NCEA

Mathematics - annotated exemplars level 1 AS91034

Apply transformation geometry in solving problems (1.9)

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This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

Low Excellence

Commentary

Student response
Student 1 (PDF, 98KB)

For Excellence, the student needs to apply transformation geometry, using extended abstract thinking, in solving problems.

This involves one or more of: devising a strategy to investigate a situation, identifying relevant concepts in context, developing a chain of logical reasoning, or proof, forming a generalisation and also using correct mathematical statements, or communicating mathematical insight.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has identified relevant concepts in context in designing the garden using rotations (1), translations (2), enlargement (3) and symmetry (4). Correct mathematical statements have been used to describe these concepts throughout the task. Insight has been shown by the consideration of the invariant features of the transformations (5) and of the impact of colour in describing the symmetries of the garden (6).

For a more secure Excellence, the student would need to strengthen the descriptions of invariance and the discussion of the impact of colour and height on the symmetry of the garden.

High Merit

Commentary

Student response
Student 2 (PDF, 77KB)

For Merit the student needs to apply transformation geometry, using relational thinking, in solving problems.

This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts and representations, demonstrating understanding of concepts, forming and using a model and also relating findings to a context, or communicating thinking using appropriate mathematical statements.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has demonstrated an understanding of concepts in designing the garden using and describing enlargement (1), reflections (2), rotation (3) and symmetry (4). Appropriate mathematical statements have been used throughout the response.

To reach Excellence, the student could produce the design of the finished garden, describe the symmetry of the garden and the invariant features of the transformations.

Low Merit

Commentary

Student response
Student 3 (PDF, 60KB)

For Merit, the student needs to apply transformation geometry, using relational thinking, in solving problems.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has demonstrated an understanding of concepts in designing the garden by using and describing the reflections (1), rotation (2), translation (3) and symmetry (4). Appropriate mathematical statements have been used in the response.

For a more secure Merit, the student would need to accurately describe the reflective and rotational symmetries in the design of their garden.

High Achieved

Commentary

Student response
Student 4 (PDF, 73KB)

For Achieved, the student needs to apply transformation geometry.

This involves selecting and using a range of methods in solving problems, demonstrating knowledge of geometrical concepts and terms and communicating solutions using geometrical terms or representations.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has, in designing the garden, selected and used a reflection (1) and a rotation (2). The student has identified line and rotational symmetries in the final design (3).

To reach Merit, the student would need to describe completely the transformations used in the design of the garden.

Low Achieved

Commentary

Student response
Student 5 (PDF, 68KB)

For Achieved, the student needs to apply transformation geometry.

This involves, selecting and using a range of methods in solving problems, demonstrating knowledge of geometrical concepts and terms and communicating solutions using geometrical terms or representations.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has selected and used a reflection (1), rotation (2) and translation (3) in designing the garden.

For a more secure Achieved, the student would need to identify the mirror line for the reflection and give more detail about the translation.

High Not Achieved

Commentary

Student response
Student 6 (PDF, 59KB)

For Achieved, the student needs to apply transformation geometry.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Geometric gardens’.

This student has selected and used a translation (1) and a rotation (2) in designing the garden.

To reach Achieved, the student would need to select and use one further method in designing the garden.