# Mathematics and Statistics - annotated exemplar Level 3 AS91576

## Use critical path analysis in solving problems (3.4)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 1.1MB)

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 June 2019.

All annotations have been changed to include the assessment resource that was used to collect the student evidence. High Not Achieved has also been altered to better illustrate the requirements of the standard.

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 228KB)

For Excellence, the student needs to use critical path analysis, with 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 task ‘The new shopping mall’.

The student has identified relevant concepts in context by drawing a correct network diagram (1), giving the correct critical path (2), scheduling the activities (3), discussing float times (4) and discussing the impact on the critical path of any other delays that are significant enough to extend the projects minimum completion time (5).

The student has used correct mathematical statements throughout the response.

For a more secure Excellence, the student could clearly communicate when the manager can visit the site to see three tasks being done, by referring to the possible scheduling of activity D.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 219KB)

For Merit, the student needs to use critical path analysis, with relational thinking, in solving problems.

This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts or 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 task ‘The new shopping mall’.

The student has connected different concepts or representations by drawing a correct network diagram (1), giving the correct critical path (2) and completing the scheduling using a Gantt chart (3).

They have also completed a backward and forward scan, allocated supervisors, determined the time for the manager’s visit and included a discussion of varying start times for task D (4).

The student started to discuss the float times for other tasks (5), and related the findings to the context throughout the response.

To reach Excellence, the student could develop the investigation of delays to tasks other than task D.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 233KB)

For Merit, the student needs to use critical path analysis, with relational thinking, in solving problems.

This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts or 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 task ‘The new shopping mall’.

The student has connected different concepts or representations by drawing a correct network diagram (1), giving the correct critical path (2) and completing the scheduling (3). They have also completed a backward and forward scan, allocated supervisors and determined the time for the manager’s visit (4).

For a more secure Merit, the student could consider the implications of varying start times for task D which do not delay the project, and fully justify the impact on the project if task D were to take longer than three weeks to complete.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 181KB)

For Achieved, the student needs to use critical path analysis in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is a response to the TKI task ‘The new shopping mall’.

The student has selected and used a network diagram (1), identified the critical events for the project (2) and completed scheduling using a Gantt chart (3). They have also demonstrated knowledge of these concepts and terms and communicated using appropriate representations.

To reach Merit, the student could provide further explanation as to why they would recommend the manager visits during weeks 6 to 10, and discuss in more detail what could happen if task D was delayed by more than 2 weeks.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 116KB)

For Achieved, the student needs to use critical path analysis in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is a response to the TKI task ‘The new shopping mall’.

The student has selected and used a network diagram (1) and identified the critical events for the project (2). They have also demonstrated knowledge of these concepts and terms and communicated using appropriate representations.

For a more secure Achieved, the student could give the length of the critical path in context and discuss the scheduling of tasks, and/or discuss the float times of all activities.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 56KB)

For Achieved, the student needs to use critical path analysis in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representation

This student’s evidence is a response to the TKI task ‘The new shopping mall’.

The student has selected and used a network diagram (1).

To reach Achieved, the student needs to select and use at least one more method from Explanatory Note 4, for example the student could state what activities form the critical path.