Find a great variety of ways of asking questions which make 8.

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

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?

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?

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

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?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

This number has 903 digits. What is the sum of all 903 digits?

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

Find out about Magic Squares in this article written for students. Why are they magic?!

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

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?

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

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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

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.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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!

How would you count the number of fingers in these pictures?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

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

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?

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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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

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

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.

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

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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

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?