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There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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A challenging activity focusing on finding all possible ways of stacking rods.

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Sort the houses in my street into different groups. Can you do it in any other ways?

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Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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

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In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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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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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Investigate the different ways you could split up these rooms so that you have double the number.

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Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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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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It starts quite simple but great opportunities for number discoveries and patterns!

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In how many ways can you stack these rods, following the rules?

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This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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This challenge extends the Plants investigation so now four or more children are involved.

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Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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How many models can you find which obey these rules?

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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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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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How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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An investigation that gives you the opportunity to make and justify predictions.

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What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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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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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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You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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How many ways can you find of tiling the square patio, using square tiles of different sizes?

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Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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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?