# Mathematics- annotated exemplars level 1 AS91030

## Apply measurement in solving problems (1.5)

 Read the STANDARD TKI mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 298KB)

### Low Excellence

Commentary
Student response

Student 1 (PDF, 64KB)

For Excellence, the student needs to apply measurement, 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 TKI assessment resource ‘Garden Sculpture’.

This student has devised a strategy to investigate or solve a problem by designing a sculpture (1) finding the length of the surrounding fence (2), the area of the paved surround (3) the total volume of the sculpture (4) and the dimensions of the blocks from which the pieces would be carved (5). They have begun to investigate the minimum volume of the crate (6). The student has used correct mathematical statements throughout the response.

For a more secure Excellence, the student would need to find the minimum volume of stone needed for the sculpture, and justify why the dimensions of the crate are a minimum. For example, they could do this by referring to the position of the pieces in the crate, and adjusting the height to provide some space between the pieces and the top of the crate.

### High Merit

Commentary
Student response

Student 2 (PDF, 57KB)

For Merit, the student needs to apply measurement, 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 ‘Garden Sculpture’.

This student has carried out a logical sequence of steps by designing a sculpture (1), finding the length of the surrounding fence (2), the area of the paved surround (3), the total volume of the sculpture (4), the dimensions of the blocks from which the pieces would be carved (5) and the minimum volume of stone needed (6). The student has communicated thinking using appropriate mathematical statements.

To reach Excellence, the student would need to investigate the minimum volume of a crate that the pieces of the sculpture will fit into neatly, for example, by considering that the pieces could be separated and adjusting the dimensions of the base so that there is some space between the pieces and the sides of the crate.

### Low Merit

Commentary
Student response

Student 3 (PDF, 60KB)

For Merit, the student needs to apply measurement, 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 ‘Garden Sculpture’.

This student has carried out a logical sequence of steps by designing a sculpture (1) finding the length of the surrounding fence (2), the total volume of the sculpture (3), the dimensions of the blocks from which the pieces would be carved (4) and the minimum volume of stone needed for the sculpture (5). The student has communicated thinking using appropriate mathematical statements.

For a more secure Merit, the student would need to correctly calculate the area of paving around the sculpture, begin to consider how the blocks might be placed in a crate to minimize the volume, and round appropriately throughout their work.

### High Achieved

Commentary
Student response

Student 4 (PDF, 45KB)

For Achieved, the student needs to apply measurement in solving problems.

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

This student’s evidence is a response to the TKI assessment resource ‘Garden Sculpture’.

This student has designed a sculpture (1) found the area of the paved surround (2), the volumes of the pieces that make up the sculpture (3) and the total volume of the sculpture (4).

To reach Merit, the student would need to find the length of the fence, together with the dimensions and volumes of the blocks required to make all of the pieces.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 57KB)

For Achieved, the student needs to apply measurement in solving problems.

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

This student’s evidence is a response to the TKI assessment resource ‘Garden Sculpture’.

This student has designed a sculpture (1), found the length of the surrounding fence (2), the area of the paved surround (3), the volumes of the pieces that make up the sculpture (4) and the total volume of the sculpture (5).

For a more secure Achieved, the student would need to improve the communication of the solution. For example, they could do this by indicating what each calculation represents and including measurements on the diagram of the sculpture.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 57KB)

For Achieved, the student needs to apply measurement in solving problems.

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

This student’s evidence is a response to the TKI assessment resource ‘Garden Sculpture’.

This student has used units correctly throughout their work and found the length of the fence (1). The calculation for the cylinder is incorrect (2). Calculating the volume of a cuboid is at too low a level of the curriculum to provide evidence of selecting and using a method (3).

To reach Achieved, the student would need to provide evidence of selecting and using another method in the solving of a problem (to demonstrate more range), and provide calculations that are at the appropriate curriculum level. For example, the student could do this by finding the correct volumes of the cylinder and the total sculpture.