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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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A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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How would you count the number of fingers in these pictures?

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Can you find different ways of creating paths using these paving slabs?

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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This problem looks at how one example of your choice can show something about the general structure of multiplication.

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Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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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?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

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Number problems at primary level that require careful consideration.

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How will you work out which numbers have been used to create this multiplication square?

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In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!

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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 this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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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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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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After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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How would you find out how many football cards Catrina has collected?

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Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

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Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

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What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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What is the smallest number of answers you need to reveal in order to work out the missing headers?

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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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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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Number problems at primary level that may require resilience.

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

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

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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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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?

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

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Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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

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Given the products of adjacent cells, can you complete this Sudoku?

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All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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

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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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Play this game and see if you can figure out the computer's chosen number.

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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56 406 is the product of two consecutive numbers. What are these two numbers?