Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Find the sum of all three-digit numbers each of whose digits is odd.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This is an adding game for two players.
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Can you substitute numbers for the letters in these sums?
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?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
What is happening at each box in these machines?
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.
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?
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!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Got It game for an adult and child. How can you play so that you know you will always win?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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!
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?
Generate large numbers then give the values of each digit.
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
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.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Ben has five coins in his pocket. How much money might he have?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Number problems at primary level that require careful consideration.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
This dice train has been made using specific rules. How many different trains can you make?