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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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Find the values of the nine letters in the sum: FOOT + BALL = GAME

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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

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By selecting digits for an addition grid, what targets can you make?

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Explore the relationship between simple linear functions and their graphs.

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Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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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Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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Find the sum of all three-digit numbers each of whose digits is odd.

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Try out this number trick. What happens with different starting numbers? What do you notice?

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Use your knowledge of place value to try to win this game. How will you maximise your score?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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Try out some calculations. Are you surprised by the results?

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There are nasty versions of this dice game but we'll start with the nice ones...

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Number problems at primary level that may require resilience.

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What happens when you add a three digit number to its reverse?

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

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Number problems at primary level to work on with others.

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Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

More upper primary number sense and place value tasks.

This feature aims to support you in developing children's early number sense and understanding of place value.

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

This article develops the idea of 'ten-ness' as an important element of place value.

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This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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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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Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

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How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

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This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!

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A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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Have a go at balancing this equation. Can you find different ways of doing it?