Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Is there an efficient way to work out how many factors a large number has?

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?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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...

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?

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

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

A jigsaw where pieces only go together if the fractions are equivalent.

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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?

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

If you move the tiles around, can you make squares with different coloured edges?

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

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Explore the effect of combining enlargements.

Explore the effect of reflecting in two parallel mirror lines.

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?