GM4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
Elaboration on this Achievement Objective
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.
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Under rotation lengths, areas, angles do not change but orientation does.
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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.
Teaching resources for this Achievement Objective
Level Four
Integrated
Units of Work
The purpose of this unit is for students apply and refine their measurement skills and to develop an understanding of enlargement and reduction, through making scale models to be used in a short animated film.
Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.
Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to provide students with the opportunity to explore the invariant properties of a shape under transformations, in order to complete a given design and to communicate the transformations necessary to achieve this design.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.
Level Four
Geometry and Measurement
Units of Work
This unit examines regular tessellations, that is, tessellations that can be made using only one type of regular polygon, and semi-regular tessellations, where more than one type of regular polygon is involved. Students are required to investigate what properties tessellating shapes must have in...
Level Four
Geometry and Measurement
Student e-Ako
This interactive learning module supports students to use, and describe the effects of, reflection, rotation, translation and enlargement.
Level Four
Geometry and Measurement
Student e-Ako
This interactive learning module supports students to use a map's scale and compass bearings to describe locations and give directions.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Integrated
Units of Work
This unit explores a variety of mathematics ideas in the context of Matariki. Matariki is a significant event in the New Zealand calendar and the Māori New Year is celebrated in many schools. Matariki is an opportunity to engage in activities such as storytelling, astronomy, song, dance, and visual...
Level Four
Integrated
Problem solving activities
This activity has a logic and reasoning focus.
Level Four
Geometry and Measurement
Problem solving activities
Level Four
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in applying transformations to create repeating tiling patterns.
Level Four
Geometry and Measurement
Picture book activities
This is an activity based on the picture book Re-Zoom
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 geometry strand activity from the Figure It Out series.
Level Four
Integrated
Units of Work
This unit requires students to enlarge and reduce the size of two-dimensional mathematical shapes by a scale factor. As students work in co-operative teams of four to complete a puzzle, they use a ruler, compass and protractor, and develop the ability to read and work through instructions to a...
Level Four
Geometry and Measurement
Units of Work
In this unit we apply our understanding of why tessellations work to form our own unique tessellating shapes. We use these shapes to create interesting pieces of art in the style of M.C. Escher, a famous Dutch artist.