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This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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This activity focuses on similarities and differences between shapes.

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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Can you find out which 3D shape your partner has chosen before they work out your shape?

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Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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Use the isometric grid paper to find the different polygons.

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Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

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Use the information on these cards to draw the shape that is being described.

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How much do you have to turn these dials by in order to unlock the safes?

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What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

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Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

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This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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

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This problem explores the shapes and symmetries in some national flags.

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This problem shows that the external angles of an irregular hexagon add to a circle.

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How many different triangles can you make on a circular pegboard that has nine pegs?

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Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

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A task which depends on members of the group noticing the needs of others and responding.

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This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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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 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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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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A task which depends on members of the group working collaboratively to reach a single goal.

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For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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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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Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

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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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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Can you find all the different triangles on these peg boards, and find their angles?

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Can you place the blocks so that you see the reflection in the picture?

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This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

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This task requires learners to explain and help others, asking and answering questions.

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This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

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A task which depends on members of the group noticing the needs of others and responding.