Mathematics - annotated exemplars level 1 AS91038

Investigate a situation involving elements of chance (1.13)

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TKI Mathematics and Statistics Assessment Resources

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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, High Merit, Low Merit and High Achieved exemplars for this standard.

The annotations have been altered to better illustrate the requirements of the standard at all the grade boundaries.

Low Excellence

Commentary
Student response

Student 1 (PDF, 226KB)

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

This involves integrating contextual information and knowledge with an understanding of applications of probability and may involve considering the possible effects of other related variables or factors.

This student’s evidence is a response to the TKI assessment resource ‘Free Throw’.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), gathered data by performing the experiment (3), selected and used appropriate displays including experimental probability distributions (4), identified and communicated patterns in the data (5) and communicated findings in a conclusion (6).

They have also integrated contextual information and knowledge with an understanding of applications of probability in the investigation (7) and considered the possible effect of a related factor on the probability (8).

For a more secure Excellence, the student would need to strengthen the integration of contextual information and knowledge with an understanding of applications of probability. For example, they could give a reason(s) why they would expect these results and give a reason(s) for the final comment about the result not being like a real game.

High Merit

Commentary
Student response

Student 2 (PDF, 226KB)

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

This involves linking aspects of the investigation to the situation and making supporting statements which refer to evidence such as summary statistics, probabilities, trends or features of visual displays.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), selected and used appropriate displays including experimental probability distributions (3), identified and communicated patterns in the data (4), compared discrete theoretical distributions and experimental distributions (5) and communicated findings in a conclusion (6).

This student response also included evidence of gathering data by performing the experiment at an appropriate level for the award of Merit.

The student has linked aspects of the investigation, made comments about the distribution and provided supporting comments in context for the answer to the question (7).

To reach Excellence, this student would need to provide more detail and greater contextual understanding of the theoretical probability in their discussion. For example, the student could have drawn a side by side comparison graph and commented in detail about the experimental and theoretical probability.

The student should also explain why not including a total of 7 as a win would have influenced the probability of winning.

Low Merit

Commentary
Student response

Student 3 (PDF, 169KB)

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

This involves linking aspects of the investigation to the situation and making supporting statements which refer to evidence such as summary statistics, probabilities, trends or features of visual displays.

This student’s evidence is a response to the TKI assessment resource ‘Free Throw’.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), gathered data by performing the experiment (3), selected and used appropriate displays including experimental probability distributions (4), identified and communicated patterns in the data (5) and communicated findings in a conclusion (6).

The student has linked aspects of the investigation to the situation by calculating the average number of free throws that were successful out of three. The student has also made some supporting comments about the distribution (7).

For a more secure Merit, the student would need a more detailed discussion about the average and the comparison for 0 and 3 goals. They would also need to discuss the distribution more thoroughly by referring to additional evidence, and more clearly link the context back to the question and the conclusion.

High Achieved

Commentary
Student response

Student 4 (PDF, 196KB)

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

This involves using the experimental probability process.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), gathered data by performing the experiment (3), selected and used appropriate displays including experimental probability distributions (4), identified and communicated patterns in the data (5) and communicated findings in a conclusion (6).

To reach Merit, the student would need to further justify comments made. For example, they could explain with supporting evidence from the experiment what they mean when they say that their findings are consistent with both their experimental and theoretical probability results.

Low Achieved

Commentary
Student response

Student 5 (PDF, 183KB)

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

This involves using the experimental probability process.

This student’s evidence is a response to the TKI assessment resource ‘Games of Chance’.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), gathered data by performing the experiment (3), selected and used appropriate displays including experimental probability distributions (4), identified and communicated patterns in the data (5) and communicated findings in a conclusion (6).

For a more secure Achieved, the student would need to provide a more detailed answer to the question and draw the graph of the experimental distribution accurately.

High Not Achieved

Commentary
Student response

Student 6 (PDF, 132KB)

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

This involves using the experimental probability process.

This student’s evidence is a response to the TKI assessment resource ‘Games of Chance’.

The student has posed a question to explore a situation involving elements of chance (1), planned an experiment to explore the situation (2), gathered data by performing the experiment (3), selected and used appropriate displays (4), identified and communicated a pattern in the data (5) and communicated findings in a conclusion (6).

To reach Achieved, the student would need to give the experimental probability distribution and identify a further pattern in the data. The student would also need to clearly discuss and define the set of possible outcomes for the experiment.

 
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