Level 1

91034: Apply transformation geometry in solving problems

Updated May 2019. The sections dealing with ‘Relational thinking’ and ‘Extended abstract thinking’ have been incorporated into a new section headed ‘Communicating solutions’. The section ‘Expected evidence for Achieved’ has been removed.

This standard is quite specialised, with a focus on applications of reflection, rotation, translation and enlargement, and the associated properties of symmetry and invariance.

Solving problems

For the award of the standard, students must apply transformation geometry in solving problems. To provide evidence, student responses need to clearly relate to the context of the problem. For example, if the context is a cartoon character, the student response needs to be clearly seen as a cartoon character, rather than as a series of unrelated transformations.

The problem needs to provide sufficient scope for students to demonstrate and develop their own thinking. If there are parts to the problem, all of the parts need to contribute to the solution.

Students also need to select and use the transformations. This means that a task which provided an object or objects and a set of instructions to transform the object(s) would not allow the student to meet the standard.

Communicating solutions

At all levels there is a requirement relating to the communication of the solutions.

At Achieved, there would need to be evidence of the transformations being identified.

At Merit, it is likely that the evidence will include accurately describing the transformations used in the solution.

The descriptions need to enable the transformations to be positioned correctly, so the object would need to be identified along with the following detail:

• the mirror line for a reflection
• the centre and angle for a rotation
• the centre and scale factor for an enlargement
• the magnitude and direction of shift for a translation, which could be described in words or using a vector.

At Excellence, it is likely that the evidence would involve describing the use of the properties of the transformations. This could include communicating an understanding of invariance or inverse transformations.