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During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

This article for teachers suggests ideas for activities built around 10 and 2010.

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Investigate the different distances of these car journeys and find out how long they take.

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A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

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Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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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?

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

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Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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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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Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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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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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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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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Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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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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This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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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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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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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 Sudoku, based on differences. Using the one clue number can you find the solution?

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Number problems at primary level that may require resilience.

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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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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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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Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

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Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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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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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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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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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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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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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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I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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Investigate what happens when you add house numbers along a street in different ways.

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If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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Play this game to learn about adding and subtracting positive and negative numbers

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These two group activities use mathematical reasoning - one is numerical, one geometric.

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