# The Game

**Materials**

- 4d6. Two dice are re-labelled 0, 1, 1, 2, 2, 3 (see notes below)
- Graph paper (we are using paper that is roughly 20 cm x 28 cm, lines about 0.5 cm apart)
- colored pencils

**Taking a turn**

Roll all four dice. Form two 2-digit numbers using the standard dice as ones digits. Then, use your color to outline and shade a rectangle in the grid so that:

- the side lengths are the 2-digit numbers you formed with the dice
- At least one unit of the rectangle's border is on the border of your block blob
- Note: the first player on their first turn must have a corner of their rectangle on the vertex at the center of the grid. The second player has a free play on their first turn.
- Write down the area of your rectangle

**Ending the game**

The game ends when one player can't place a rectangle of the required dimensions legally.

When that happens, add up the area of your block blob. Higher value wins.

# Notes

**"Counting" sides**

The side lengths of the rectangles are long enough that counting on the graph paper will be irritating. Instead of counting directly, they can measure the side lengths. For our graph paper, the link between the measurement and the count is nice, since the paper is very nearly 5mm ruled, so they just double the measure. I think this is a really nice measurement and doubling practice, too.

**Dice labels**

Other labels could be used on the special dice. We chose this arrangement because of the size of the graph paper. Rectangles with sides longer than 40 often won't fit and we think we will even need some single digit rectangles to allow a fun game length. An alternative we are considering is 0, 0, 1, 1, 2, 2.

As an alternative to labeling the dice with new numbers, you could label them with colored dots and give out a mapping table. For example:

blue corresponds to 3

red corresponds to 2

green corresponds to 2

yellow corresponds to 1

black corresponds to 1

white corresponds to 0

**Reinforcing the distributive law**

To facilitate calculating the area and reinforce the distributive law, you might have the students split their rectangles into two (or four or more) pieces and calculate the partial products. You can further decide whether to ask them to split the sides in particular ways or encourage them to find the easiest way to split to help them calculate.

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