# Mathematics - annotated exemplars level 1 AS91032

## Apply right-angled triangles in solving measurement problems (1.7)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 823KB)

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.

Last updated May 2019.

There is new student evidence for the Low Excellence exemplar for this standard.

The annotations to the Low Excellence and Low Merit have been altered to better illustrate the requirements of the standard.

### Low Excellence

Commentary
Student response

Student 1 (PDF, 225KB)

For Excellence, the student needs to apply right-angled triangles, using extended abstract thinking, in solving measurement 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 TKI assessment resource ‘Demolition RATs’.

The student has devised a strategy to determine the perimeter of the new cafeteria (1), investigated whether the interior angles of the new cafeteria meet the Board requirement (2) and found the perimeter of both options for the enlarged cafeteria (3). Correct mathematical statements have been used throughout the response.

For a more secure Excellence, the student would need to develop the discussion about the enlarged cafeteria and clearly communicate the minimum perimeter.

### High Merit

Commentary
Student response

Student 2 (PDF, 160KB)

For Merit, the student needs to apply right-angled triangles, using relational thinking, in solving measurement 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 ‘What’s the Angle?’.

The student has selected and carried out a logical sequence of steps to correctly determine most of the dimensions of the sail (1) and the minimum dimensions of the van without including the extra 2.5 m in the length of the pole (2). Appropriate mathematical statements have been used throughout the response.

To reach Excellence, the student would need to determine all dimensions of the sail, relate the findings to the context by describing its shape, consider the extra 2.5 m in the length of the pole and identify the minimum dimensions of the van.

### Low Merit

Commentary
Student response

Student 3 (PDF, 119KB)

For Merit, the student needs to apply right-angled triangles, using relational thinking, in solving measurement 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 ‘What’s the Angle?’.

The student has selected and carried out a logical sequence of steps in calculating the lengths of AB (1) and AC (2) correctly, but there is a transfer error in calculating the angle in the sail (3).

The student has demonstrated relational thinking by considering the correct length of the pole in finding minimum dimensions for the van (4).

For a more secure Merit, the student would need to calculate the correct dimensions of the sail and relate the findings to the context by clearly describing the shape of the sail.

### High Achieved

Commentary
Student response

Student 4 (PDF, 99KB)

For Achieved, the student needs to apply right-angled triangles in solving measurement problems.

This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms, and communicating solutions which would usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘What’s the Angle?’.

The student has measured at a level of precision appropriate to the task, calculated the height of the pole (1), the length of one side of the sail (2) and an angle in the sail (3).

To reach Merit, the student would need to identify the shape and size of the sail and correctly link the length of the pole to the dimensions of the trailer.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 75KB)

For Achieved, the student needs to apply right-angled triangles in solving measurement problems.

This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms, and communicating solutions which usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘What’s the Angle?’.

The student has measured at a level of precision appropriate to the task, and calculated the height of the pole (1) and the length of one side of the sail (2).

For a more secure Achieved, the student would need to more clearly communicate what the second and third calculations represent.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 62KB)

For Achieved, the student needs to apply right-angled triangles in solving measurement problems.

This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms, and communicating solutions which usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘What’s the Angle?’.

The student has taken some measurements at a level of precision appropriate to the task and found the length of one edge of the sail (1). The student has not calculated the length of AB correctly.

To reach Achieved, the student would need to provide evidence of selecting and using another method correctly in solving the problem.