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### There are 60 results

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.

### Can You Explain Why?

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

Can you explain why it is impossible to construct this triangle?

### ...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?

### 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?

### 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?

##### 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:

Numbers arranged in a square but some exceptional spatial awareness probably needed.

### 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.

### Matrix Meaning

##### Age 16 to 18 Challenge Level:

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

### Reflector ! Rotcelfer

##### Age 7 to 11 Challenge Level:

Can you place the blocks so that you see the relection 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 ?.

### Quaternions and Reflections

##### Age 16 to 18 Challenge Level:

See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.

### 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.

### 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. . . .

### Shuffles

##### Age 16 to 18 Challenge Level:

An environment for exploring the properties of small groups.

### 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.

### Matching Frieze Patterns

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

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

### 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.

### Complex Rotations

##### Age 16 to 18 Challenge Level:

Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?

### 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?