Exploring and noticing

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Have a go at this 3D extension to the Pebbles problem.

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

Can you find examples of magic crosses? Can you find all the possibilities?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?