Search by Topic

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 71 results

Broad Topics > Transformations and their Properties > Compound transformations

problem icon

Who Is the Fairest of Them All?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore the effect of combining enlargements.

problem icon

...on the Wall

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the effect of reflecting in two intersecting mirror lines.

problem icon

Mirror, Mirror...

Stage: 3 Challenge Level: Challenge Level:1

Explore the effect of reflecting in two parallel mirror lines.

problem icon

Transformation Game

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Why not challenge a friend to play this transformation game?

problem icon

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.

problem icon

Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Twice as Big?

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Square Tangram

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Advent Calendar 2006

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Sketching Families of Graphs

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

In this trail, a new type of NRICH resource, learn about transformations of graphs. Given patterns made from families of graphs find all the equations in the family.

problem icon

Grouping Transformations

Stage: 3, 4 and 5

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

problem icon

Simplifying Transformations

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

Combining Transformations

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Decoding Transformations

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Mathematical Patchwork

Stage: 2 and 3

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

problem icon

Sorting Symmetries

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

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. . . .

problem icon

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. . . .

problem icon

Squares, Squares and More Squares

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Matching Frieze Patterns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Transforming the Letters

Stage: 2 Challenge Level: Challenge Level:1

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

problem icon

Bow Tie

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Transformations Tables

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Trees and Friezes

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Friezes Using Logo

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Experimenting with variables and friezes.

problem icon

World of Tan 29 - the Telephone

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 28 - Concentrating on Coordinates

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 27 - Sharing

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 26 - Old Chestnut

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 25 - Pentominoes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 24 - Clocks

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 22 - an Appealing Stroll

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 21 - Almost There Now

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 20 - Fractions

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 19 - Working Men

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 18 - Soup

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 17 - Weather

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 16 - Time Flies

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 15 - Millennia

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 14 - Celebrations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 13 - A Storm in a Tea Cup

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 12 - All in a Fluff

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 11 - the Past, Present and Future

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 10 - Butterflies

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

problem icon

World of Tan 9 - Animals

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 8 - Sports Car

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 7 - Gat Marn

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 6 - Junk

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 5 - Rocket

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

World of Tan 4 - Monday Morning

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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