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?

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

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?

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

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.

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?

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?

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?

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.

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.

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

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

Number problems at primary level that may require determination.

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

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

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

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

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

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?

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.

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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

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.

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

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

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?

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

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?

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

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?

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?

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?

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?

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.

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

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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.

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

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?

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