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Factors and Multiples game for an adult and child. How can you make sure you win this game?

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A game in which players take it in turns to choose a number. Can you block your opponent?

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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A game to make and play based on the number line.

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Here is a version of the game 'Happy Families' for you to make and play.

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Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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Use the tangram pieces to make our pictures, or to design some of your own!

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Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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What is the greatest number of squares you can make by overlapping three squares?

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Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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Surprise your friends with this magic square trick.

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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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Delight your friends with this cunning trick! Can you explain how it works?

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Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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Here is a chance to create some Celtic knots and explore the mathematics behind them.

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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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Can you make the birds from the egg tangram?

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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Here are some ideas to try in the classroom for using counters to investigate number patterns.

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I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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How can you make an angle of 60 degrees by folding a sheet of paper twice?

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How many models can you find which obey these rules?

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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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What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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These practical challenges are all about making a 'tray' and covering it with paper.

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These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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An activity making various patterns with 2 x 1 rectangular tiles.

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You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?