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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'.

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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?

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Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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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. . . .

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Can you each work out the number on your card? What do you notice? How could you sort the cards?

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Find your way through the grid starting at 2 and following these operations. What number do you end on?

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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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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?

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This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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Surprise your friends with this magic square trick.

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What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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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.

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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.

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What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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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?

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You have 5 darts and your target score is 44. How many different ways could you score 44?

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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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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.

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Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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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?

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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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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.

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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?

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Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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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?

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

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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?

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Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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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?

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Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

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In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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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?

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This task follows on from Build it Up and takes the ideas into three dimensions!

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Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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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?

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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?