# Level 3

## Mathematics and Statistics clarifications

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## New level 3 standards

As the result of trialling the following information is available to assist teachers to assess level three standards.

This document will be updated as soon as suitable material can be collected from students through the external moderation process.

This document should be read in conjunction with the achievement standard, the Conditions of Assessment document and the Teaching and Learning Guide. Additional information for the statistics standards is available.

**91573 Apply the geometry of conic sections in solving problems**

- To be used as evidence for the award of Achieved, a ‘method’ must be relevant to the solution of the problem and at the appropriate curriculum level.
- At all levels there is a requirement relating to the communication of the solutions.

**91574 Apply linear programming methods in solving problems**

- To be used as evidence for the award of Achieved, a ‘method’ must be relevant to the solution of the problem and at the appropriate curriculum level.
- At all levels there is a requirement relating to the communication of the solutions.

**91575 Apply trigonometric methods in solving problems**

- To be used as evidence for the award of Achieved, a ‘method’ must be relevant to the solution of the problem and at the appropriate curriculum level.
- At all levels there is a requirement relating to the communication of the solutions.

**91576 Use critical path analysis in solving problems**

- At all levels there is a requirement relating to the communication of the solutions.

**91580 Investigate time series data**

- The assessment requires multiple sessions to allow time for students to research the context and develop a purpose prior to completing the analysis.
- Students need to have knowledge about the context and statements that are made need to be related to the context.
- Use of a statistical graphing package is expected.
- Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.
- Features of the data include the trend and seasonal pattern.
- While students could investigate more than one time series or combine series this is not a requirement of the standard.

**91581 Investigate bivariate measurement data**

- The assessment requires multiple sessions to allow time for students to research the context and develop a purpose prior to completing the analysis.
- Students need to have knowledge about the context and statements that are made need to be related to the context.
- Use of a statistical graphing package is expected.
- Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.
- The scatter plot needs to be inspected visually before any model is fitted. It is possible a linear model may not be appropriate for the data that is being investigated and this should be determined by looking at a scatter plot of the raw data.
- Use and interpretation of R
^{2}is not expected at this level.

**91582 Use statistical methods to make a formal inference**

- The assessment requires multiple sessions to allow time for students to research the context and develop a purpose prior to completing the analysis.
- Students need to have knowledge about the context and statements that are made need to be related to the context.
- Use of a statistical graphing package is expected.
- Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.
- The analysis will involve students determining if there is a difference between the population medians (or means) and quantifying the difference in the medians (or means) by using the bootstrap confidence interval.
- A suitable investigative question would be ‘I wonder what the difference in median heights is between NZ year 13 boys and NZ year 13 girls?’

**91583 Conduct an experiment to investigate a situation using experimental design principles**

- Use of a statistical graphing package is expected.
- Students need to provide evidence of each component of the investigation process detailed in Explanatory Note 3 of the standard.
- There needs to be a clear and meaningful purpose for the experiment.
- Students need to identify experimental units, the treatment and the response variable and how the treatment is to be allocated to the experimental units.
- Students need to make a formal statistical inference which will be a causal inference based on the strength of evidence. This will involve the use of randomisation.
- The conclusion needs to be consistent with the analysis and answer the investigative question.

**91587 Apply systems of simultaneous equations in solving problems**

- To be used as evidence for the award of Achieved a ‘method’ must be relevant to the solution of the problem and at the appropriate curriculum level.
- At all levels there is a requirement relating to the communication of the solutions.