This problem solving activity has a geometry focus.
Grace’s kitchen floor is square and is fitted by 64 square tiles in a 8 x 8 array.
Grace choses black and white tiles.
She can have the tiles laid so that they look like a chessboard but she is hoping for something a bit unusual.
The tile man sketches something that has reflective and rotational symmetry.
What does he suggest?
Grace’s kitchen floor is square and is fitted by 64 square tiles in a 8 x 8 array. Grace choses black and white tiles. She can have the tiles laid so that they look like a chessboard but she is hoping for something a bit unusual. The tile man sketches something that has reflective and rotational symmetry. What does he suggest?
Grace decides to have the floor tiles laid like a chessboard after all. While redecorating her kitchen, Grace has some cupboards built. Two of these are placed in the opposite corners of the room and take up a whole tile each. (She needs to use 62 square tiles now.)
The tile man says there's a special on. He has a combined tile that consists of a black tile stuck to a white tile. Can Grace tile her floor with these combination tiles and save herself some money?
There are a large number of possible answers here. Each one can easily be checked to see that it has the right symmetries.
For the extension, colour the squares like a chessboard. When you remove two opposite squares you remove two squares of the same colour. Thus, you have 30 squares left of one colour and 32 of the other. You can’t cover these with the combination tiles as each combination covers one square of each colour.
Printed from https://nzmaths.co.nz/resource/grace-s-kitchen-floor at 7:05pm on the 19th April 2024