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

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.

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

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

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.

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

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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

Delight your friends with this cunning trick! Can you explain how it works?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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.

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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.

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

There are nasty versions of this dice game but we'll start with the nice ones...

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

Can you use the information to find out which cards I have used?

Here is a chance to play a version of the classic Countdown Game.

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

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?