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

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

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.

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?

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

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!

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

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?

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 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.

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

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.

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?

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?

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?

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

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?

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?

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?

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

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

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

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

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

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?

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

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

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.

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

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?

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?

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

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.

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

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?

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?

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?

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.

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

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

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.