Describing patterns and sequences

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
Times tables shifts

Age

7 to 11

Challenge level

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
problem
Expanding pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?
problem
Knights and knaves

Age

11 to 14

Challenge level

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
problem
So it's 28

Age

5 to 7

Challenge level

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.
problem
Mean sequence

Age

11 to 14

Challenge level

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
problem
Shifting times tables

Age

11 to 14

Challenge level

Can you find a way to identify times tables after they have been shifted up or down?
problem
Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Holes

Age

5 to 11

Challenge level

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?