I’ll be commenting here on several time-honored, popular card games that are great vehicles for practicing and sharpening your child’s math fact skills and number sense. You’ll have to look up the rules for play elsewhere; my remarks point out the mathematical value of playing these games.

In this blog, we’ll look at the card game *Ten-Twenty-Thirty*. [For how to play the game, go online to the following Youtube video: https://www.youtube.com/watch?v=ogDqB8aWsHw. Please note my comment [below the video] where the teacher in the video overlooks a combination of cards that would add to 20.]

*Ten-Twenty-Thirty* can be played solo, or cooperatively in pairs, or in small groups of 3 or 4. The object of the game is to have as few cards left as possible. There’s a lot of math at different levels in this game.

First, simple addition. We have add a set of three cards (always three!) to get a sum of 10 or 20 or 30. This is great practice for basic addition facts.

Second, there’s mental math. If the first two cards I’ve turned over are 6♣ and 5♥, then I’m doing mental math to find the sum (so far) is 11.

Third, there’s subtraction at this point as well. I’ve turned over a 6♣ and a 5♥ with a sum of 11, so now I’m hoping the next card will be 20 – 11 = a 9. So if I want to anticipate what the next card is, then I’m practicing some subtraction.

Fourth, there’s some implicit experiential algebra involved with anticipating what I’d like the next card to be. Let’s say the cards laid out (without regard to suit) are 5, 10, 8, 6, 3. What is the value of the next card I’ll turn over? I simply don’t know! So let’s call that next card *x*. So now the cards on the table are 5, 10, 8, 6, 3, *x*. Let’s examine the 3-card sets that might give a sum of 10 or 20 or 30:

• the two left-most cards, with the *x* on the right: I want 5 + 10 + *x* to equal 20.

5 + 10 + *x* = 20. How much is *x*? Here, *x *must equal 5.

• the left-most card with two right-most cards: I want 5 + 3 + *x* to equal 10.

5 + 3 + *x* = 10. How much is this *x*? Here, *x* must equal 2.

• the three right-most cards: I want the 6 + 3 + *x* to equal 10:

6 + 3 + *x* = 10. How much is this *x*? Here, *x* must equal 1 (the ace).

So, by anticipating what I’d like that next unknown card to be (the *x*), I’m doing some algebra. Note well: a player can do this mental math work without realizing the implicit algebra that’s taking place. But even for players who *aren’t*aware of this algebra connection, those players are still acquiring *experience* with algebra.

In summary, this game of *Ten-Twenty-Thirty* is great practice in several ways:

– players get lots of experience with simple addition (and some subtraction);

– players get a lot of practice with mental math; and

– players acquire solid experience in implicitly working with a variable (the unknown number of that next card) and solving for that variable.

P.S. A few years ago, a nationally known university professor with a PhD in math told me that he still occasionally picks up a deck of cards and plays *Ten-Twenty-Thirty*. Hooray for math!