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Broad Topics > Transformations and their Properties > Translations

Decoding Transformations

Stage: 3 Challenge Level:

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

Matching Frieze Patterns

Stage: 3 Challenge Level:

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

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. . . .

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?

Combining Transformations

Stage: 3 Challenge Level:

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

Topkapi Palace

Stage: 2 and 3 Challenge Level:

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and. . . .

Arrow Arithmetic 1

Stage: 4 Challenge Level:

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

It's Times Again

Stage: 2 and 3 Challenge Level:

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

Arrow Arithmetic 2

Stage: 4 Challenge Level:

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

Twizzle Arithmetic

Stage: 4 Challenge Level:

Arrow arithmetic, but with a twist.

Transformation Game

Stage: 3 Challenge Level:

Why not challenge a friend to play this transformation game?

Arrow Arithmetic 3

Stage: 4 Challenge Level:

How can you use twizzles to multiply and divide?

Plex

Stage: 2, 3 and 4 Challenge Level:

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

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?

Mirror, Mirror...

Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.

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?

Surprising Transformations

Stage: 3 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?

Overlaid

Stage: 2, 3 and 4 Challenge Level:

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Who Is the Fairest of Them All?

Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

Symmetric Trace

Stage: 4 Challenge Level:

Points off a rolling wheel make traces. What makes those traces have symmetry?

Is There a Theorem?

Stage: 3 Challenge Level:

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Translating Lines

Stage: 3 Challenge Level:

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

A Knight's Journey

Stage: 4 and 5

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

Stage: 4 Challenge Level:

Explore the two quadratic functions and find out how their graphs are related.