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Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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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 challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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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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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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This number has 903 digits. What is the sum of all 903 digits?

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In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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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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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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Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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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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Number problems at primary level that require careful consideration.

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

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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Use the information to work out how many gifts there are in each pile.

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Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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

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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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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?

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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What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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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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Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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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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Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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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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A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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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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On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.