NCEA

Mathematics - annotated exemplars level 1 AS91033

Apply knowledge of geometric representations in solving problems (1.8)

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TKI Mathematics and Statistics Assessment Resources	Download all these exemplars and commentary (PDF, 380KB)

Low Excellence

Commentary

Student response
Student 1 (PDF, 88KB)

For Excellence, the student needs to apply knowledge of geometric representations, using extended abstract thinking, in solving problems.

This involves one or more of: devising a strategy to investigate or solve a problem, 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 ‘Dig a little deeper’.

This student has identified relevant concepts in context in designing the garden using a scale diagram (1), two-dimensional co-ordinate systems (2), bearings (3) and a net (4). Correct mathematical statements have been used to describe these concepts.

Insight has been shown in the report on the design of the garden by the consideration of the locus of the shadow over the garden and the impact of colour on the design brief (5).

For a more secure Excellence, the student could consider the positioning of the shadow at different times of the day and year and describe more fully the dimensions of the raised flower beds.

High Merit

Commentary

Student response
Student 2 (PDF, 64KB)

For Merit, the student needs to apply knowledge of geometric representations, 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 TKI assessment resource ‘Logo Design’.

This student has demonstrated an understanding of concepts in designing the logo by using a scale drawing (1), a two-dimensional co-ordinate system (2), a construction (3) and a locus (4). Appropriate mathematical statements have been used throughout the instructions for creating the logo and for the sewing machine.

To reach Excellence, the student would need to provide more detailed instructions for sewing the logo from the inside of the garment.

Low Merit

Commentary

Student response
Student 3 (PDF, 73KB)

For Merit, the student needs to apply knowledge of geometric representations, using relational thinking, in solving problems.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Dig a little deeper’.

This student has demonstrated an understanding of concepts in designing the garden by using a scale drawing (1), a two-dimensional co-ordinate system (2), and bearings (3). Appropriate mathematical statements have been used throughout the design of the garden.

For a more secure Merit, the student would need to describe the location of the flower beds and identify more clearly how the plan can be used to construct the garden.

High Achieved

Commentary

Student response
Student 4 (PDF, 69KB)

For Achieved, the student needs to apply knowledge of geometric representations in solving problems.

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 TKI assessment resource ‘Logo Design’.

This student has, in designing the logo, selected and used a two-dimensional co-ordinate system (1), a construction (2) and a scale diagram (3). The instructions use correct geometrical concepts and terms.

To reach Merit, the student would need to clearly identify the position of the equilateral triangles, and start to modify the instructions for sewing the design backwards.

Low Achieved

Commentary

Student response
Student 5 (PDF, 68KB)

For Achieved, the student needs to apply knowledge of geometric representations in solving problems.

This student’s evidence is a response to the Vocational Pathways assessment resource ‘Dig a little deeper’.

This student has, in designing the garden, selected and used a two-dimensional co-ordinate system (1), bearings (2) and a scale diagram (3). The design uses correct geometrical concepts and terms.

For a more secure Achieved, the student would need to strengthen the communication in the response, for example, by indicating measurements, the direction of North on the diagram and linking the bearings to directions from one point to another on the diagram.

High Not Achieved

Commentary

Student response
Student 6 (PDF, 70KB)

For Achieved, the student needs to apply knowledge of geometric representations in solving problems.

This student’s evidence is a response to the TKI assessment resource ‘Logo Design’.

This student has, in designing the logo, selected and used a two-dimensional co-ordinate system (1) and a scale diagram (2).

To reach Achieved, the student would need to select and use one further method. For example, they could do this by identifying the centre of the circles and using loci to describe their colouring.