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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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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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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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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.

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

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This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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.

More upper primary number sense and place value tasks.

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

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

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

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

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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?

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.

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Where should you start, if you want to finish back where you started?

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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. . . .

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The Number Jumbler can always work out your chosen symbol. Can you work out how?

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.

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

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

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Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

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

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

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Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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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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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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The number 3723(in base 10) is written as 123 in another base. What is that base?

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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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The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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

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When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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How many six digit numbers are there which DO NOT contain a 5?

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Can you work out some different ways to balance this equation?

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