# Mathematics and Statistics - annotated exemplars level 2 AS91268

## Investigate a situation involving elements of chance using a simulation (2.13)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 652KB)

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 work extract

Student 1 (PDF, 194KB)

For Excellence, the student needs to investigate a situation involving elements of chance using a simulation, with statistical insight.

This involves integrating statistical and contextual knowledge throughout the simulation process and may involve reflecting about the process, or considering other variables.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has designed a simulation for a given situation by identifying the tool to be used (1), defining a trial and deciding the number of trials (2) and determining data recording methods (3).

They have also carried out the simulation and recorded the outcomes (4), selected and used appropriate displays and measures (5) and communicated findings in a conclusion (6).

The student has reflected on the process by linking the assumptions to the design of the simulation (7).

For a more secure Excellence, the student could consider other variables. For example, by considering a simulation for a situation where two friends swap symbols so that they can collect a set more quickly.

The student could also develop the comment about the simulation results being different if the experiment was repeated, by providing an explanation for the results being estimates.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 181KB)

For Merit, the student needs to investigate a situation involving elements of chance using a simulation, with justification.

This involves linking components of the simulation process to the context, explaining relevant considerations made in the design of the simulation, and supporting findings with statements which refer to evidence gained from the simulation.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has designed a simulation for a given situation by identifying the tool to be used (1), defining a trial and deciding the number of trials (2) and determining data recording methods (3).

They have also carried out the simulation and recorded the outcomes (4), selected and used appropriate displays and measures (5) and communicated findings in a conclusion (6).

The student has explained relevant considerations made in the design of the simulation (7) and supported findings with statements which refer to evidence from the simulation (8).

To reach Excellence, the student could clearly link the assumptions to the design of the simulation and provide a fuller explanation for the probability and mean being estimates.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 129KB)

For Merit, the student needs to investigate a situation involving elements of chance using a simulation, with justification.

This involves linking components of the simulation process to the context, explaining relevant considerations made in the design of the simulation, and supporting findings with statements which refer to evidence gained from the simulation.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has designed a simulation for a given situation by identifying the tool to be used (1), defining a trial and deciding the number of trials (2) and determining data recording methods (3).

They have also carried out the simulation and recorded the outcomes (4), selected and used appropriate displays and measures (5) and communicated findings in a conclusion (6).

The student has explained relevant considerations made in the design of the simulation (7) and supported findings with statements which refer to evidence from the simulation (8).

For a more secure Merit, the student would need to expand on the assumptions made in designing the simulation.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 169KB)

For Achieved, the student needs to investigate a situation involving elements of chance using a simulation.

This involves showing evidence of using each component of the simulation process.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has designed a simulation for a given situation by identifying the tool to be used (1), defining a trial and deciding the number of trials (2) and determining data recording methods (3).

They have also carried out the simulation and recorded the outcomes (4), selected and used appropriate displays and measures (5) and communicated findings in a conclusion (6).

To reach Merit, the student would need to discuss assumptions made in designing the simulation.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 136KB)

For Achieved, the student needs to investigate a situation involving elements of chance using a simulation.

This involves showing evidence of using each component of the simulation process.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has designed a simulation for a given situation by identifying the tool to be used (1), defining a trial and deciding the number of trials (2) and determining data recording methods (3).

They have also carried out the simulation and recorded the outcomes (4), selected and used appropriate displays and measures (5) and communicated findings in a conclusion (6).

For a more secure Achieved, the student could strengthen the findings by more clearly communicating the probability of winning a movie ticket. The student could also calculate the mean number of days Grace will buy ice blocks.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 100KB)

For Achieved, the student needs to investigate a situation involving elements of chance using a simulation.

This involves showing evidence of using each component of the simulation process.

This student’s evidence is a response to the TKI assessment resource ‘Fruity Freezes’.

The student has defined a trial and decided the number of trials (1), determined data recording methods (2), carried out the simulation and recorded the outcomes (3) and selected and used appropriate displays and measures (4).

To reach Achieved, the student would need to identify the tool used in the simulation and clearly communicate the findings in a conclusion.