Numeracy problems to solve for Key Stage 1, 2 and 3

"Honey, I shrunk the shape!"

It's easy to make a shape smaller and smaller - here's how!

You will need pencil, paper and colouring pens.

Draw a square (about 8 cm x 8 cm) and mark a point at the centre of each side. Join the points to make a smaller square inside the first. How much smaller is the second square than the first?

Mark centre points in this smaller square and join them up.

Carry on doing this, getting smaller and smaller until you have got too small to do any more.

Try starting with other regular shapes like triangle, hexagons. Does it work with rectangles? What stays the same as your shapes gets smaller and smaller?

How much smaller is the pink triangle than the yellow triangle?

Can Shelly pocket the ball in one?

Max makes really cool pool tables. They are always crazy shapes and only have a single pocket!

Max and his friend are playing 'pot in one'. They both take turns to start from the same spot and try to get the ball in the pocket with just one shot. Max has made his shot (see the diagram below). Shelly made a shot at a different angle that also 'potted in one'.

There are a few things you ought to know about Max's pool tables. A ball always bounces off a cushion (side) at an angle exactly equal to the angle at which it hits the side. The ball will continue to move forever unless it goes down a pocket.

The yellow line shows how max potted in one shot. The ball hit the cushions five times, the first bounce at a different angle to the next four, before going into the pocket. Shelley's shot only bounced once, at 45°. Can you work out what her shot was?

Max and shelly both found different ways to 'pot in one' on this table as well. Can you work out what both their shots were?