The tasks in this feature for Primary teachers offer opportunities for learners to dig deeply into geometrical ideas. With no obvious routes to a solution, the activities encourage children to be creative in their approaches and provide contexts in which they can communicate their findings clearly.

Please do send in your learners' solutions to our Live Problems - the deadline is Monday 6 December. Read this short article to find out what we are looking for as we decide which solutions to publish.

You can also watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these activities.

This article for Primary teachers outlines how providing opportunities to engage with increasingly complex problems, and to communicate thinking, can help learners 'go deeper' with geometry.

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Can you put these shapes in order of size? Start with the smallest.

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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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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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Make one big triangle so the numbers that touch on the small triangles add to 10.

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Can you sort these triangles into three different families and explain how you did it?

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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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Can you each work out what shape you have part of on your card? What will the rest of it look like?

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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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Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

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

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

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

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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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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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How good are you at estimating angles?

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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?