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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 Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

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

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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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?

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Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

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Investigate what happens when you add house numbers along a street in different ways.

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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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These two group activities use mathematical reasoning - one is numerical, one geometric.

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Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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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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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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Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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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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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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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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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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Can you score 100 by throwing rings on this board? Is there more than way to do it?

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Can you substitute numbers for the letters in these sums?

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

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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!

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Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

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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?

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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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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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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?

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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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If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

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Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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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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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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This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

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

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Investigate the different distances of these car journeys and find out how long they take.

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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?