Resources tagged with: Reflections

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There are 53 NRICH Mathematical resources connected to Reflections, you may find related items under Transformations and constructions.

Broad Topics > Transformations and constructions > Reflections

National Flags

Age 7 to 11 Challenge Level:

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

Exploded Squares

Age 5 to 7 Challenge Level:

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

Surprising Transformations

Age 14 to 16 Challenge Level:

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?

Reflecting Lines

Age 11 to 14 Challenge Level:

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.

...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

Mirror, Mirror...

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

Transformation Game

Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game?

Let Us Reflect

Age 7 to 11 Challenge Level:

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

Shady Symmetry

Age 11 to 14 Challenge Level:

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

Reflecting Squarely

Age 11 to 14 Challenge Level:

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

Clocks

Age 7 to 11 Challenge Level:

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

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?

What Am I?

Age 7 to 11 Challenge Level:

Can you draw the shape that is being described by these cards?

It's Times Again

Age 7 to 14 Challenge Level:

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!

Building with Longer Rods

Age 7 to 14 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

Building with Rods

Age 7 to 11 Challenge Level:

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

So It's Times!

Age 7 to 14 Challenge Level:

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

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.

Reflector ! Rotcelfer

Age 7 to 11 Challenge Level:

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

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?

The Fire-fighter's Car Keys

Age 14 to 16 Challenge Level:

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 ?.

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. . . .

One Reflection Implies Another

Age 14 to 16 Challenge Level:

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. . . .

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.

Orbiting Billiard Balls

Age 14 to 16 Challenge Level:

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

Screen Shot

Age 14 to 16 Challenge Level:

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. . . .

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. . . .

Hidden Meaning

Age 7 to 11 Challenge Level:

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

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.

Two Triangles in a Square

Age 14 to 16 Challenge Level:

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.

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?

Reflect Again

Age 16 to 18 Challenge Level:

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.

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.

Snookered

Age 14 to 18 Challenge Level:

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?

Friezes

Age 11 to 14

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?

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 11 Challenge 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. Play with card, or on the computer.

Transformation Tease

Age 7 to 11 Challenge 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?

Tricircle

Age 14 to 16 Challenge Level:

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. . . .

A Problem of Time

Age 14 to 16 Challenge Level:

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?

Retracircles

Age 16 to 18 Challenge Level:

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.