What can you cover with dominoes?

### Task

Supplies:a coin, dominoes, a chessboard, and masking tape. If you don't have dominoes, cut out rectangles that would cover two squares of the chessboard.Preparation:use the masking tape to select a smaller part of the chessboard. Start with putting tape around 3x3 square.What to do: - ask your child if she can cover the 3x3 square with dominoes. Let her explore (she will probably realize that every attempt would leave one small square not covered) - place the coin on a small square then invite your child to cover the remaining 8 squares. When can she cover it? Now try placing the coin in a different spot. Is it possible to cover the remaining 8 squares?

### How it went

I drew a 3×3 square on a piece of paper where the side of each smaller inside square matches the width of a domino instead of using a board.

Only Bel did this activity and she seemed equally interested in measuring and drawing the 3×3 square as in the activity itself. I shaded every other small square:

Bel said there was always one square left. I then gave her a coin and ask her to put it on a random square, then figure out whether she can cover the remaining 8 squares with dominoes, she played with it a little bit. I showed her that she could keep track of her progress by drawing a smaller 3×3 square, and putting checkmarks or frowny face, depending on the success. She did figure out that, if the coin was on a dark square, it was possible to cover the rest with dominoes and if it was on a white square, she couldn’t do it. She did not have an explanation for it though.

We did a little bit of the 3×4 extension below, but Bel became bored very fast, perhaps because of the overwhelming number of ways to put two coins on the board.

### Extensions

This can be extended as much as you want:

- use the masking tape to get a 3×4 rectangle and place two coins on two small squares.
- Can you cover the remaining 10 squares with dominoes? When can you do it, when can’t you? It will depend on where you put the coins – can you figure it out?
- Do larger rectangles.

Next week, we will revisit and play with variations of previous activities.

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