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

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

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

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

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

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

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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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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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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?

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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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Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

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

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

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

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Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

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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!

Number problems for you to work on with others.