This week I’m starting to do a little math with my daughter everyday to dust off the cobwebs before 4th grade starts in September. One of the resources I’m using is the centers from the Illustrative Mathematics K-5 curriculum (Link to Kendall Hunt’s version of IM K-5 Math).

We kicked things off on Monday with a center called Can You Build It? (Link) One thing I like about the IM centers is that they often contain multiple stages within the same center, so you can choose just the right starting point within a given concept. Since my goal was to revisit arrays and the meaning of multiplication, we started with Stage 1. In the original IM version, one person builds an array secretly and then describes it to their partner and the partner tries to recreate it.

I changed this stage into a cooperative game that turned out to be really fun for my daughter. Here’s how it works:

- Draw a target area card. (I created a deck of cards that have the numbers 10 – 27 on them. This means there are 18 possible target areas, which feels like a good range. The numbers are also small enough that you won’t spend all your time counting out the tiles you need before making your array.)
- Each player secretly makes an array with that target area.
- Share your arrays. If you made the same array, you collectively earn 1 point. If you each made a different array, you collectively earn 2 points. (To clarify, a 2 by 6 array is the same as a 6 by 2 array.)
- Earn 5 points in as few rounds as possible.

If you don’t have square tiles handy, you could use a free app like Number Frames from the Math Learning Center (Link) which can be used in a browser or downloaded onto a tablet.

Or if you still want something hands-on, you could always use some crackers!

After a couple of days playing Stage 1 and revisiting how to build and describe arrays, we moved on to Stage 2. There are a couple of key differences here:

- Instead of secretly making only
*one*array, the goal now is to make*as many different arrays as possible*with the target area. - The game is competitive now. The player who makes more arrays earns 2 points and the other player earns 0. If both players make the same number of arrays, they both earn 1 point. The winner is the first to 5 points. (The original IM center used a slightly different scoring scheme. I opted for something similar to the game we played for Stage 1.)

My daughter immediately started bumping into ideas related to prime numbers. Here are some highlights from our conversation as we played for the first time:

1/ Daddy: Today our game is slightly different. This time when we draw a target area, our goal is to make as many different arrays as possible. If we get the same number of arrays, we each earn 1 point. If one of us makes more than the other, that person earns 2 points.

2/ Daddy: (draws card) Our first target area is 20.

(both make arrays in secret)

Daddy: I made a 2 by 10 and a 4 by 5. How about you?

Me: I made those, and I made a 1 by 20.

Daddy: Oh! I forgot that one!

Me: You have to remember you can *always* make a 1 by array!

3/ Daddy: (draws card) Okay, this time our target area is 13.

(both make arrays in secret)

Me: Ugh! I can only make one.

Daddy: Me, too. What did you make?

Me: 1 by 13.

Daddy: Hmm, I wonder why we could only make one array.

Me: Maybe because it’s an odd number.

4/ Daddy: (draws card) Now our target area is 11.

(both make arrays in secret)

Me: No! You can only make one again.

Daddy: Huh, is this an odd number, too?

Me: Yeah.

Daddy: That’s interesting.

5/ Daddy: (draws card) Ok, our target area is 10.

Me: I’m just going to write down the 1 by array. I don’t even need to make it.

(both make arrays in secret)

Daddy: What did you make?

Me: A 1 by 10 and a 2 by 5.

Daddy: Same here. Is 10 odd?

Me: No, it’s even.

Daddy: Hmm…

6/ Daddy: You made two really interesting observations today. Do you remember what they were?

Me: …if a number is odd you can probably only make one array?

Daddy: What else?

Me: …and you can always make a 1 by array for every number!

*Originally tweeted by Splash (@SplashSpeaks) on August 18, 2021.*

I love how this game has a simple premise – make arrays – but it creates opportunities for students to notice deeper ideas about numbers and multiplication. If you woudl like to try this game out with your own child or students, here’s a link to the center. (Link)

If you work in a grade level that introduces prime and composite numbers, I also recommend checking out 4th Grade Unit 1 of the IM curriculum for well-designed, ready-to-go lessons. (Link)

**[UPDATE]** Alyson Eaglen shared a great idea on Twitter. She said that instead of using cards with pre-printed target areas, she suggests rolling three 9-sided die and the sum is the target area. What a great way to bring in some bonus addition practice! If you don’t have 9-sided dice, you could always use five 6-sided dice or whatever combination of dice yields the range of target areas you’re interested in for the game. If you don’t have physical dice handy, Polypad’s free virtual manipulatives (Link) include a variety of dice under the Probability and Statistics menu.

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