Working systematically

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?