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Resources tagged with Compound transformations similar to Shaping up with Tessellations:

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Broad Topics > Transformations and constructions > Compound transformations

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. . . .

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?

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?

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?

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.

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. . . .

Mirror, Mirror...

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

Grouping Transformations

Age 11 to 18

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

Mathematical Patchwork

Age 7 to 14

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

Frieze Patterns in Cast Iron

Age 11 to 16

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

The Frieze Tree

Age 11 to 16

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Transformation Game

Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game?

...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

Making Rectangles, Making Squares

Age 11 to 14 Challenge Level:

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

Friezes Using Logo

Age 11 to 14 Challenge Level:

Experimenting with variables and friezes.

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.

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.

Trees and Friezes

Age 11 to 14 Challenge Level:

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

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.

Transformations Tables

Age 7 to 11 Challenge Level:

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

Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

World of Tan 5 - Rocket

Age 7 to 11 Challenge Level:

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

World of Tan 9 - Animals

Age 7 to 11 Challenge Level:

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

World of Tan 2 - Little Ming

Age 7 to 11 Challenge Level:

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

Flight of the Flibbins

Age 11 to 14 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. . . .

World of Tan 3 - Mai Ling

Age 7 to 11 Challenge Level:

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

World of Tan 10 - Butterflies

Age 7 to 11 Challenge Level:

Can you use the interactive to complete the tangrams in the shape of butterflies?

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?

World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Counting Triangles

Age 11 to 14 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?

Triangular Tantaliser

Age 11 to 14 Challenge Level:

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

Screwed-up

Age 11 to 14 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?

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?

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.

Square to L

Age 7 to 11 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.

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 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 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 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 24 - Clocks

Age 7 to 11 Challenge Level:

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

World of Tan 29 - the Telephone

Age 7 to 11 Challenge Level:

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

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?

Cutting Corners

Age 7 to 11 Challenge Level:

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Cut and Make

Age 7 to 11 Challenge Level:

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

World of Tan 6 - Junk

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the silhouette of the junk?

Chess

Age 11 to 14 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?