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In this activity, we are going to shade the squares of this grid with one colour to make different designs.
There are a few rules that our designs need to follow:
Have a go at making some designs. How many can you find? You might like to shade your designs on squared paper or on this sheet of blank grids.
If you wanted to find every possible design, how would you do this?
The problem requires learners to recognise and visualise the transformation of a 2D shape, and invites them to work systematically in a spatial environment. It is a problem that is accessible to most pupils even if they need support in organising and presenting their ideas and ensuring the completeness of their solution.
You could start by displaying these two shaded grids on the board to simulate a discussion about reflection symmetry. It might also help to have some blank $3$ by $3$ grids on the board for learners to shade as they talk.
The problem can be extended to discuss larger square lattices, e.g. $4$ by $4$ and whether there are any differences between even and odd lengths of side. The activity Shady Symmetry is also an extension possibility.
This activity investigates how you might make squares and pentominoes from Polydron.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?