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There are **60** NRICH Mathematical resources connected to **Rotations**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### National Flags

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Poly Plug Pattern

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Rotations

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Turning Man

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### ...on the Wall

Explore the effect of reflecting in two intersecting mirror lines.

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Transformation Game

Why not challenge a friend to play this transformation game?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Challenge

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rollin' Rollin' Rollin'

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### John's Train Is on Time

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

Problem
Primary curriculum
Secondary curriculum
### Shady Symmetry

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arrow Arithmetic 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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Mapping

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rearrange the Square

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Peg Rotation

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

Age 7 to 11

Challenge Level

General
Primary curriculum
Secondary curriculum
### Making Maths: Indian Window Screen

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Simplifying Transformations

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Combining Transformations

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Decoding Transformations

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rotations Are Not Single Round Here

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 one centre of rotation ? Or if you thought that was impossible, could you say why ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Roll of Patterned Paper

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Symmetric Trace

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

Age 14 to 16

Challenge Level

General
Primary curriculum
Secondary curriculum
### Watch Those Wheels

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

Age 5 to 7

Challenge Level

General
Primary curriculum
Secondary curriculum
### Lafayette

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

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Coordinating Classroom Coordinates

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

Age 7 to 11

Article
Primary curriculum
Secondary curriculum
### Shaping up with Tessellations

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 children to take over.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Flipping Twisty Matrices

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Napoleon's Theorem

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transforming the Letters

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rots and Refs

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### The Frieze Tree

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

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Frieze Patterns in Cast Iron

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

Age 11 to 16

Game
Primary curriculum
Secondary curriculum
### Penta Play

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformation Tease

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Shapes

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Spin

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Overlap

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Middle Man

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rolling Triangle

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Weighty Problem

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hand Swap

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubic Spin

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut Cube

Find the shape and symmetries of the two pieces of this cut cube.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Star Find

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Age 7 to 11

Challenge Level