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.
- Understand the principles of scale.
- Create scale drawings.
- Calculate scale dimensions.
- Make accurate metric length measurements.
- Understand that the value of the scale factor of a reduction is less than 1 and for an enlargement is300
design a logo using transformation elements
enlarge a two dimensional shape using a scale factor
explore transformations through tessellations
explore fractals
explore fractals
explore the properties of shapes under enlargement
identify attributes of polygons
rotate an object
describe patterns using the language of transformation
- Create geometric shapes that satisfy the no three in a line condition on 4 by 4 grids.
- Devise a systematic approach to find possible outcomes.
- Use symmetry as a game strategy.
- Apply problem solving strategies to a game context.
- Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
- Make conjectures in a mathematical context.
- Critically follow a chain of reasoning.
- 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 two300
- Alter polygons to create unique shapes that tessellate.
- Describe the reflection or rotational symmetry of a shape or tessellation.
- Recognise invariant properties of tessellations.
- Apply invariant properties to continue and complete given tessellating patterns.
- Use translations, rotations and reflections to create Escher-type tessellations.
- Apply knowledge of tessellations to the creation of a piece of art.
- Recognise and invent patterns with reflection symmetry.
- Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).
- Recognise when one figure is a reflection of another using invariant properties such as perpendicular distance from the mirror line, equalities of lengths, areas and angles, and opposite orientation in relation to the mirror line.
- Recognise the rotational symmetry of a figure, including identifying300