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Broad Topics > Transformations and their Properties > Symmetry

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Coordinate Challenge

Stage: 2 Challenge Level: Challenge Level:1

Use the clues about the symmetrical properties of these letters to place them on the grid.

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Stringy Quads

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Octa-flower

Stage: 5 Challenge Level: Challenge Level:1

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

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Symmetry Challenge

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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A Cartesian Puzzle

Stage: 2 Challenge Level: Challenge Level:1

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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Attractive Tablecloths

Stage: 4 Challenge Level: Challenge Level:1

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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Arclets

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

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Witch of Agnesi

Stage: 5 Challenge Level: Challenge Level:1

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

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Folium of Descartes

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

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Logosquares

Stage: 5 Challenge Level: Challenge Level:1

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

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Mean Geometrically

Stage: 5 Challenge Level: Challenge Level:1

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

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Colouring Triangles

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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Shape Draw

Stage: 2 Challenge Level: Challenge Level:1

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

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Flower Power

Stage: 3 and 4 Challenge Level: Challenge Level:1

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.

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National Flags

Stage: 2 Challenge Level: Challenge Level:1

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

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Poly Plug Pattern

Stage: 1 Challenge Level: Challenge Level:1

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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More Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

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Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

Can you devise a fair scoring system when dice land edge-up or corner-up?

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Troublesome Dice

Stage: 3 Challenge Level: Challenge Level:1

When dice land edge-up, we usually roll again. But what if we didn't...?

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Sorting Letters

Stage: 1 and 2 Challenge Level: Challenge Level:1

This interactivity allows you to sort letters of the alphabet into two groups according to different properties.

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Paint Rollers for Frieze Patterns.

Stage: 3 and 4

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

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Exploded Squares

Stage: 1 Challenge Level: Challenge Level:1

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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Rose

Stage: 5 Challenge Level: Challenge Level:1

What groups of transformations map a regular pentagon to itself?

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Attractive Rotations

Stage: 3 Challenge Level: Challenge Level:1

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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Mirror, Mirror

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Topkapi Palace

Stage: 2 and 3 Challenge Level: Challenge Level:1

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and. . . .

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Drawing Celtic Knots

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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Trominoes

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?

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Tiles in a Public Building

Stage: 2 Challenge Level: Challenge Level:1

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

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A Resource to Support Work on Transformations

Stage: 4 Challenge Level: Challenge Level:1

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

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Animated Triangles

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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Triangle Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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Notes on a Triangle

Stage: 3 Challenge Level: Challenge Level:1

Can you describe what happens in this film?

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Turning Tangles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Look carefully at the video of a tangle and explain what's happening.

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Dancing with Maths

Stage: 2, 3 and 4

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?

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Beat the Drum Beat!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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Plex

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

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Making Maths: Five-point Snowflake

Stage: 2 Challenge Level: Challenge Level:1

Follow these instructions to make a five-pointed snowflake from a square of paper.

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Making Maths: Indian Window Screen

Stage: 2 Challenge Level: Challenge Level:1

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

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Making Maths: Snowflakes

Stage: 2 Challenge Level: Challenge Level:1

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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Tubular Path

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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A Maze of Directions

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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Rotations Are Not Single Round Here

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

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One Reflection Implies Another

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

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A Roll of Patterned Paper

Stage: 4 Challenge Level: Challenge Level:1

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

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Symmetric Trace

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points off a rolling wheel make traces. What makes those traces have symmetry?

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Building Patterns

Stage: 2 Challenge Level: Challenge Level:1

Can you deduce the pattern that has been used to lay out these bottle tops?

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Watch Those Wheels

Stage: 1 Challenge Level: Challenge Level:1

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!