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There are **53** NRICH Mathematical resources connected to **Reflections**, 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
### So It's Times!

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exploded Squares

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reflector ! Rotcelfer

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Surprising Transformations

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reflecting Lines

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Age 11 to 14

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

Problem
Primary curriculum
Secondary curriculum
### Mirror, Mirror...

Explore the effect of reflecting in two parallel 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
### Let Us Reflect

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Age 7 to 11

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
### Reflecting Squarely

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clocks

These clocks have been reflected in a mirror. What times do they say?

Age 7 to 11

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
### Building with Rods

In how many ways can you stack these rods, following the rules?

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Paint Rollers for Frieze Patterns.

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

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### 2010: A Year of Investigations

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

Age 5 to 14

Problem
Primary curriculum
Secondary curriculum
### Hexpentas

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Fire-fighter's Car Keys

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

Age 14 to 16

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
### One Reflection Implies Another

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 was impossible, could you explain 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
### Orbiting Billiard Balls

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Screen Shot

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.

Age 14 to 16

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
### Hidden Meaning

What is the missing symbol? Can you decode this in a similar way?

Age 7 to 11

Challenge Level

Problem
Live 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
### Two Triangles in a Square

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

Age 14 to 16

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
### Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Age 16 to 18

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

Problem
Primary curriculum
Secondary curriculum
### Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Age 14 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Friezes

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?

Age 11 to 14

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
### Tricircle

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Retracircles

Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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
### Times

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

Age 7 to 11

Challenge Level