math games class: 24 game and connect 4 dice

First grade

As a warm-up, the first grade played tic-tac-toe. This was to prepare them for the main game of they day: dice connect 4.

Dice Connect 4
Two players alternate occupying spaces on this grid:

The constraint is that, each turn, the player first throws two dice and then can only select a space in the column that corresponds to the sum. The winner is the first to get four in a row (horizontally, vertically, diagonally.) In our version, the winning spaces need to be a chain of neighbors, in the sense that each space has 8 neighbors.

Second and third grade

In both older grades, we played the 24 game. I saw this mentioned recently on Benjamin Leis's blog about his own math club (maybe just in passing here, I thought he had a more extensive post about the game elsewhere, too).

We played the "war" variation:
players: 4 (when necessary, three players can have a ghost player, or two players can modify each round slightly)
material: deck of playing cards with face cards removed
set-up: deal out all cards to the four players, cards stay in piles face down.
each round: players all turn over the top card in their pile and then race to get as close to 24 using the values of the four cards and standard arithmetic operations. In our version, we allowed addition, subtraction, multiplication, and division, but we didn't insist on using all four cards. When we played, someone would call out a value they could make and the number of cards, say "21 with 3 cards." The other players would then have a minute to try to improve that, either getting closer to 24 or making the same value with more cards.

The player who wins each round collects the four cards and puts them on the bottom of their pile, face down.

Ending the game: when any player runs out of cards, the game is over. The player with the most cards wins. Note: you can also keep going until only one player remains, but this wasn't suited for classroom play.

Playing at home: As mentioned above, you can play the game with 2-4 players. With two players, just have each player turn over their top two cards. With three, we used a dummy/ghost pile of cards to make sure each turn had four open cards. Another variation that is flexible is to keep all cards in one pile, turn over four each round, and then the player who is fastest or has the best result collects them. After the main pile is exhausted, the winner is the player who collected the most cards.

If no one else is available, this can also become a practice or puzzle session. Just turn over 4 cards and see how close you can get to 24. Write down your equations!