## Mathematical Tiling

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Tiling allows us to mathematizes the world around us, providing game play with classroom tile floors or kitchen counters. The nice aspect of doing tiling while doing mathematical outreach is how nicely challenge activities can be provided for students who understand the basic game and are ready to take it to the next step.

In addition to the description of the gamethis lesson plan includes activity notes of required supplies, discussion on the mathematics included in the activity, guiding questions, and a list of additional resources to support the lesson.

# How to play the game

Start with a square 7x7 grid. Given a pile of dominoes (2x1 tiles), can you cover every square? What about an 8x8 grid? What if there are 2 holes in your 8x8 grid where you can’t place a tile. If one hole is on each corner (top right and top left), then can you still cover the entire grid?

# Activity notes

## Supplies needed

• Worksheet, we really like the Julia Robinson Math Festival tiling torment: handout (.pdf)
• 7x7 and 8x8 square boards, here is a 1 inch square tiling grid (.pdf).
• At least 32 dominos (2x1 tiles)
• Alternative: Use the activity-sheet whiteboards (8x8 grid inserted into plastic sheet protector ) and have students draw the dominos with whiteboard markers.
• Challenge activity supplies: Different types of tiles (straight 3x1, L-shaped 3x1)

## Where's the Math?

The level of student will determine the level of mathematics to be introduced. Possible topics include:

• Patterns, parity, and coloring arguments.
• Extensions of the problem provide opportunities for students to think about the number of a specific size of polyomino and this will introduce the idea of non-standard sequences.

## A list of Guiding Questions

• How can we prove our solution?
• Does your approach work for a different tile?
• What other games can you think of that use dominoes? How many ways can you arrange dominoes to cover a 3x4 rectangle?