The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Given the products of adjacent cells, can you complete this Sudoku?

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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...

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you replace the letters with numbers? Is there only one solution in each case?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

An investigation that gives you the opportunity to make and justify predictions.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Can you make square numbers by adding two prime numbers together?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

These two group activities use mathematical reasoning - one is numerical, one geometric.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Investigate the different ways you could split up these rooms so that you have double the number.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?