Exploring and noticing

Can you find the missing number(s)? The square is the average (mean) of the numbers surrounding it.

Can you find pairs of differently sized windows that cost the same?

What do you think is going to happen in this video clip? Are you surprised?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?

Find at least one way to put in some operation signs to make these digits come to 100.