Grades 3–5Geometry & TopologyPlanned
Symmetry: slides, turns and flips
Line and rotational symmetry, and moving shapes by slides (translations), turns (rotations) and flips (reflections), including doing one move after another and undoing a move.
math.geom.symmetry-transformations
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 1
You will learn to
- Identify lines of symmetry and the order of rotational symmetry of shapes.
- Perform slides, turns and flips on a grid and describe them precisely.
- Find a move that undoes a given move, and explore what happens when two flips are done one after the other.
Definition
- A line of symmetry divides a shape into two mirror-image halves.
- A shape has rotational symmetry of order n if exactly n turns within one full revolution (including the full turn) leave it looking the same.
- A slide moves every point the same distance in the same direction; a turn rotates about a fixed point; a flip reflects in a line.
Theorem
- A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
- Slides, turns and flips do not change lengths or angles.
- Flipping twice in the same line returns every point to where it started.
- Two flips in parallel lines give a slide, and two flips in crossing lines give a turn about the crossing point.
Common misconceptions
- Thinking the diagonals of every rectangle are lines of symmetry; this is true only for squares.
- Believing a flip and a half turn always have the same effect.
Leads to
Optional discoveries
- Groups The symmetries of a shape can be combined and undone; together they form a group, such as the 8-element dihedral group of a square.
- One thing after another Doing one move after another, and undoing a move, are early examples of composing and reversing actions.