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Transformations Tables

These grids are filled according to some rules - can you complete them?


We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

The Great Tiling Count

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.


Age 7 to 11 Challenge Level:

Imagine a matchstick. 4 rows of matchsticks : 1st row - 1 stick; 2nd row - 4 sticks making a square; 3rd row - 7 sticks making two joined squares; 4th row - 10 sticks making 3 joined squares
How many more are needed to make a square?
How many more need adding to make yet another square along side it?
Carry on adding more squares ...
How many matches have you added?
How many matches are there when you have made 10 squares in the row?
20 squares? 50 squares?