Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This number has 903 digits. What is the sum of all 903 digits?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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.
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.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
You have 5 darts and your target score is 44. How many different ways could you score 44?
What is happening at each box in these machines?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Can you score 100 by throwing rings on this board? Is there more than way 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.
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?
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?
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?
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?
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.
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?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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!
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?
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.
Investigate what happens when you add house numbers along a street in different ways.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Are these statements always true, sometimes true or never true?
This task follows on from Build it Up and takes the ideas into three dimensions!
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.