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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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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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In this game for two players, the aim is to make a row of four coins which total one dollar.

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Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

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

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Using the statements, can you work out how many of each type of rabbit there are in these pens?

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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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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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This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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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.

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How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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What do you notice about these squares of numbers? What is the same? What is different?

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Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

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Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

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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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Order these four calculations from easiest to hardest. How did you decide?

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Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

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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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Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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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!

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Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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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?

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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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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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Here is a chance to play a version of the classic Countdown Game.

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

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

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Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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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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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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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?

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The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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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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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?

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Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Some additional activities to develop children's understanding of addition and subtraction of number through playing with number.