This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

This challenge extends the Plants investigation so now four or more children are involved.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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

This article for teachers suggests ideas for activities built around 10 and 2010.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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

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

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.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

This Sudoku, based on differences. Using the one clue number can you find the solution?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

If you have only four weights, where could you place them in order to balance this equaliser?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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.

Number problems at primary level that require careful consideration.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?