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Broad Topics > Transformations and their Properties > Rotations

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Turning Man

Stage: 1 Challenge Level: Challenge Level:1

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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...on the Wall

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

Explore the effect of reflecting in two intersecting mirror lines.

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Transformation Game

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

Why not challenge a friend to play this transformation game?

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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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Rollin' Rollin' Rollin'

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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John's Train Is on Time

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

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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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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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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Turning Triangles

Stage: 3 Challenge Level: Challenge Level:1

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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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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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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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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2010: A Year of Investigations

Stage: 1, 2 and 3

This article for teachers suggests ideas for activities built around 10 and 2010.

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Matrix Meaning

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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Stereoisomers

Stage: 5 Challenge Level: Challenge Level:1

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.

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Hexpentas

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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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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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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Turning Granny

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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Flip

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

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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Interpenetrating Solids

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!

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Quaternions and Rotations

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

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

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Twizzle Arithmetic

Stage: 4 Challenge Level: Challenge Level:1

Arrow arithmetic, but with a twist.

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Arrow Arithmetic 3

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

How can you use twizzles to multiply and divide?

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Arrow Arithmetic 2

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

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

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Arrow Arithmetic 1

Stage: 4 Challenge Level: Challenge Level:1

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

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Shape Mapping

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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Rearrange the Square

Stage: 1 Challenge Level: Challenge Level:1

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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Peg Rotation

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

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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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: 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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Simplifying Transformations

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

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

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Combining Transformations

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

Does changing the order of transformations always/sometimes/never produce the same transformation?

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Decoding Transformations

Stage: 3 Challenge Level: Challenge Level:1

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

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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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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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Footprints

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a footprint pattern using only reflections.

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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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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!

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Zodiac

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

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Shuffles

Stage: 5 Challenge Level: Challenge Level:1

An environment for exploring the properties of small groups.

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Lafayette

Stage: 2 Challenge Level: Challenge Level:1

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

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Sorting Symmetries

Stage: 2 Challenge Level: Challenge Level:1

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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Posting Triangles

Stage: 1 Challenge Level: Challenge Level:1

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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Coordinating Classroom Coordinates

Stage: 2

This article describes a practical approach to enhance the teaching and learning of coordinates.