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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.

Which Quadratic?

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?

Advent Calendar 2006

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.

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.