Exploring and noticing

An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Look for the common features in these graphs. Which graphs belong together?

It starts quite simple but great opportunities for number discoveries and patterns!

Why does the tower look a different size in each of these pictures?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?