## Level 2

### Mathematics standards

The titles of all of the Mathematics standards are Apply xxx in solving problems.

xxx comes from content specified in the New Zealand Curriculum that students need to apply in solving problems so students need to be given a problem to solve. Problems need to allow for all levels of achievement.

Within the problem there may be sub tasks but evidence for any level of achievement needs to come from the solution of the overall problem. This means there needs to be sufficient scope within the problem for the thinking that is needed. Problems are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and methods. Situations should be set in a real-life or mathematical context.

Students should not be presented with a task in an unfamiliar context. It is acceptable for students to know the context before the assessment.

The SOLO taxonomy has been used to describe the different levels of thinking in the standards.

The stages in the SOLO taxonomy are increasing in quantity and quality of thought.

Achieved level is the multistructural stage where students need to know or use more than one piece of given information, fact, or idea, but do not integrate their ideas.

Merit is relational thinking where students see the significance of how the various pieces of information relate to one another. ‘Questions’ that provide evidence for relational thinking will require students to integrate more than one piece of given knowledge, information, fact or idea.

Excellence is extended abstract thinking where students can make connections beyond the scope of the problem or question, to generalise or transfer learning into a new situation. Going beyond the given information, knowledge or ideas, or deducing a more general rule or proof that applies to all cases are examples of extended abstract thinking.

At Achieved level all of the standards include the wording ‘selecting and using methods’. The evidence for this aspect can not come from a situation where students are told what method to use to solve problems. Problems needs to be presented so there are no instructions about the method of solution.

For the ‘method’ to provide evidence for the standard it needs to be relevant to the solution of the problem and also at the appropriate curriculum level. The ‘methods’ which provide evidence for each standard are listed in Explanatory Note 4 of the standard.

The appropriate curriculum level can be determined by looking at Explanatory Note 1 of the standard which lists the achievement objectives from The New Zealand Curriculum (NZC) which are covered by the standard. There is further information about the achievement objectives at level 7 of the curriculum in the Teaching and Learning Guide. This information can be found by selecting the relevant achievement objective from the Mathematics and Statistics Achievement objectives by level page on the TKI website.

### Statistics standards

All of the statistics standards involve students using a specified ‘process’. The process varies from standard to standard depending on what aspect of statistics is involved. The ‘process’ is detailed in Explanatory Note 3 of the standard.

The wording of the Achievement Criteria in the Statistics Standards reflects the step up in the quality of the response that is required at the different levels. Merit level is ‘with justification’ and Excellence is ‘with statistical insight’.

At Excellence students need to integrate statistical and contextual knowledge throughout the ‘process’. They need to have an understanding about the context and are expected to demonstrate they have thought about the ‘process’ they have undertaken and their findings.

Information about the statistics achievement objectives can be found in the Teaching and Learning Guide on the TKI website. Additional information for the statistics standards is available from the Census at School website.

#### On this page

## Level 3

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 R2 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.