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There are **40** NRICH Mathematical resources connected to **Compound transformations**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### Twice as Big?

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Who is the fairest of them all ?

Explore the effect of combining enlargements.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### ...on the Wall

Explore the effect of reflecting in two intersecting mirror lines.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mirror, Mirror...

Explore the effect of reflecting in two parallel mirror lines.

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Transformation Game

Why not challenge a friend to play this transformation game?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Paint Rollers for Frieze Patterns.

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Which Quadratic?

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Tangram

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

Article
Primary curriculum
Secondary curriculum
### Grouping Transformations

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

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Simplifying Transformations

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Combining Transformations

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Decoding Transformations

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

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Mathematical Patchwork

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

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Maurits Cornelius Escher

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 intertwined.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Going Places with Mathematicians

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 things.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Squares, Squares and More Squares

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matching Frieze Patterns

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transforming the Letters

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bow Tie

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reflect Again

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rots and Refs

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformations Tables

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trees and Friezes

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

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### The Use of Mathematics in Computer Games

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Frieze Tree

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

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Frieze Patterns in Cast Iron

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

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Making Rectangles, Making Squares

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Midpoint Triangle

Can you cut up a square in the way shown and make the pieces into a triangle?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square to L

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flight of the Flibbins

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 the new planet?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangular Tantaliser

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counting Triangles

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squaring the Rectangle

Can you find a way to turn a rectangle into a square?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Screwed-up

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut and Make

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cutting Corners

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

Age 7 to 11

Challenge Level