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Broad Topics > Transformations and their Properties > Compound transformations

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.

Who Is the Fairest of Them All ?

Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

...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?

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.

Conway's Chequerboard Army

Stage: 3 Challenge Level:

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

Square Tangram

Stage: 2 Challenge Level:

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Stage: 2 Challenge Level:

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

Grouping Transformations

Stage: 3, 4 and 5

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

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?

Mathematical Patchwork

Stage: 2 and 3

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

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.

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. . . .

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. . . .

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?

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?

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.

Transformations Tables

Stage: 2 Challenge Level:

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

Trees and Friezes

Stage: 3 Challenge Level:

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

Friezes Using Logo

Stage: 3 Challenge Level:

Experimenting with variables and friezes.

World of Tan 29 - the Telephone

Stage: 2 Challenge Level:

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

World of Tan 28 - Concentrating on Coordinates

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

World of Tan 27 - Sharing

Stage: 2 Challenge Level:

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

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 25 - Pentominoes

Stage: 2 Challenge Level:

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

World of Tan 24 - Clocks

Stage: 2 Challenge Level:

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

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 20 - Fractions

Stage: 2 Challenge Level:

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

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 18 - Soup

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

World of Tan 17 - Weather

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

World of Tan 16 - Time Flies

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the candle and sundial?

World of Tan 15 - Millennia

Stage: 2 Challenge Level:

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

World of Tan 14 - Celebrations

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

World of Tan 13 - A Storm in a Tea Cup

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of these convex shapes?

World of Tan 12 - All in a Fluff

Stage: 2 Challenge Level:

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

World of Tan 11 - the Past, Present and Future

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the telescope and microscope?

World of Tan 9 - Animals

Stage: 2 Challenge Level:

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

World of Tan 8 - Sports Car

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this sports car?

World of Tan 7 - Gat Marn

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this plaque design?

World of Tan 6 - Junk

Stage: 2 Challenge Level:

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

World of Tan 5 - Rocket

Stage: 2 Challenge Level:

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

World of Tan 4 - Monday Morning

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

World of Tan 3 - Mai Ling

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Mai Ling?