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This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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Can you each work out the number on your card? What do you notice? How could you sort the cards?

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Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Here is a chance to play a fractions version of the classic Countdown Game.

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This Sudoku requires you to do some working backwards before working forwards.

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Can you match these calculation methods to their visual representations?

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You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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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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If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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Here is a chance to play a version of the classic Countdown Game.

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

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

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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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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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The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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

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Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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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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Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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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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Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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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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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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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?

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

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

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

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

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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 find different ways of creating paths using these paving slabs?

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

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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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When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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