Conjecturing and generalising

Are these statements always true, sometimes true or never true?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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

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

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

Try out some calculations. Are you surprised by the results?

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

Here are two kinds of spirals for you to explore. What do you notice?