Conjecturing and generalising

problem

Squaring the Circle and Circling the Square

Age

14 to 16

Challenge level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
problem

Three Times Seven

Age

11 to 14

Challenge level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem

Next-Door Numbers

Age

5 to 7

Challenge level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
problem

Logic Block Collections

Age

5 to 7

Challenge level

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
problem

Unexpected Ordering

Age

5 to 7

Challenge level

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?
game

Stop the Clock for Two

Age

5 to 7

Challenge level

Stop the Clock game for an adult and child. How can you make sure you always win this game?
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?
problem

Fit These Shapes

Age

5 to 11

Challenge level

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
problem

Count the Digits

Age

5 to 11

Challenge level

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
game

Strike It Out for Two

Age

5 to 11

Challenge level

Strike it Out game for an adult and child. Can you stop your partner from being able to go?