Little Squares

'Little Squares' printed from https://nrich.maths.org/

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Little Squares

Here are some squares:

This square is 1 little square long and 1 little square wide. It has 1 little square inside it.

square: 2 little squares long, 2 little squares wide This square is 2 little squares long and 2 little squares wide. It has 4 little squares inside it.

square: 3 little squares long, 3 little squares wide This square is 3 little squares long and 3 little squares wide. It has 9 little squares inside it.

Here is the next square:

square: 4 little squares long, 4 little squares wide

How many little squares are inside it?

What does the next square look like? How many little squares will there be inside it? I draw a square with 81 little squares inside it. How long and how wide is my square?

Why do this problem?

This activity gives the pupils experience in starting very simple investigations. There is a possibility of prediction, counting, addition and multiplication.

This investigation could be used in small groups to allow pupils time to play with the squares and count with no pressure. They should be encouraged to discuss their ideas between themselves. Plenty of squared paper will be needed.

Key questions

What numbers have you found?

What is special about those numbers?

What do you notice?

Could you find the difference between two numbers that follow each other?

Have you drawn any other squares?

How many little squares do you think there will be in the next big square?

Possible extension

Learners can explore other shapes that can be enlarged in a similar way and explore by counting.