# Search by Topic

Filter by: Content type:
Stage:
Challenge level:

### There are 82 results

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.

##### Stage: 4 and 5 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

##### Stage: 5 Challenge Level:

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

### 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.

### Ding Dong Bell Interactive

##### Stage: 5 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

##### 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?

### Footprints

##### Stage: 5 Challenge Level:

Make a footprint pattern using only reflections.

### Mathematical Patchwork

##### Stage: 2 and 3

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

### Parallel Parking

##### Stage: 4

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

##### 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.

### Reflect Again

##### Stage: 5 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

##### Stage: 5 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

##### 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 30 - Logical Thinking

##### Challenge Level:

Can you logically construct these silhouettes using the tangram pieces?

### 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 23 - Transform This...into...that

##### Challenge Level:

Can you fit the tangram pieces into these outlines?

### 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?