Transformations

A transformation moves a shape to a new position without changing its size or shape. You can slide it (a translation), flip it over a mirror line (a reflection) or turn it about a point (a rotation). In this topic you'll draw and describe all three on grids and on the number plane, use coordinates to track where each point goes, and combine several moves one after the other. You'll also find out which shapes tessellate and look for line and rotational symmetry in shapes, letters and designs.

What you'll learn

• 14.01 Transformation of shapes: objects and images, and how to tell a translation, a reflection and a rotation apart.
• 14.02 Translations: sliding points and shapes left or right and up or down, and describing translations in words and with coordinates.
• 14.03 Reflections: reflecting shapes in mirror lines, including the x-axis and the y-axis, and finding a mirror line.
• 14.04 Rotations: turning shapes by 90°, 180° and 270° about the origin and about other points, clockwise and anticlockwise.
• 14.05 Multiple transformations: doing two or three transformations in a row, working backwards, and finding one move that does the same job.
• Investigation: which regular polygons tessellate, and why? Test them with cut-out shapes, then design your own tessellating tile.
• 14.06 Line and rotational symmetry: finding lines of symmetry and the order of rotational symmetry, and completing symmetrical designs.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler shapes and moves on small grids, with more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: coordinate rules, finding mirror lines and centres of rotation, working backwards and harder puzzles, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes. When a question asks you to draw an image, draw it on the grid printed on the worksheet with a sharp pencil and a ruler. Tracing paper is a big help for reflections and rotations.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.