Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
If you have only four weights, where could you place them in order to balance this equaliser?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Choose a symbol to put into the number sentence.
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. . . .
Got It game for an adult and child. How can you play so that you know you will always win?
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!
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Here is a chance to play a version of the classic Countdown Game.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
There are nasty versions of this dice game but we'll start with the nice ones...
Number problems at primary level that require careful consideration.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Fill in the numbers to make the sum of each row, column and diagonal equal to 15.
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.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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!
There were 22 legs creeping across the web. How many flies? How many spiders?