# Resources tagged with: Rotations

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There are 60 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 16Challenge Level

How did the the rotation robot make these patterns?

### National Flags

##### Age 7 to 11Challenge Level

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

### Poly Plug Pattern

##### Age 5 to 7Challenge Level

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

### Attractive Rotations

##### Age 11 to 14Challenge 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 7Challenge 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 14Challenge Level

Explore the effect of reflecting in two intersecting mirror lines.

### Transformation Game

##### Age 11 to 14Challenge Level

Why not challenge a friend to play this transformation game?

### Coordinate Challenge

##### Age 7 to 11Challenge Level

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

### Rollin' Rollin' Rollin'

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

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

### Attractive Tablecloths

##### Age 14 to 16Challenge 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?

### 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 18Challenge 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 18Challenge Level

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

### Hexpentas

##### Age 5 to 11Challenge 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 11Challenge 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 7Challenge 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 14Challenge Level

Can you describe what happens in this film?

### Flip

##### Age 7 to 11Challenge 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 18Challenge 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 16Challenge 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 11Challenge 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 7Challenge 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 11Challenge 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 11Challenge Level

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

### Simplifying Transformations

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

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

### Decoding Transformations

##### Age 11 to 14Challenge 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 16Challenge 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 16Challenge 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 18Challenge Level

Make a footprint pattern using only reflections.

### Symmetric Trace

##### Age 14 to 16Challenge Level

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

### Watch Those Wheels

##### Age 5 to 7Challenge 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 11Challenge Level

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

### 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 18Challenge 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.

### Napoleon's Theorem

##### Age 14 to 18Challenge 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 11Challenge 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 18Challenge 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.

### Penta Play

##### Age 7 to 11Challenge Level

A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.

### Transformation Tease

##### Age 7 to 11Challenge Level

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

### Same Shapes

##### Age 5 to 7Challenge Level

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

### In a Spin

##### Age 14 to 16Challenge Level

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

### Overlap

##### Age 14 to 16Challenge Level

A red square and a blue square overlap. Is the area of the overlap always the same?

### Middle Man

##### Age 16 to 18Challenge Level

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?