In what ways might symmetry characterize shape?

Students investigate symmetry as a geometric property.

A 2-D shape has reflection symmetry if there is a straight line over which the shape reflects and the two halves exactly match.

A 3-D shape has reflection symmetry if there is a plane over which the shape reflects and the two halves exactly match.

A 2-D shape has rotation symmetry if it exactly overlaps itself one or more times within a rotation of less than 360° around its centre point.

Order of rotation symmetry describes the number of times a shape coincides with itself within a rotation of 360° around its centre point.

Central symmetry is the rotational symmetry by 180°.

The straight line that connects a point with its image in the central symmetry passes through the centre of rotation.

Symmetry can be found in First Nations, Métis, and Inuit designs, such as

• basket weaving

• wampum belts

• quilts

• First Nations beadwork, Inuit beadwork, or Métis floral beadwork

• architecture such as tipis or longhouses

In a regular polygon, the number of sides equals the number of reflection symmetries and the number of rotation symmetries.

A circle has infinitely many reflection and rotation symmetries.

Symmetry is a property of shapes.

Symmetry can be created and can occur in nature.

Symmetry is related to other geometric properties.

How can location enhance the ways in which space is defined?

Students relate location to position on a grid.

Coordinate grids use coordinates to indicate the location of the point where the vertical and horizontal grid lines intersect.

Coordinates are ordered pairs of numbers in which the first number indicates the distance from the vertical axis and the second number indicates the distance from the horizontal axis.

Positional language includes

• left

• right

• up

• down

Location can describe the position of shapes in space.

Location can be described precisely using a coordinate grid.