One of our favorite math games for the past few months has been the “bears in the cave” game. It’s a great, 5-10 minute game that helps kids think through how numbers are formed.

The idea of the game is simple – you have a total number of “bears” (in our house, we use unifix cubes but you could use any manipulative – this could easily be played at a restaurant with sugar packets or creamers when you’re waiting for food). The kiddo covers his/her eyes while you put some bears “to sleep in the cave” (tuck a few of the cubes out of sight), leaving some remainder of bears “playing in the field”. The kiddo’s job is then to figure out, based on how many bears are playing, how many bears must be sleeping. Here are the three iterations the game has taken in our house so far:

*Version 1: Working to five*

We introduced this game with five bears and played a few rounds. Pretty quickly it became obvious to me that L was adept at the number pairs 0,5; 1,4; and 2,3 as making five. I gave her control of the bears for a few rounds so I had to do the guessing. Then we upped the ante…

*Version 2: Working to ten*

Same as above, but with ten bears. This provided much more of a challenge. We played this game in this form on and off for 2-3 months. Each session was about 10 minutes in duration. We spent some time at the beginning talking through ways to solve the problem, including using your fingers, counting on from the bears you could see, and using a chart we’d made of number pairs to ten (* see bottom of this post).

We took turns being in charge of the bears. I had planned on continuing this game indefinitely because it’s hands-on and concrete and she wasn’t automatic with all of the number pairs yet. But then, a few weeks ago, she asked to play again and added, “Can we add more bears?” Ok, that brings us to…

*Version 3: Working to twenty*

We added a second set of 10 unifix cubes, but these of a different color. We played the game the same way, except the questions consisted of an extra level.

Whereas before, she simply had to count on to 10, now she had to count on to 20. In doing so, she has to consider the unifix cubes as the same units, regardless of color (so, there are 11 bears showing here, meaning that 9 bears are asleep in the cave). But then I followed up by asking how many green bears were sleeping and how many orange bears are sleeping. Here she had to then subdivide the bears by color to answer (so here, 6 green bears and 3 orange bears are sleeping). I think this version because she has to move flexibly among the thinking.

I’m not sure what’s next, but I do like that she asks for this game and even asks for new challenges with it. To me, that seems like it’s building a solid mathematical foundation while also being fun!

* Our number chart of how to make tens:

We began with 10 unifix cubes each – she had 10 purple and I had 10 red. We then colored in how many purple cubes she had to make ten (so the first line is 0 reds and 10 purples). We then traded – she got one of my reds and I got one of her purples. We colored in the next line, showing 1 red and 9 purples. We continued through until she’d traded all of her cubes for all of mine, making the final row all reds. We ended by counting the numbers of reds and writing those numbers down the left-hand side of the chart and doing the same on the right-hand side for the purple cubes.

In the early iterations of the bears in the cave game version 2, I would show her how to count how many bears she saw, locate that number on the left-hand side, then trace across to find the corresponding right-hand side number. Over time, the pairs have become much more automatic.