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Teaching Geometry – Properties Of Shapes KS2: A Guide For Primary School Teachers From Year 3 To Year 6

Neil Almond

In Key Stage 2, properties of 2-d shapes and properties of 3-d shapes are an important section of geometry. In this blog, Neil Almond provides his theories for teaching shape, help with lesson plans and plenty of teaching resources. 

For some pupils, shape can be the topic they struggle with the most in KS2 maths , as it is so different to topics like place value which fall under Number. Even pupils who are fluent in numeracy may have difficulties up until upper KS2. 

By looking back at the theory behind the subject and finding alternate ways to teach your lessons, both pupils who excel at shape and those who find it difficult will be able to find a deeper understanding.

• Theory behind teaching geometry: properties of shapes

Properties of shapes Year 3 lesson ideas

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• Properties of shapes Year 6 word problems

Theory behind teaching geometry: properties of shape s

While there is no specific ‘theory’ as such to the teaching behind the property of shapes, there are some dos and don’ts that I feel are important from the outset, particularly in regard to resourcing for this subject. In too many classrooms, there will be a drawer labelled 2-d shapes that we believe to contain 2-d shapes like those below.

The issue here is that they are not 2-d. In the physical plane, where items can be manipulated, there exists exactly 3 dimensions. A piece of paper for example, despite its appearance, has a minuscule measurement of depth, and is therefore 3-d. 

Every shape in that drawer is in fact a 3-d shape. Their purpose however is to represent 2-d shapes in an interactive way. Therefore, the teacher is left with two choices. Keep the label ‘2-d shapes’ but take out all the shapes and replace them with drawn shapes on a piece of paper or change the label to ‘3-d shapes used to represent 2-d shapes’. 

The fact of the matter is that holding up one of these shapes and asking pupils to identify the 2-d shape you are holding is categorically wrong. Asking them what 2-d shape is represented by this 3-d shape is, however, perfectly permissible. It is for this reason that I recommend that 3-d shapes are taught before 2-d shapes.

When it comes to the lesson delivery of property of shape, leaning into variation theory can be a useful tool for educators to deploy. The application of variation theory is far more complicated and nuanced than even the best crafted worksheet could ever get across to pupils. 

Rather, one of its possible uses involves the intellectual pursuit of skilful examples, where great care has been considered not only in the examples selected but the order in which they will be revealed.. 

It is very easy to get wrong but the rewards of getting variation theory correct are bountiful and shape, I believe, provides teachers who are interested in its application an easier route into how it works.

Those subscribed to Third Space Learning’s premium content can access a staff CPD powerpoint on variation theory and its application.  

2D Shapes Worksheet Year 3

Download this FREE recognising 2D shapes Geometry worksheet for Year 3 pupils, from our Independent Recap collection.

Geometry – properties of shapes KS2: Year 3

In the national curriculum for maths in England, for each area of maths outlined, there is both a statutory requirement and a non-statutory requirement. The statutory requirement is as follows:

• Draw 2-d shapes and make 3-d shapes using modelling materials; recognise 3-d shapes in different orientations and describe them
• Recognise angles as a property of shape or a description of a turn
• Identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle
• Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

The non-statutory notes and guidance suggests: 

Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-d and 3-d shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle. Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.

It is here we can begin our first foray into what variation theory may look like in the classroom. To do this, we will examine the objective ‘ identify horizontal and vertical lines and pairs of perpendicular and parallel lines.’  

As has been a theme throughout this series, the objectives from the national curriculum do not equate to a lesson. It is quite right that objectives taken from the national curriculum are dissected into smaller, more manageable parts. Therefore, I will only be discussing the idea of parallel lines. 

When thinking about the examples we will carefully select, it is best to consider the boundaries of the concept itself. By that, I mean when parallel lines are no longer parallel lines. In order to understand what parallel lines are, they must also know what they are not. 

Secondly, we must also consider whether examples that do demonstrate the concept are shown and whether these are typical or not. For example, many pupils will have no issues in identifying the shape below as a square.

But will struggle to do the same for the following:

Often, this will be called a diamond despite it having all the properties of a square (the rotation of a shape does not alter the name of the shape). The reason for this struggle is that when ‘squares’ are shown to pupils they are often just shown the first example and not the second. 

It is from these cues that we can build up standard and non-standard examples as well as non-examples to build up the concept of parallel lines. How best to introduce these examples is up to you and below are just some examples.

Standard example:

Non-example:

Non-standard example:

Already we can see here that the use of example and non-example demonstrates that parallel lines require more than one line.

When introducing each example, I would do so one at a time telling pupils whether each example does show parallel lines or not. 

Once you have demonstrated a set that draws out differences, probe the pupils’ understanding of the examples with the questions ‘What is the same and what is different?’ 

The quality of conversation and the conjecturing that the pupils will make will be worth the time and effort put into constructing your sequence of examples and non-examples.

There would not be any standard ‘word problem’  that would look at the mathematics behind parallel lines that was so convoluted that it would hold any mathematical relevance.

The most effective use of reasoning and problem solving when working with a concept and drawing on ideas of variation are sentence stems. For example, the following sentence stem could be used when looking at non-standard examples:

Despite the fact that______________, these are parallel lines because___________.

Despite the fact that these lines are not exactly vertical or horizontal, these are parallel lines because they are the same distance apart from each other and will never meet if extended.

Geometry – properties of shapes KS2: Year 4

• Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• Identify acute and obtuse angles and compare and order angles up to 2 right angles by size
• Identify lines of symmetry in 2-d shapes presented in different orientations
• Complete a simple symmetric figure with respect to a specific line of symmetry

Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles triangle, equilateral triangle, scalene triangle) and quadrilaterals (for example, parallelogram, rhombus, trapezium). Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular. Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape.

The objective this will look at will be ‘Identify lines of symmetry in 2-d shapes presented in different orientations.’ In this objective, ‘orientation’ is the key word and here we can draw on variation theory again. The objective makes no reference if the shapes should be regular or irregular, so it is best to spread this over two days and tackle both. Ideally, mirrors will be provided for each pupil. 

When using mirrors it is best to provide pupils with two types of questions. One where they are required to find a line of symmetry or denote whether an already given line represents a line of symmetry or not. 

Once pupils are comfortable with this, they should then use their skill with a mirror to draw the other half of a shape.  At the beginning stages, this should be done on isometric paper so that the drawings themselves can be as accurate as possible. 

I would start with simple shapes and gradually, over a sequence of a couple of lessons, make the shapes harder by including irregular shapes. I would not, at this stage, expect pupils to complete a ‘picture’ only shape. 

There would not be any standard ‘word problem’ that would look at the mathematics behind symmetry that was so convoluted that it would hold any mathematical relevance.

A great investigation for symmetry would be to dislodge the misconception that a circle only has one side. 

To do this you can look at lines of symmetry of regular shapes. When pupils are aware that regular shapes have all equal sides and equal angles, they can then investigate what this means for lines of symmetry. 

As long as you provide regular polygons, they will quickly see a pattern where the number of lines of symmetry are associated with the number of sides. A square has 4 lines of symmetry, a regular pentagon has 5 lines of symmetry etc. 

Once pupils notice the pattern you can get them to conjecture about all manner of regular shapes. 

At this point, I would ask about a circle. Pupils are often taught that a circle has one continuous side and so therefore, if our pattern holds true, should only have one line of symmetry. 

A quick attempt of getting 30 pupils to find just one line of symmetry will, in more cases than not, provide at least two cases where pupils have drawn the one line in different places of the circle. 

Here we can draw the distinction between a circle and a polygon (must have straight sides) and that there are actually an infinite number of lines of symmetry and this leads some mathematicians to conjecture that a circle also has an infinite number of sides. 

Geometry – properties of shapes KS2: Year 5  

• Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
• Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• Draw given angles, and measure them in degrees (°)
• Angles at a point and 1 whole turn (total 360°)
• Angles at a point on a straight line and half a turn (total 180°)
• Other multiples of 90°
• Use the properties of rectangles to deduce related facts and find missing lengths and angles
• Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.

In this lesson, it will take its objective from being able to identify angles in a straight line and, as the non-statutory guidance says, ‘ Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems’.

Prior to teaching this objective, it is important that the following have been learn by the pupils:

Pupils should draw on their knowledge of right angles and know that 2 right angles next to each other will constitute a half turn and that a half turn is equal to 180 degrees. 

Prior to this lesson, I would spend considerable time getting pupils to complete missing number type questions with two and three integers where the answer is equal to 180. 

This would be done under the guise of regular fluency practice and I would not explain its true purpose at the time. 

To begin with, I would ensure that all missing angles can be solved by measuring it with a protractor and expect the questions to be solved this way. Furthermore, the orientation of the questions would greatly vary so pupils get practice in using a protractor in a manner of different situations.  

Once pupils have begun to grow comfortable with measuring, only then would I introduce questions not drawn to scale and where pupils will have to rely on their application of number to solve the missing angles. Once again, this would take place where there are 2 or 3 given angles that pupils would have to solve. It would be at this point that all the prior training of finding missing values that equal 180 would begin to make sense and ensure that this objective is taught as efficiently as possible.

Angles in a straight line allow for the retrieval of other number facts that have been taught previously. A common reasoning activity in my classroom involved pupils recollecting squared and cubed numbers to solve missing angles in a straight line. This worked in multiple ways. 

First, questions such as the one below where angle b was a square number between 20-50.

Pupils would then have to use their knowledge of square numbers and angles in a straight line to find all the possibilities. 

B = 25 degrees A = 155 degrees

B = 36 degrees A = 144 degrees

B = 49 degrees A = 131 degrees

The other way it would be used would be with cubed numbers where A was an obtuse angle and also a cubed number. What are angles A and B?

Again, here pupils would have to recall their knowledge of cubed numbers and obtuse angles and know that there is only one possible outcome here. A must be 125 degrees as it is the result of 5 cubed and the only cubed number that is an obtuse angle. Therefore, angle b must be 155 degrees.

Geometry – properties of shapes KS2: Year 6

• Draw 2-D shapes using given dimensions and angles
• Recognise, describe and build simple 3-D shapes, including making nets
• Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
• Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
• Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
• Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.
• Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.
• These relationships might be expressed algebraically for example, d = 2 × r; a = 180 − (b + c).

Somewhat surprisingly, it is not until Y6 that we see the use of the net explicitly mentioned. A primary favourite is the deconstruction of 3d shapes into their component pieces to see how they are created. 

It is quite common for this to be done earlier in school and so when Y6 teachers wish to look at this objective, it is important to extend pupils’ thinking.

The joy of the above lesson would be to allow pupils to physically cut the shapes and attempt to match them up – though it would be possible to look at pupils’ special thinking by only using the 2D representations. 

When modelling the activity, I would be sure to look at K and E as this is the most obvious pairing that pupils may go for. By using this as the model, we are getting pupils to extend their thinking as we are eliminating the easier option from the list. 

The answers and the name of the shapes can be found below.

Properties of s hapes Year 6 word problems

A simple true or false question can provide valuable insight into pupils’ understanding of shape. For example, 

True or false?

In order to be regarded as a quadrilateral, a shape must have at least one right angle. 

While pupils may know the answer is false, you can push this thinking on by getting pupils to draw some quadrilaterals that do not contain a right angle. These would include a parallelogram and a trapezium.

Looking for some more ideas of how to do this? You can find plenty of free resources and shapes worksheets on the Third Space Learning maths hub . You may also find our blog, What Are Vertices, Faces and Edges? , useful to pair alongside this topic!

For guidance on other KS2 subjects, check out the rest of the series:

• Teaching Decimals KS2
• Teaching Place Value KS2
• Teaching Fractions KS2
• Teaching Percentages KS2
• Teaching Statistics KS2
• Teaching Ratio and Proportion KS2
• Teaching Multiplication KS2
• Teaching Division KS2
• Teaching Addition and Subtraction KS2
• Teaching Geometry – Position, Direction and Coordinates KS2

Looking to get ahead on other KS2 maths topics? We have the lowdown from expert primary teachers on all the trickiest KS2 maths concepts to teach, including teaching times tables , telling the time , as well as the long division method and the long multiplication method .

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Related articles

What Are Vertices, Faces And Edges? Explained For Primary School

What Are Types of Triangles? Isosceles, Scalene, Equilateral And Right Angle Triangles: Explained For Primary School

What Are Angles? Acute, Obtuse, Reflex And Right Angles: Explained For Primary School Parents & Teachers

Teaching Geometry – Position, Direction and Coordinates KS2: A Guide For Primary School Teachers From Year 3 To Year 6

FREE Let’s Practise Telling The Time Activity Sheets (KS1 & KS2)

Secure and embed key time concepts such as: o’ clock, half past, quarter past, and the position of the minute hand.

Ideal for pupils who struggle to tie together the multiple concepts required to effectively tell the time.

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Missing Angles

Related worksheets.

Find the missing angles in a triangle, around a point, in a quadrilateral, find opposite and supplementary angles, or find angles which require multi-step problem solving skills.

For more shape and space resources click here.

Game Objectives

New Maths Curriculum:

Year 3: Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle

Year 4: Identify acute and obtuse angles and compare and order angles up to two right angles by size

Year 5: Identify: multiples of 90°, angles at a point on a straight line and ½ a turn (total 180°); angles at a point and one whole turn (total 360°); reflex angles; and compare different angles

Year 6: Find unknown angles where they meet at a point, are on a straight line, and are vertically opposite

Missing Angles Practice Questions

Click here for questions, click here for answers.

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Triangles - Levelled SATs questions

Subject: Mathematics

Age range: 7-11

Resource type: Assessment and revision

Last updated

11 October 2014

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Another set of great questions.. thank you!

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Problem solving with triangles and rectangles

This shapes problem solving resource provides a fun challenge and a stimulus for maths talk. In the first task, children are challenged to find as many rectangles as they can. An extension activity then asks children to make their own rectangle pattern challenge for a partner. The second task asks children how many triangles they can find. The extension task asks the children to make up their own triangle puzzle. The children's own puzzles could be used for a display. N.B. Squared paper and rulers will be needed for the extension tasks.

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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

• National Curriculum Tool

Year 6 - Geometry - properties of shapes

New curriculum.

draw 2-D shapes using given dimensions and angles

• recognise, describe and build simple 3-D shapes including making nets

compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

• illustrate and name parts of circle, including radius, diameter and circumference and know that the diameter is twice the radius
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Non-Statutory Guidance

Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.

Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.

These relationships might be expressed algebraically for example:

d = 2 × r ; a = 180 – ( b + c ).

Links and Resources

• Making connections
• Exemplification

Connections within Mathematics

When solving practical problems, there are many links to be made between geometry, measures and elements of number and place value. Calculating percentages of angles, e.g. 15% of a circle, of 25% of 360˚ can bring the two mathematical strands together.

Shapes of given properties can be translated, rotated and reflected, and positions described on the full 4-quadrant coordinate grid. Measurement skills can be used to define scale factors between similar shapes, and to calculate areas of parallelograms and triangles.

Making connections to this topic in adjacent year groups

• identify 3-D shapes, including cubes and other cuboids, from 2-D representations
• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• draw given angles, and measure them in degrees (˚)
• angles at a point and one whole turn (total 360˚)
• angles at a point on a straight line and ½ a turn (total 180˚) other multiples of 90˚
• use the properties of rectangles to deduce related facts and find missing lengths and angles
• distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Key Stage 3

• calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
• derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
• understand and use the relationship between parallel lines and alternate and corresponding angles
• use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
• interpret mathematical relationships both algebraically and geometrically

Cross-curricular and real life connections

Learners will encounter properties of shape in:

The world around them – using their ability to recognise and describe 3-D shapes used in building houses, packaging used by supermarkets and storage boxes used in and around the home.

Design and Technology – using an ability to draw 2-D shapes using given dimensions and angles to make and construct technology projects. Building simple and more complex 3-D shapes using plastic toy construction materials as an example.

Physical Education – e.g. in orienteering, pupils use knowledge of angles to find clues and use an understanding of properties of shapes to solve problems.

ICT - use of programming technology to design sequences, using knowledge of angles, to compare and classify geometric shapes based on their properties. Pupils use knowledge of angles to support program writing and building of 3-D models.

History – Pyramids and obelisks – using plasticine or modelling equipment to build models and gain an understanding of the faces and angles used in building 3-D shapes used throughout history.

Art – the NCETM Primary Magazine provides many useful links for looking at shape within art. Issue 34 provides some useful starting points, using the snail work of Matisse as a stimulus.

Key understandings in mathematics learning – Paper 5: Understanding space and its representation in mathematics

• Bryant, P. (2007) Key understandings in mathematics learning, Paper 5, Nuffield Foundation, University of Oxford

This paper is about children’s informal knowledge of space and spatial relations as well as their formal learning of geometry. It deals with the connection between these two kinds of knowledge.

Going round in circles

• Clausen-May, T. (2005) Teaching Maths to Pupils with Different Learning Styles, London: Paul Chapman PDF

This article describes how a pair of PowerPoint presentations can be used to establish mental images that can help pupils to understand, and so recall, the principles that underlie the formulae to calculate the circumference and the area of a circle

You will need to be logged in to the ATM site to view this article – joining as an associate member is simple, quick and free.

Activity A - Thinking 3D

A series of activities designed to support the development of transferring a 2D representation of a 3D object into a model of the object itself as well as gaining an understanding of positional language.

Activity B - Round a Hexagon

An activity from Nrich supporting the finding of missing angles, including internal and external angles and the use of a protractor.

Activity C - Watching the wheels go round and round

An Nrich activity to support understanding of the term circumference. Links are made to converting units of measure.

Activity D - Quadrilaterals Game

An activity to compare and classify geometric shapes based on their properties in a game that is linked to the card game rummy.

Activity E - Property Chart

This activity used property charts to compare and classify geometric shapes based on their properties.

Activity F - Cut Nets

An Nrich activity to support the skills of visualisation in building simple 3-D shapes from nets.

Activity G - Dynamic Geometry

An introduction to dynamic geometry with helpful links to websites offering free software to support the exploration of properties of circles and the formation of nets for a comprehensive selection of 3-D shapes.

Useful Resources

Protractors or angle measurers, rulers, dot isometric paper, pair of compasses, set squares, dynamic geometry software, set of folding geometric shapes, pinboards and geoboards, Perspex mirrors, 2-D shape dice, class sets of ‘polydron’ or other 3D shape construction materials.

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

Children should be able to construct a triangle given two sides and the included angle

Here is a sketch of a triangle. (It is not drawn to scale).

Draw the full size triangle accurately, below. Use an angle measurer (protractor) and a ruler. One line has been drawn for you.

recognise, describe and build simple 3-D shapes, including making nets

Children should be able to identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes and identify and draw nets of 3-D shapes

They should be able to respond accurately to questions such as;

‘I am thinking of a 3D shape. It has a square base. It has four other faces which are triangles. What is the name of the 3D shape?’

‘Which of these nets are of square based pyramids? How do you know?

‘Is this a net for an open cube?’ How do you know?

Children should be able to make and draw shapes with increasing accuracy and knowledge of their properties.

They should be able to carry out activities such as;

‘Give me instructions to get me to draw a rhombus using my ruler and a protractor’

‘On the grid below, use a ruler to draw a pentagon that has three right angles’

illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

They should know that:

• The circumference is the distance round the circle
• The radius is the distance from the centre to the circumference
• The diameter is 2 x radius

recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

Children should be able to estimate angles, use a protractor to measure and draw them, on their own and in shapes. They should know that the angle sum of a triangle is 180˚, and the sum of angles around a point is 360˚.

They should be able to use this knowledge to respond accurately to questions such as;

‘There are nine equal angles around a point. What is the size of each angle?’

‘There are a number of equal angles around a point. The size of each angle is 24°. How many equal angles are there?’

Children should be able to calculate the size of angle ‘y’ in this diagram without using a protractor.

• KS2 Maths Geometry

This resource from Teachers TV (sign-in required to view) features Richard Dunne, Mathematics consultant, who explains that mathematics involves abstraction and symbolism, the ingredients of higher order mental processes, an essential skill that students need to develop.

• Nrich Air Nets

This series of 24 very short video clips (each lasting a few seconds) challenges children to determine whether a given net can be assembled to make a 3D shape. A good, interactive resources for use in the classroom.

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Visualising at KS2 - Primary Teachers

Young children are often good at imagining - in these tasks we ask them to use their imaginations in a mathematical way.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Have a look at these photos of different fruit. How many do you see? How did you count?

Seeing Squares

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.

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

How Would We Count?

An activity centred around observations of dots and how we visualise number arrangement patterns.

Hundred Square

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Nine-pin Triangles

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

Brush Loads

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Snake Coils

This challenge asks you to imagine a snake coiling on itself.

A Puzzling Cube

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?

Square Corners

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?

Tumbling Down

Watch this animation. What do you see? Can you explain why this happens?

Twice as Big?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Odd Squares

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

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

Arranging Cubes

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

Stringy Quads

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

Sponge Sections

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.

Regular Rings 1

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Overlapping Again

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.

Eight Hidden Squares

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Cubes Within Cubes

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

What can you see? What do you notice? What questions can you ask?