We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Can you complete this jigsaw of the multiplication square?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Can you find a way to identify times tables after they have been shifted up?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
Reasoning about the number of matches needed to build squares that
share their sides.
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
These grids are filled according to some rules - can you complete
A story for students about adding powers of integers - with a festive twist.
Cellular is an animation that helps you make geometric sequences composed of square cells.