Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Properties of Shapes KS2

### Seeing Squares

### Triple Cubes

### Sorting Logic Blocks

### Four Triangles Puzzle

### The Third Dimension

### Square Corners

### Six Places to Visit

### Building Blocks

### Counters in the Middle

### Always, Sometimes or Never? Shape

### National Flags

### Round a Hexagon

### Nine-pin Triangles

### Let Us Reflect

### Name That Triangle!

### Bracelets

### Guess What?

### The Numbers Give the Design

### Where Are They?

### Seeing Parallelograms

### Shape Draw

### A Puzzling Cube

### How Safe Are You?

### Cut Nets

### Seeing Rhombuses

### Arranging Cubes

### Move Those Halves

### Overlapping Again

### Egyptian Rope

### Shapes on the Playground

### Quad Match

### Stringy Quads

### Making Cuboids

### Sponge Sections

### Cut it Out

### Quadrilaterals

### Triangles All Around

### Reflector ! Rotcelfer

### Olympic Turns

### Board Block Challenge

### Symmetry Challenge

### Making Spirals

### Stick Images

### What Shape?

### Making Rectangles

Y*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*

Or search by topic

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

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.

Age 5 to 11

Challenge Level

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

Age 5 to 11

Challenge Level

This activity focuses on similarities and differences between shapes.

Age 5 to 11

Challenge Level

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?

Age 5 to 11

Challenge Level

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

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?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

Use the isometric grid paper to find the different polygons.

Age 7 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 parallelogram.

Age 7 to 11

Challenge Level

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

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?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 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 rhombus.

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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 ...

Age 7 to 11

Challenge Level

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.

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?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

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

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!

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

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.

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

How many symmetric designs can you make on this grid? Can you find them all?

Age 7 to 11

Challenge Level

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

Age 7 to 14

Challenge Level

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

Age 7 to 14

Challenge Level

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.

Age 7 to 14

Challenge Level

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

Y