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

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Watch this animation. What do you see? Can you explain why this happens?

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Can you find a way of counting the spheres in these arrangements?

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Are these statements always true, sometimes true or never true?

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Are these statements always true, sometimes true or never true?

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Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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Are these statements relating to odd and even numbers always true, sometimes true or never true?

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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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This challenge is about finding the difference between numbers which have the same tens digit.

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In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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What happens when you round these numbers to the nearest whole number?

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This activity involves rounding four-digit numbers to the nearest thousand.

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In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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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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If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

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Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Can you work out how to win this game of Nim? Does it matter if you go first or second?

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Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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

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Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

To celebrate NRICH's 25th birthday, why not play this special version of our classic game, Got It? Can you devise a strategy so that you will always win?

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I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?

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