Conjecturing and generalising

problem
Simple train journeys

Age

5 to 11

Challenge level

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
problem
More twisting and turning

Age

11 to 16

Challenge level

It would be nice to have a strategy for disentangling any tangled ropes...
problem
Four go

Age

7 to 11

Challenge level

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
problem
Dotty circle

Age

7 to 11

Challenge level

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
problem
Perpendicular lines

Age

14 to 16

Challenge level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
problem
Parallel lines

Age

11 to 14

Challenge level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
problem
Growing garlic

Age

5 to 11

Challenge level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
problem
Sums of pairs

Age

11 to 16

Challenge level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
problem
Music to my ears

Age

7 to 11

Challenge level

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
problem
Clapping times

Age

5 to 7

Challenge level

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?