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"?

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

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.

Can you explain the strategy for winning this game with any target?

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

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.

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.

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

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?

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

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

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?

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

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

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

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

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

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?

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

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?

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

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?

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

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

How can we help students make sense of addition and subtraction of negative numbers?

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?

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

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

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?

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.

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?

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

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!

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?

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

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

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

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.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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!

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?

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?

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?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

You have 5 darts and your target score is 44. How many different ways could you score 44?