Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Which set of numbers that add to 10 have the largest product?

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?