Puzzles allow children to use their hands and minds to explore the challenges.  Engaging in puzzles allows for an exploration about what information matters, how to break the solution down into smaller steps, and how to reason in favor of certain strategies over others. These are the skills that allow children to puzzle through problems and determine for themselves what makes sense.



This activity will challenge your children to explore how numbers are composed, by having them look at different ways of grouping them.  Your family may want to use actual pennies, draw diagrams, and use charts to keep track of your information.


When the pennies are put in groups of 2, there is one penny left over.

When they are put in groups of three, five and six there is also one penny left over.

But when they are put in groups of seven there are no pennies left over.

How many pennies could there be?


NIM – 7

Place your 7 counters in a group and decide who will go first.  (In the next game, the other player will go first.

>Each player takes turns to take away either one or two counters.

>The player who has the last turn loses.

>Keep playing until you figure out how to win, find a winning strategy.

Does it matter who has the first turn??



Mathematical games are often simple to play, but hard to master and Nim Games are no exception. You have already played NIM – 7, but there are many versions of NIM Games you can play.  You only need a handful of beans or coins to play.

BASIC IDEA: Players take turns taking a number of items from the piles available. The player who takes the last item loses.

Rules that can vary…….

  • Number of objects: Any number of objects can work! For younger children you might want to start with under 10 items, older students might want to extrapolate and think about who would win in a game with more objects than they can count.

  • Number of piles: You can start with a single pile or split the items into a few piles (not necessarily evenly split). In their turn, a player can only take items from a single pile.

  • Number of items you can take: You can have rules from “you have to take one item in your turn” to “you can take any amount of items from a single pile each turn”. In between, you can have a rule like “you can take 1 or 3 items from a single pile”. Passing on your turn or collecting zero items, however, is not an option.

  • Number of players: Nim Games are traditionally played between two players, but how do three or four players taking turns affect the game? Do your strategies change?