In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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.

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

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

Investigate what happens when you add house numbers along a street in different ways.

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

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

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

Can you make square numbers by adding two prime numbers together?

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.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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 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?

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.

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.

A game for 2 players. Practises subtraction or other maths operations knowledge.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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?

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

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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?

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

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!

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

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?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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