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

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

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Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

In this article for primary teachers, Ems outlines how we can encourage learners to be flexible in their approach to calculation, and why this is crucial.

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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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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 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.

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

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

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

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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 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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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?

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Can you put these four calculations into order of difficulty? How did you decide?

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

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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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On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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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?

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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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Number problems at primary level that may require resilience.

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Number problems at primary level that require careful consideration.

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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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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?

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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Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

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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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Resources to support understanding of multiplication and division through playing with number.

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

More resources to support understanding multiplication and division through playing with numbers

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Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?