Challenge Level

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

Challenge Level

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?

Challenge Level

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2?

Challenge Level

Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?

Challenge Level

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Challenge Level

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Challenge Level

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Challenge Level

Mum, Dad, Tim and Jill moved into a new house. If they cut down the big tree, will it miss the greenhouse?

Challenge Level

Use the ratio of cashew nuts to peanuts to find out how many peanuts Rachel has. What would the ratio be if Rachel and Marianne mixed their bags?

Challenge Level

Can you work out how to produce different shades of pink paint?

Challenge Level

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Challenge Level

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Challenge Level

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Challenge Level

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Challenge Level

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Challenge Level

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .

Challenge Level

How long will it take Mary and Nigel to wash an elephant if they work together?

Challenge Level

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

Challenge Level

When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?

Challenge Level

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Challenge Level

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

Challenge Level

In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

Challenge Level

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

Challenge Level

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

Challenge Level

Is there a temperature at which Celsius and Fahrenheit readings are the same?

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

Challenge Level

Build a scaffold out of drinking-straws to support a cup of water

Challenge Level

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Challenge Level

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?