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Broad Topics > Transformations and constructions > Compound transformations

Twice as Big?

Age 7 to 11 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 ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

...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?

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.

Age 14 to 18 Challenge Level:

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

Curve Fitter 2

Age 16 to 18 Challenge Level:

Can you construct a cubic equation with a certain distance between its turning points?

Conway's Chequerboard Army

Age 11 to 14 Challenge Level:

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

Square Tangram

Age 7 to 11 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?

Age 7 to 11 Challenge Level:

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

Ding Dong Bell Interactive

Age 16 to 18 Challenge Level:

Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.

Grouping Transformations

Age 11 to 18

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

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?

Footprints

Age 16 to 18 Challenge Level:

Make a footprint pattern using only reflections.

Mathematical Patchwork

Age 7 to 14

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

Parallel Parking

Age 14 to 16

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.

Sorting Symmetries

Age 7 to 11 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

Age 7 to 14

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

Age 7 to 14

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

Age 11 to 14 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

Age 11 to 14 Challenge Level:

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

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?

Bow Tie

Age 11 to 14 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.

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.

Transformations Tables

Age 7 to 11 Challenge Level:

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

Trees and Friezes

Age 11 to 14 Challenge Level:

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

Friezes Using Logo

Age 11 to 14 Challenge Level:

Experimenting with variables and friezes.

World of Tan 30 - Logical Thinking

Can you logically construct these silhouettes using the tangram pieces?

World of Tan 29 - the Telephone

Age 7 to 11 Challenge Level:

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

World of Tan 28 - Concentrating on Coordinates

Age 7 to 11 Challenge Level:

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

World of Tan 27 - Sharing

Age 7 to 11 Challenge Level:

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

World of Tan 26 - Old Chestnut

Age 7 to 11 Challenge Level:

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

World of Tan 25 - Pentominoes

Age 7 to 11 Challenge Level:

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

World of Tan 24 - Clocks

Age 7 to 11 Challenge Level:

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

World of Tan 23 - Transform This...into...that

Can you fit the tangram pieces into these outlines?

World of Tan 22 - an Appealing Stroll

Age 7 to 11 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

Age 7 to 11 Challenge Level:

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

World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

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

World of Tan 19 - Working Men

Age 7 to 11 Challenge Level:

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

World of Tan 18 - Soup

Age 7 to 11 Challenge Level:

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

World of Tan 17 - Weather

Age 7 to 11 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

Age 7 to 11 Challenge Level:

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

World of Tan 15 - Millennia

Age 7 to 11 Challenge Level:

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

World of Tan 14 - Celebrations

Age 7 to 11 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

Age 7 to 11 Challenge Level:

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

World of Tan 12 - All in a Fluff

Age 7 to 11 Challenge Level:

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