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?

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

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

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

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.

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

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

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

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

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

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!

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

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

An environment which simulates working with Cuisenaire rods.

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

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

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

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?

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.

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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?

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

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?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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 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.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

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?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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?

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!

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.

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?

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 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!

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

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