Patterns on tiles, cloth and floors are built from a few moves repeated: slide, flip, turn and scale. This unit starts with the moves themselves on a coordinate grid, with a rule for each, and asks what each one keeps and what it changes. Three of them keep every length and angle, and the fourth keeps only the shape.
Then the moves are combined and described fully, and the last lesson asks a question every tile maker meets: which shapes will cover a floor with no gaps? The answer comes from the angles that meet at a corner. No calculator is needed in this unit.
The lessons, in order
- Lesson 1 · Translations: sliding a shape Naming a pre-image and an image, translating a point or a shape by a vector, and finding the vector from a pre-image and its image. Slide a triangle with two sliders, then find the vector that carries it onto a given image. No calculator
- Lesson 2 · Reflections: flipping over a mirror line Reflecting points and shapes in the axes, the line y = x and lines such as x = 3, and using equal distances from the mirror. Reflect a triangle in four mirror lines, then slide a mirror and watch every corner stay as far from it as its image. No calculator
- Lesson 3 · Rotations: turning about a centre Rotating points and shapes through 90 and 180 degrees about the origin and about another point, and describing a rotation with centre, angle and direction. Turn a triangle a quarter turn each way and a half turn, then move the centre of the turn. No calculator
- Lesson 4 · Enlargements: changing size, keeping shape Enlarging and reducing points and shapes from the origin by a scale factor, finding a scale factor, and how lengths, angles and areas change. Multiply the corners of a triangle by a scale factor, then compare lengths, angles and area before and after. No calculator
- Lesson 5 · Combining and describing transformations Performing two transformations in order, describing a transformation fully from a pre-image and image, and deciding whether it is a congruence or a similarity transformation. Reflect and translate in both orders and compare, then see what each of the four types keeps. No calculator
- Lesson 6 · Tessellations: which shapes tile a plane Interior angles of regular polygons, why angles at a vertex must sum to 360 degrees, regular tessellations and semi-regular tessellations. Put copies of a regular polygon round a point and see the gap, then try mixed polygons for 360 degrees exactly. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.