What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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

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?

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

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find 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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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

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?

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

Use the information to work out how many gifts there are in each pile.

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?

Number problems at primary level that may require determination.

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

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?

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

This task combines spatial awareness with addition and multiplication.

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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.

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.

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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?

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?

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?

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

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

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

There were 22 legs creeping across the web. How many flies? How many spiders?

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?

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?

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

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?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?