loves the sparkly dice I found in a bag of dice I had lying around.

Have fun!

Decisions, Decisions

This week our Math Rocks cohort met for the fourth time. We had two full days together in July, and we had our first after school session two weeks ago. One of our aims this year is to create a community of practice around an instructional routine, specifically the number talks routine. We spent a full day building a shared understanding of number talks back in July. You can read about that here. We also debriefed a bit about them during our session two weeks ago.

This week we put the spotlight on number talks again. We actually broke the group up by grade levels to focus our conversations. Regina led our K-2 teachers while I led our 3-5 teachers. The purpose of today’s session was to think about the decisions we have to make as teachers as we record students’ strategies. How do you accurately capture what a student is saying while at the same time creating a representation that everyone else in the class can analyze and potentially learn from?

We started the session with a little noticing and wondering about various representations of 65 – 32:

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Very quickly someone brought up exactly what I was hoping for which is that some of the representations show similar strategies but in different ways. For example, the number line in the top left corner shows a strategy of counting back and so do the equations closer to the bottom right corner.

This discussion also led into another discussion about the constant difference strategy – what it is and how it works. It wasn’t exactly in my plans to go into detail about it this afternoon, but since my secondary goal for the day was to focus specifically on recording subtraction strategies, it seemed a worthwhile time investment.

After our discussions I shared the following two slides that I recreated from an amazing session I attended by Pam Harris back in May. (For the record, every session I attend with her is amazing.)

The first slide differentiates strategies from models. Basically, if you have students telling you their strategy is, “I did a number line,” and you’re cool with that, then you should read this slide closely:

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The second slide differentiates tools for building relationships from tools for computation. This slide is crucial because it shows that while we want students to use tools like a hundred chart to learn about navigating numbers within 100, the goal is to eventually draw out worthwhile strategies, such as jumping forward and/or backward by 10s and then 1s.

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The strategy on the right that shows 32 + 30 followed by 62 + 3 is totally the type of strategy students should eventually do symbolically after building relationships with a tool like the hundred chart.

After blowing their minds with those two slides, I led them in a number talk of 52 – 37. During my recording of their strategies, I stopped a lot to talk about why I chose to do what I did, to solicit their feedback, and even to make some changes on the fly based on our discussion.

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For example, in the top right corner of the board I initially used equations to represent a compensation strategy. Someone asked if this could be modeled on a number line because she thought it might make more sense, so I did just that in the top left corner. By the time we were done they were like, “Oh, hey! That ends up looking like a strip diagram!”

It was amusing that the first strategies they shared involved constant difference. They were so excited about learning how the strategy worked that they wanted to give it a try. I didn’t want to quash their excitement by telling them that the strategy tends to work better, especially for students, when you adjust the second number to a multiple of ten. I wanted to stay focused on my goals for the day. We’ll discuss the strategy more in a future session.

(Unless you’re in Math Rocks and you’re reading this! In which case, see if you can figure out why that’s the case and share it at our next meeting.)

After some great discussion about recording a variety of strategies, we watched Kristin Gray in action leading a number talk of 61 – 27.

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We talked about how she recorded the students’ strategies. We also talked about some really lovely teacher moves that I made sure to draw attention to.

We wrapped up our time together talking about what new ideas they learned that they wanted to try out with their students. I had asked one of the teachers to lead us in another number talk, but we ran out of time so I think I’m going to have her do that at the start of our next session together. Hopefully everyone will have had some intentional experiences with recording strategies between now and then to draw on during that number talk.

Oh, another thing we talked about at various points during the session was how to lead students in the direction of certain strategies. This gets into problem strings, which may or may not happen in number talks depending on whom you talk to. Regardless, here are some we came up with. Can you figure out what strategies they might be leading students to notice and think about?

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Play With Me

On Wednesday I had the chance to visit my first classroom this school year. Sadly, in my role as curriculum coordinator, I don’t get to do this nearly enough. So I relish opportunities like this. Even better than visiting, the teacher allowed me to play a math game with her class.

I had so much fun!

I wanted something simple and quick to get the kids engaged before moving on to another activity. I also wanted it to involve adding 3-digit numbers because her class is in the middle of a unit on that very topic. I also wanted to bring in some place value understanding and reasoning, which are very much related to adding multi-digit numbers.

Basically I brought two decks of cards – one had Care Bears on the back and the other had Spider-Man on the back. I wanted different backs to the cards so it would be easier to tell which cards were mine and which were my opponent’s in case we needed to reference them during or after the game. I also pulled out all of the 10s and face cards, with the exception of the aces. I kept those and we decided to use them as zeroes. I tell you this because if you ever want to play a game that involves digit cards, here is a great way to get some without having to painstakingly cut out cards to make your own sets. Decks of cards are cheap enough. Just use those.

The game was me vs. the class. The goal is to make two 3-digit numbers. Whoever has the greater sum wins. On my turn, I drew a card, and I had a choice of putting it blank spots that I used to create two 3-digit numbers. Once a digit was placed it couldn’t be moved. On the class’ turn, I drew the card for them, but I let them tell me where to place the digit.

My favorite part of the game was at the end when the kids started shouting out that they’d won without even finding the sum. Take a look and see why they got excited: (Just pretend I hadn’t written the sums yet. I took the picture after the game was over.)

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“You have a 9 and a 4 in the hundreds place. We have a 5 and a 9.”

“Interesting, and how does that tell you you’ve won?”

“Because the 9s are the same. And we have a 5 which is greater than 4. You should have put your 5 in the hundreds place.”

“I was hedging my bets and I lost.”

Such wonderful thinking from a 3rd grader! How often do students rush to calculate and find an answer to a problem? How amazing that these students were paying attention to the place value that matters most in these numbers – the hundreds – and then comparing the digits to determine who had a greater sum?

Since I was just the lead-in to the day’s activities we only got to play once, but I would have loved to play again. I would have liked to change it up a bit. I would still construct my number on the board, but then I would have allowed everyone to create their own number at their desk using the cards that I drew on their turn. At the end we would discuss who thinks they have the greatest sum and talk about their placement of digits.

Even though I didn’t get to play again, I’ll take the time I did have. It was the highlight of my week!