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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Here is a chance to play a fractions 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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
This is an adding game for two players.
Here is a chance to play a version of the classic Countdown Game.
This dice train has been made using specific rules. How many different trains can you make?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
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?
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?
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This task follows on from Build it Up and takes the ideas into three dimensions!
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Surprise your friends with this magic square trick.
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.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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'.
What is happening at each box in these machines?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Choose a symbol to put into the number sentence.
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?
If the answer's 2010, what could the question be?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Can you substitute numbers for the letters in these sums?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.