Transformations and Symmetry

Students learn how to describe a shape’s reflective symmetry and identify the planes of symmetry in 3D shapes.  As learning progresses students perform and describe reflections, rotations, translations and enlargements on a grid.

This unit takes place in Term 6 of Year 7 and follows properties of shapes.


Transformations and Symmetry Lessons

 



Prerequisite Knowledge
  • Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
  • Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D.

Key Concepts
  • A mirror line or tracing paper can be used to check if a shape has a line of reflective symmetry.    A mirror line is called a line of reflective symmetry.
  • Students tend to find reflections in a diagonal line of symmetry more difficult than those in horizontal or vertical.
  • A plane of symmetry bisects a shape into halves that are mirror images of each other.
  • A 2D shape has rotational symmetry if it can be rotated so that it fits perfectly on itself in a new position.
  • The order of rotational is the number of positions the shape looks the same when it is rotated 360°.
  • A translation vector is used to describe a translation.
  • To rotate a shape a centre, direction and amount of turn is needed.  Students should use tracing paper when rotating shapes.
  • A positive scale factor greater than 1 increases the size of a shape.  A postive scale factor less than one decreases the size.  More advanced students should enlarge a shape from a centre.
  • Rotations, reflections and translations result in congruent shapes.  Enlargements result in similar shapes.


Working mathematically

Develop fluency

  • Use language and properties precisely to analyse 2-D and 3-D shapes.

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
    Begin to reason deductively in geometry including using geometrical constructions

Solve problems

  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Geometry and measures

  • Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
  • Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
  • Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
  • Interpret mathematical relationships both algebraically and geometrically.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

How Write 3 Part Ratios

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out.  This is presented to the class as they come into the lesson.    Writing Equivalent Ratios  A few students immediately go […]