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Broad Topics > Transformations and constructions > Reflections

National Flags

Stage: 2 Challenge Level:

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

Reflecting Lines

Stage: 3 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?

Stage: 3 Challenge Level:

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

...on the Wall

Stage: 3 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

Mirror, Mirror...

Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

Transformation Game

Stage: 3 Challenge Level:

Why not challenge a friend to play this transformation game?

Let Us Reflect

Stage: 2 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?

Stage: 3 Challenge Level:

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

Reflecting Squarely

Stage: 3 Challenge Level:

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

Clocks

Stage: 2 Challenge Level:

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

What Am I?

Stage: 2 Challenge Level:

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

It's Times Again

Stage: 2 and 3 Challenge Level:

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

Building with Longer Rods

Stage: 2 and 3 Challenge Level:

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

Building with Rods

Stage: 2 Challenge Level:

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

So It's Times!

Stage: 2 and 3 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.

Stage: 3 and 4

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

2010: A Year of Investigations

Stage: 1, 2 and 3

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

Reflector ! Rotcelfer

Stage: 2 Challenge Level:

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

Hexpentas

Stage: 1 and 2 Challenge Level:

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

Making Maths: Indian Window Screen

Stage: 2 Challenge Level:

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

Simplifying Transformations

Stage: 3 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

Stage: 3 Challenge Level:

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

Decoding Transformations

Stage: 3 Challenge Level:

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

Coordinating Classroom Coordinates

Stage: 2

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

Shaping up with Tessellations

Stage: 2 and 3

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

Stage: 2 Challenge Level:

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

Matching Frieze Patterns

Stage: 3 Challenge Level:

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

Transforming the Letters

Stage: 2 Challenge Level:

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

Friezes

Stage: 3

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

Stage: 3 and 4

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

Stage: 3 and 4

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

L-ateral Thinking

Stage: 1 and 2 Challenge Level:

Try this interactive strategy game for 2

Penta Play

Stage: 2 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

Stage: 2 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?

Times

Stage: 2 Challenge Level:

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!