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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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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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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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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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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?

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

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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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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.

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

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

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

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

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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?

Number problems for you to work on with others.

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

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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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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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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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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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Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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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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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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Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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Use these head, body and leg pieces to make Robot Monsters which are different heights.

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Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

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

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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?

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Number problems at primary level that require careful consideration.

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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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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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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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These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?