# GM4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).

This means students will know invariant properties are those features of a figure that do not change as it is reflected, rotated, translated or enlarged.

Under rotation lengths, areas, angles do not change but orientation does.

Under reflection lengths, areas and angles do not change but orientation does.

Under translation lengths, areas, angles and orientation do not change.

Under positive enlargement angles and orientation do not change but lengths and areas do.

At Level Four students should be able to use the above invariant properties to create symmetrical patterns such as tessellations, logos and friezes, and to create enlarged copies of graphics.

- Understand and describe proportion using the language of mathematics.
- Make accurate metric length measurements.
- Understand the principles of scale.
- Understand that the value of the scale factor of a reduction is less than 1 and for an enlargement is greater than 1.
- Understand that the scale300

design a logo using transformation elements

enlarge a two dimensional shape using a scale factor

explore transformations through tessellations

explore fractals

- Create regular and semi-regular tessellations of the plane.
- Demonstrate why a given tessellation will cover the plane.

- Recognising translation, reflection and rotation in designs.
- Using combinations of transformations to create a pattern.
- Carrying out enlargements.

- Using a map grid reference to locate a position and to give and follow directions.
- Using compass directions and angles of turn to give directions
- Using the scale on a map to determine distances.

explore fractals

explore the properties of shapes under enlargement

identify attributes of polygons

rotate an object

describe patterns using the language of transformation

**Session One **

- Recognise the properties of a figure stay constant as the figure is rotated (turned).
- Use compass directions to locate objects.
- Represent the relationship between numeric variables using tables and graphs.

**Session Two **

- Collect, sort and display multivariate data to find300

- Students will be able to express the enlargement relationship between two figures in multiplicative terms.
- Students will be able to transform an existing image to a specified enlargement.

describe patterns using the language of transformation

explore rotational symmetry

explore symmetry in geometric patterns

explore rotational symmetry

- follow instructions, in diagram form, to construct two-dimensional mathematical shapes, e.g. triangles, quadrilaterals, pentagons and hexagons
- enlarge and reduce two-dimensional mathematical shapes by a given scale factor
- identify invariant properties when enlarging and reducing two-dimensional300

- Alter polygons to create unique shapes that tessellate.
- Describe the reflection or rotational symmetry of a shape or tessellation.