Conjecturing and generalising

problem
Dice stairs

Age

7 to 11

Challenge level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
problem
Centred squares

Age

7 to 11

Challenge level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
problem
Same answer

Age

11 to 14

Challenge level

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
problem
Subtraction surprise

Age

7 to 14

Challenge level

Try out these calculations. Are you surprised by the results?
$Build it \Up more$

problem
Build it up more

Age

7 to 11

Challenge level

This task follows on from Build it Up and takes the ideas into three dimensions!
problem
Spirals, spirals

Age

7 to 11

Challenge level

Here are two kinds of spirals for you to explore. What do you notice?
problem
Circles, circles

Age

5 to 11

Challenge level

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
problem
Build it up

Age

7 to 11

Challenge level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
list
Generalising

Age

5 to 11

These tasks give learners chance to generalise, which involves identifying an underlying structure.