There are 53 NRICH Mathematical resources connected to Reflections, you may find related items under Transformations and constructions.
Broad Topics > Transformations and constructions > Reflections
This problem explores the shapes and symmetries in some national flags.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
Can you place the blocks so that you see the reflection in the picture?
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?
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.
Explore the effect of reflecting in two intersecting mirror lines.
Explore the effect of reflecting in two parallel mirror lines.
Why not challenge a friend to play this transformation game?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
How many different symmetrical shapes can you make by shading triangles or squares?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
These clocks have been reflected in a mirror. What times do they say?
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?
In how many ways can you stack these rods, following the rules?
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
This article for teachers suggests ideas for activities built around 10 and 2010.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 ?.
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
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?
Does changing the order of transformations always/sometimes/never produce the same transformation?
See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?
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 ?
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 ?
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
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
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.
This article describes a practical approach to enhance the teaching and learning of coordinates.
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.
What is the missing symbol? Can you decode this in a similar way?
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
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.
What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?
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.
Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
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?
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?
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
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.
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?
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.
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?
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.
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?
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?
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!