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#### Resources tagged with Compound transformations similar to Going Places with Mathematicians:

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Broad Topics > Transformations and their Properties > Compound transformations

### Going Places with Mathematicians

##### Stage: 2 and 3

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .

### Mirror, Mirror...

##### Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

### Maurits Cornelius Escher

##### Stage: 2 and 3

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

### Screwed-up

##### Stage: 3 Challenge Level:

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

### Mathematical Patchwork

##### Stage: 2 and 3

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

### Matching Frieze Patterns

##### Stage: 3 Challenge Level:

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

### Friezes Using Logo

##### Stage: 3 Challenge Level:

Experimenting with variables and friezes.

### 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?

### 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?

### Trees and Friezes

##### Stage: 3 Challenge Level:

This problem is based on the idea of building patterns using transformations.

### 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?

### ...on the Wall

##### Stage: 3 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

### Decoding Transformations

##### Stage: 3 Challenge Level:

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

### Making Rectangles, Making Squares

##### Stage: 3 Challenge Level:

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

### Transformation Game

##### Stage: 3 Challenge Level:

Why not challenge a friend to play this transformation game?

### Who Is the Fairest of Them All?

##### Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

### Square to L

##### Stage: 2 Challenge Level:

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

### 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.

### Counting Triangles

##### Stage: 3 Challenge Level:

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

### Coloured Edges

##### Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

### Appearing Square

##### Stage: 3 Challenge Level:

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

### Disappearing Square

##### Stage: 3 Challenge Level:

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

### Flight of the Flibbins

##### Stage: 3 Challenge Level:

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

### Grouping Transformations

##### Stage: 3, 4 and 5

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.

### Conway's Chequerboard Army

##### Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

### Chess

##### Stage: 3 Challenge Level:

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

### 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.

### 2001 Spatial Oddity

##### Stage: 3 Challenge Level:

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

### Sorting Symmetries

##### Stage: 2 Challenge Level:

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

### Triangular Tantaliser

##### Stage: 3 Challenge Level:

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

### World of Tan 5 - Rocket

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the rocket?

### Squares, Squares and More Squares

##### Stage: 3 Challenge Level:

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

### World of Tan 6 - Junk

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this junk?

##### Stage: 2 Challenge Level:

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

### World of Tan 9 - Animals

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this goat and giraffe?

### Transformations Tables

##### Stage: 2 Challenge Level:

These grids are filled according to some rules - can you complete them?

### Bow Tie

##### Stage: 3 Challenge Level:

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

### World of Tan 20 - Fractions

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

### World of Tan 12 - All in a Fluff

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of these rabbits?

### Twice as Big?

##### Stage: 2 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

### World of Tan 1 - Granma T

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Granma T?

### World of Tan 24 - Clocks

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these clocks?

### World of Tan 25 - Pentominoes

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these people?

### World of Tan 22 - an Appealing Stroll

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the child walking home from school?

### World of Tan 21 - Almost There Now

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

### World of Tan 19 - Working Men

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

### World of Tan 26 - Old Chestnut

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

### World of Tan 27 - Sharing

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Fung at the table?