Going Deeper with Geometry

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.

Sizing Them Up 

Age 5 to 7
Challenge Level
Can you put these shapes in order of size? Start with the smallest.

Always, Sometimes or Never? KS1 

Age 5 to 7
Challenge Level
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Let's Investigate Triangles 

Age 5 to 7
Challenge Level
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?

One Big Triangle 

Age 5 to 7
Challenge Level
Make one big triangle so the numbers that touch on the small triangles add to 10.

Matching Triangles 

Age 5 to 7
Challenge Level
Can you sort these triangles into three different families and explain how you did it?

Skeleton Shapes 

Age 5 to 7
Challenge Level
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Jig Shapes 

Age 5 to 11
Challenge Level
Can you each work out what shape you have part of on your card? What will the rest of it look like?

Seeing Squares 

Age 5 to 11
Challenge Level
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.

A Cartesian Puzzle 

Age 7 to 11
Challenge Level
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Shape Draw 

Age 7 to 11
Challenge Level
Use the information on these cards to draw the shape that is being described.

Square Corners 

Age 7 to 11
Challenge Level
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?

Always, Sometimes or Never? Shape 

Age 7 to 11
Challenge Level
Are these statements always true, sometimes true or never true?

A Puzzling Cube 

Age 7 to 11
Challenge Level
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?

Stringy Quads 

Age 7 to 11
Challenge Level
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Egyptian Rope 

Age 7 to 11
Challenge Level
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?

Fitted 

Age 7 to 11
Challenge Level
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?

Estimating Angles 

Age 7 to 14
Challenge Level
How good are you at estimating angles?

Treasure Hunt 

Age 7 to 14
Challenge Level
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?