A Spatial Pattern Exploration Idea

…With lots of other ideas intertwined!

I love using counters with my math intervention students and I use them in a variety of ways. I have a bunch of different kinds of counters, organized in different ways and for different purposes in my classroom.

One day, I gave each of my three first graders a condiment cup with 7 round magnet counters in each. For this activity, I had all of the counters the same color and I pre-counted the collection. I said, “Go ahead and figure out how many counters you have.”

They each dumped their counters on the table. Each child approached the task differently. One of them counted them by ones very quickly and he lost track and started over, looking nervously at the other two kids as they were counting their collections. One of them grouped them in twos and stress-counted by ones, “One, two, three, four, five, six, seven.” The third child meticulously moved one counter to the other side of her counting surface, carefully saying one number word at a time.

Bullet Journal entry…helps me remember my seed ideas.

I asked the kids to verbalize how they counted their collections and then I asked them if there is a way that they could arrange them that kind of looks like dice or a domino so that we can all look at their collection and not have to count by ones to figure out the amount (see the illustration).

I love having kids do this because they’re making sense of the number and they are partitioning it in a spatial pattern that make sense to them. Then through the students talking about what they’re noticing in their own and in each other’s designs, they’re hopefully building onto their understanding of “seven”.

Child 1 said, “I made a 5 and a 2. It’s 7.”

Child 2 said, “I made a 6 and a 1. Well, I counted by 2s and I don’t have enough for another 2, so it’s 7.”

Child 3 said, “I made a 3 and a 4. Yup, it’s 7.”

So then I had this idea to have them flip their counters over because on this day, I used magnet counters that were colored on top and black on the other side. So they flipped their counters carefully (I should have started with them flipped to the magnet-side-up or used ones that are a magnet on both sides). I grabbed a magnetic board and I made a sound effect “thwaaaaannnnggg” and smacked a magnetic sheet over part of their design and with a certain amount of finesse, I was able to not reveal how many I took.

Well, the student I started with said, “HEY!”

I quickly realized that he was mad that I took some of his magnets. I didn’t expect him to get angry, but I had to go with it and think fast and I switched on my charm as I smiled really big and said, “How many did I take away?” He took a deep breath when he realized that this would be fun (phew!) and his shoulders dropped as he relaxed and his fingers came out.

He said, “Well, I had 5…” As he talked, he made 5 and 2 more on his fingers “…and I see 5 there. YOU TOOK TWO!”

“Yes!” I gave him his magnets back (and he proceeded to rearrange his 7 into a different pattern and talk about what he was noticing) as I quickly did the same with the other two children’s designs. I made sure I gave all three kids equal amounts of turns, rotating my way around the table. It’s important to the kids that things are fair.

We kept going on this activity for a few minutes and math talk was amazing. The kids were noticing the reciprocity of the facts like 3 + 4 = 4 + 3. They were using their fingers to represent. They sometimes counted on to figure out the missing addend. We talked about the different strategies they used, prompted by my observations and questioning.

My goal was to get them to talk about what they were noticing and to get them to build and own some understanding of “seven”. My hope is that they’ll start to do this kind of thinking and talking organically in their classroom or at home or even just in our group at first.

I’m trying really hard to make sure it’s the kids who do the noticing and the verbalizing as much as possible. It is so hard for me not to say what I notice because I’m so excited to watch the kids and how they arrange their chips…it fascinates me to watch kids approach the same exact amount of a manipulative in different ways. I’m constantly making connections in my mind and it’s my goal for the students that they make connections as they’re working every day in my intervention groups.

For the wrap-up, I asked, “What did you learn or notice about seven today?” I recorded their ideas on a group poster so that we could add to our knowledge of seven as we progress. I jotted their words and ideas as best I could into my notes, along with my observations within the lesson so I can use this knowledge to inform future lessons.

For this activity, we worked inside of finger range because that’s what my students needed that day. This activity works well with larger numbers, up to 20 I’d say. After 20, you might want to use a different manipulative like strips of ten and singles.

After I completed the activity, I jotted it in my bullet journal. I think it might make a good partner game? Maybe? It kind of reminded me of Splat! by Steve Wyborney…kind of like a build-your-own-splat? If you don’t know about Splat! you should check it out. 🙂

I’d love to hear your thoughts!

On another day, if I want to work on the verbal counting sequence and work on 1:1, I might have them get 16 or so counters, paying close attention to their verbal count and watching how they approach a 1:1 counting activity, but I suppose this would be another blog post!