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GM5-9: Define and use transformations and describe the invariant properties of figures and objects under these transformations.

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Elaboration on this Achievement Objective

This means that students will accurately describe the transformation a figure or object has undergone and describe the invariant properties. At Level Five this will include the angle and centre of rotation, the distance and direction of translation, the magnitude and centre of enlargement (including fractional changes for example 1 1/2), and the line of reflection. Students will also draw the results of transformations on objects. 

Students will be able to describe which properties of shapes change for each transformation:

  1. Under rotation lengths, areas, angles do not change but orientation does.
  2. Under reflection lengths, areas and angles do not change but orientation does.
  3. Under translation lengths, areas, angles and orientation do not change.
  4. Under positive enlargement angles and orientation do not change but lengths and areas do.

 

 

Teaching resources for this Achievement Objective
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Ancient Architecture

Level Five
Integrated
Figure It Out activities
This is a level 5 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

investigate ratios when enlarging

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No three in a line again

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a logic and reasoning focus.
  • Use symmetry and rotation to create geometric shapes that satisfy the no three in a line condition.
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Pizza pans

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in using ratios to find a common ratio (scale factor).
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Russian Boxes

Level Five
Geometry and Measurement
Units of Work
In this unit a number of small boxes are produced (by folding), that fit inside one another like Russian dolls. Lengths are measured and areas and volumes are calculated in order to make scale comparisons.
  • Find the scale factors for length, area and volume.
  • Identify the center point of an enlargement.
  • Place similar objects to show a negative enlargement.
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Scale Factors for Areas and Volumes

Level Five
Integrated
Units of Work
This unit of work provides students with the opportunity to discover the effect of a change of length by a given factor on area and volume.
  • Use scale factors to investigate areas being enlarged.
  • Use scale factors to investigate volumes being enlarged.
  • Solve real life context problems involving scale factors.
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Steep Streets

Level Five
Geometry and Measurement
The purpose of this unit is to engage students in applying their knowledge and skills of measurement to investigate gradients, angles, elevation in a range of practical situations.
  • apply measurement sense
  • use problem solving methods to find unknown lengths and angles
  • find angles of elevation and apply these to problem solving
  • find gradients and apply these to problem solving
  • find and apply angles of elevation
  • compare and use gradients to find unknown lengths
  • use maps, measuring300
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Synchronised Swim Shapes

Level Five
Geometry and Measurement
The purpose of this unit is to engage students in applying their understanding of geometric thinking to design and describe formations and the translations and/or rotations needed to create those formations. This is explored in the context of choreographing a synchronised swimming routine and...
  • Find the size of angles. 
  • Describe the features of regular polygons, including the size of their interior angles. 
  • Apply knowledge of angles, quadrilaterals, and regular polygons to problem solving contexts.
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Transforming shapes

Level Five
Geometry and Measurement
Units of Work
This unit applies geometry and measurement concepts (tessellations, reflections, rotations, symmetry, circles, 3D shapes, nets) in the creation of bags, door stops and other fabric items.
  • Identify translation, vertical and horizontal reflection (line symmetry), rotational symmetry, total symmetry, glide reflections, and half turn rotations.
  • Use geometric concepts (translation, vertical and horizontal reflection and symmetry, glide reflections, and half turn rotations) create friezes300