# 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.

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.

Teaching resources for this Achievement Objective

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.

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 scale factor...

Units of Work

Number and Algebra

Level Four

The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.

Rich learning activities

Geometry and Measurement

Level Four

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.

Rich learning activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.

design a logo using transformation elements

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.

enlarge a two dimensional shape using a scale factor

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore transformations through tessellations

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.A PDF of the student activity is included.

explore fractals

Figure It Out activities

Geometry and Measurement

Level Four

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...

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

Units of Work

Geometry and Measurement

Level Four

This interactive learning module supports students to use, and describe the effects of, reflection, rotation, translation and enlargement.

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

Student e-Ako

Geometry and Measurement

Level Four

This interactive learning module supports students to use a map's scale and compass bearings to describe locations and give directions.

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.

Student e-Ako

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore fractals

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

explore the properties of shapes under enlargement

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

identify attributes of polygons rotate an object

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

describe patterns using the language of transformation

Figure It Out activities

Geometry and Measurement

Level Four

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...

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 find patterns and...

Units of Work

Geometry and Measurement

Level Four

This activity has a logic and reasoning focus.

create geometric shapes that satisfy the no three in a line condition on 4 by 4 grids. devsie a systematic approach to find possible outcomes

Problem solving activities

Geometry and Measurement

Level Four

Use symmetry as a game strategyApply problem solving strategies to a game contextDevise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment)Make conjectures in a mathematical contextCritically follow a chain of reasoning

Problem solving activities

Geometry and Measurement

Level Four

The purpose of this activity is to engage students in applying transformations to create repeating tiling patterns.

Rich learning activities

Geometry and Measurement

Level Four

This is an activity based on the picture book Re-Zoom

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.

Picture book activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

describe patterns using the language of transformation

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore rotational symmetry

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

explore symmetry in geometric patterns

Figure It Out activities

Geometry and Measurement

Level Four

This is a level 4 geometry strand activity from the Figure It Out series.

explore rotational symmetry

Figure It Out activities

Geometry and Measurement

Level Four

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...

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-dimensional...

Units of Work

Geometry and Measurement

Level Four

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. All M. C. Escher works (C) Cordon Art, Baarn, the Netherlands. All rights reserved. Used by permission.

alter polygons to create unique shapes that tessellate describe the reflection or rotational symmetry of a shape or tessellation

Units of Work

Geometry and Measurement

Level Four