shopping cart

Dice Shapes

Age range: 8-14
Estimated material cost: Free
Time required: 15 minutes

This activity is a fun math game for two players that teaches about arrays. An array is a way of arranging things in rows and columns. When you buy things like a pack of cookies or a carton of eggs, the items in the package are lined up to create an array. Understanding the difference between rows and columns is an important step in making the jump from two-dimensional to three-dimensional thinking and building.

Use this PDF for the Graph Paper opens in a new window


  • Cup
  • Water
  • Ice Cubes
  • String
  • Salt
  • Optional: Food Coloring

Step-by-step Instructions:

The goal of the game is to try and fill in more of the paper than your opponent.

  1. If you don’t have a sheet of graph paper at home, download and print our graph paper fileopens in a new window.
  2. Each player gets a die and rolls–whoever rolls higher goes first. Player 1 starts at the top left square of the graph paper and Player 2 starts at the bottom right square.
  3. Player 1 rolls twice: first for the number of rows, then for the number of columns. Rows are horizontal (left-to-right) and columns are vertical (up-and-down). Player 1 then draws their array at their starting point. Label the array with number of rows X number of columns (see example below). Player 2 does the same.

grid with 3x4 and dice with numbers 3 and 4

  1. As play progresses, players will have to get creative with where they add their new arrays. New arrays must touch one of the player’s existing arrays.

Grid with different size boxes

  1. The game ends when it is impossible to add any newer arrays. The winner is the player that fills in more squares on the grid.

What’s happening?

You could count every square in an array individually, but it’s much faster to multiply. Multiplying the number of rows and columns will tell you the total number of squares in your array. Tip for grownups: when we multiply to find the number of squares in an array, we’re calculating the array’s area. Area is the total space taken up by the array. By calculating the area of each array and adding them, you’re calculating the total area you controlled in the game.

Where can you find arrays? Everywhere! Cars in a parking lot, mailboxes at the post office, and a box of chocolates are examples of how we use arrays to arrange objects. We also use arrays in computer software, like spreadsheet applications and programming languages. You can even find arrays in nature, like honeycombs. Can you think of other examples of arrays?

Cars in a parking lotVariety of small chocolates in a boxBees on a honeycomb