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.

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?

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

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.

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

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

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?

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

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

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

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

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

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

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?

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?

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

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.

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

This article suggests some ways of making sense of calculations involving positive and 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.

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

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 this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

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

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

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

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?

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

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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

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

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.

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!

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

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?