Exploring and noticing

problem

The Numbers Give the Design

Age

7 to 11

Challenge level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
problem

Sending and Receiving Cards

Age

7 to 11

Challenge level

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
problem

Sports Equipment

Age

7 to 11

Challenge level

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?
problem

Eye View

Age

7 to 11

Challenge level

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

Fencing

Age

7 to 11

Challenge level

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

Sticky Dice

Age

7 to 11

Challenge level

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
problem

Move Those Halves

Age

7 to 11

Challenge level

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
problem

Centred Squares

Age

7 to 11

Challenge level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
problem

Dice Stairs

Age

7 to 11

Challenge level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
problem

Diagonal in a Spiral

Age

7 to 11

Challenge level

Investigate the totals you get when adding numbers in threes on the diagonal of this pattern.