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There are 66 NRICH Mathematical resources connected to Rotations, you may find related items under Transformations and constructions.

Broad Topics > Transformations and constructions > Rotations

### Robotic Rotations

##### Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns?

### National Flags

##### Age 7 to 11 Challenge Level:

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

### Poly Plug Pattern

##### Age 5 to 7 Challenge Level:

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

### Attractive Rotations

##### Age 11 to 14 Challenge Level:

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

### Turning Man

##### Age 5 to 7 Challenge Level:

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

### ...on the Wall

##### Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

### Transformation Game

##### Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game?

### Coordinate Challenge

##### Age 7 to 11 Challenge Level:

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

### Rollin' Rollin' Rollin'

##### Age 11 to 14 Challenge Level:

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?

### John's Train Is on Time

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

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

### Attractive Tablecloths

##### Age 14 to 16 Challenge Level:

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?

### Turning Triangles

##### Age 11 to 14 Challenge Level:

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.

### Paint Rollers for Frieze Patterns.

##### Age 11 to 16

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

### Rose

##### Age 16 to 18 Challenge Level:

What groups of transformations map a regular pentagon to itself?

### 2010: A Year of Investigations

##### Age 5 to 14

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

### Stereoisomers

##### Age 16 to 18 Challenge Level:

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

### Hexpentas

##### Age 5 to 11 Challenge Level:

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

### Tiles in a Public Building

##### Age 7 to 11 Challenge Level:

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

### Animated Triangles

##### Age 5 to 7 Challenge Level:

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

### Notes on a Triangle

##### Age 11 to 14 Challenge Level:

Can you describe what happens in this film?

### Turning Tangles

##### Age 11 to 14 Challenge Level:

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

### Turning Granny

##### Age 7 to 11 Challenge Level:

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?

### Flip

##### Age 7 to 11 Challenge Level:

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

### Interpenetrating Solids

##### Age 16 to 18 Challenge Level:

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

### Arrow Arithmetic 1

##### Age 14 to 16 Challenge Level:

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.

### Shape Mapping

##### Age 7 to 11 Challenge Level:

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

### Rearrange the Square

##### Age 5 to 7 Challenge Level:

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?

### Peg Rotation

##### Age 7 to 11 Challenge Level:

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

### Making Maths: Indian Window Screen

##### Age 7 to 11 Challenge Level:

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

### Simplifying Transformations

##### Age 11 to 14 Challenge Level:

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?

### Combining Transformations

##### Age 11 to 14 Challenge Level:

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

### Decoding Transformations

##### Age 11 to 14 Challenge Level:

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

### Rotations Are Not Single Round Here

##### Age 14 to 16 Challenge Level:

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. . . .

### A Roll of Patterned Paper

##### Age 14 to 16 Challenge Level:

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

### Footprints

##### Age 16 to 18 Challenge Level:

Make a footprint pattern using only reflections.

### Symmetric Trace

##### Age 14 to 16 Challenge Level:

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

### Watch Those Wheels

##### Age 5 to 7 Challenge Level:

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

### Lafayette

##### Age 7 to 11 Challenge Level:

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

### Sorting Symmetries

##### Age 7 to 11 Challenge Level:

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

### Posting Triangles

##### Age 5 to 7 Challenge Level:

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

### Coordinating Classroom Coordinates

##### Age 7 to 11

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

### Shaping up with Tessellations

##### Age 7 to 14

This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your. . . .

### The Matrix

##### Age 16 to 18 Challenge Level:

Investigate the transfomations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0. -1 and +1.

### Matching Frieze Patterns

##### Age 11 to 14 Challenge Level:

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

### Napoleon's Theorem

##### Age 14 to 18 Challenge Level:

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

### Transforming the Letters

##### Age 7 to 11 Challenge Level:

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

### Rots and Refs

##### Age 16 to 18 Challenge Level:

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

### The Frieze Tree

##### Age 11 to 16

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

### Frieze Patterns in Cast Iron

##### Age 11 to 16

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.