Activities for Families

This can also be played, with essentially the same rules, by starting at 0 and adding your way up to the target. Once children learn to play this without writing anything down, it is a fun travel game.

One Pile

Set a starting total, say 20. Let your child choose whether to go first or second. During the first turn, a player chooses to subtract 1 or 2 from the current total. After the first turn, a player may subtract any number from 1 up to twice the number used on the last turn. The first person to reach 0 wins.

There are many alternative versions of this game. Some of them are:

• The first person to reach the target loses.
• Instead of using the range of 1 to 2, the initial range is from 1 to one less (or two less) than the target number.
• Practice adding, rather than subtracting, by starting at 0 and having the first person to reach the target win (or lose).
• The initial limit is one (or two) less than the target number, and instead of doubling the value used of the last turn, use the value of the last turn as the limit.
• The initial limit is one (or two) less than the target number, and instead of doubling the value used of the last turn, use the triple of the value of the last turn.

As you can see, there are lots of variations. Make up your own family rules if you are enjoying the game.

For the most part, these games are much harder to analyze than the versions of Nim that use a fixed set of choices for each move.

More Than One Pile

Yet another way to make new versions of this game is to use more than one number. Picture this version as having several piles of tokens (pebbles, bits of food). For example, you could have two piles with 12 tokens in one pile and 8 in the other. A standard rule to use is that you can take any number of tokens, but they must all be from one pile.

Alternative versions of this game are:

• There are more than two piles.
• You have the option of taking the same number of tokens from all the piles.
• You have the option of taking the same number of tokens from the piles you choose.
• You can only take tokens from the largest pile.

As you can imagine, there are even more versions of this game; however, perhaps this is more than enough for now!

First and foremost, playing math games should be fun, like any other game your family plays together!

Please let your child make poor plays (mistakes) without correction, and resist the urge to tell them the best ways to play. Bit by bit, your child will get better at the game, and they will learn so much more if you let them figure things out. There is no hurry.

If you see your child make a mistake, ask them to describe why they decided to do what they did. If your child is stuck and doesn’t know which play to make, ask them to describe the pros and cons of their choices, or ask them about how they solved a similar situation in the past. If your child doesn’t remember how to do a calculation, discuss with them the methods they know for figuring it out. These conversations are important for helping your child to develop mathematically.

Through math game play and math conversations, you are helping your child learn to enjoy math and develop important problem solving skills!