Exploring and noticing

problem
Attractive rotations

Age

11 to 14

Challenge level

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
problem
Planning a school trip

Age

7 to 11

Challenge level

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.
problem
Counting cogs

Age

7 to 14

Challenge level

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
problem
Doughnut percents

Age

7 to 14

Challenge level

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.
problem
Next size up

Age

7 to 11

Challenge level

The challenge for you is to make a string of six (or more!) graded cubes.
problem
Table patterns go wild!

Age

7 to 11

Challenge level

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
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
Partly painted cube

Age

14 to 16

Challenge level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
problem
It's a fence!

Age

5 to 11

Challenge level

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
problem
Jig shapes

Age

5 to 11

Challenge level

Can you each work out what shape you have part of on your card? What will the rest of it look like?