Conjecturing and generalising

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

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?”

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?

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?

Can you describe this route to infinity? Where will the arrows take you next?

Delight your friends with this cunning trick! Can you explain how it works?

Explore the effect of combining enlargements.

Explore the effect of reflecting in two intersecting mirror lines.

Explore the effect of reflecting in two parallel mirror lines.

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?