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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

What is the sum of all the digits in all the integers from one to one million?

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?

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?

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

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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 addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Got It game for an adult and child. How can you play so that you know you will always win?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

An environment which simulates working with Cuisenaire rods.

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.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

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.

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

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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!

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

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?