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# Achievement standards with achievement objectives

**
Level 1 Achievement standards**

- AS91026
- AS91027 Mathematics and statistics 1.2
- AS91028
- AS91029
- AS91030
- AS91031
- AS91032
- AS91033
- AS91034
- AS91035
- AS91036
- AS91037
- AS91038 Mathematics and statistics 1.13

## Level 1 Achievement standards with achievement objectives

### Number and algebra

**AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problem:**

- Reason with linear proportions.
- Use prime numbers, common factors and multiples, and powers (including square roots).
- Understand operations on fractions, decimals, percentages, and integers.
- Use rates and ratios.
- Know commonly used fraction, decimal, and percentage conversions.
- Know and apply standard form, significant figures, rounding, and decimal place value.
- Apply direct and inverse relationships with linear proportion.
- Extend powers to include integers and fractions.
- Apply everyday compounding rates.

**AS91027 Mathematics and statistics 1.2 Apply algebraic procedures in solving problems:**

- Generalise the properties of operations with fractional numbers and integers.
- Generalise the properties of operations with rational numbers including the properties of exponents.
- Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

**AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs:**

- Find optimal solutions, using numerical approaches.
- Solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
- Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
- Relate rate of change to the gradient of a graph.

**AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems:**

- Form and solve linear equations.
- Solve linear equations and inequations and simultaneous equations in two unknowns.
- Relate graphs, tables, and equations to linear relationships, relate rate of change to the gradient of a graph.

### Geometry and measurement

**AS91030 Mathematics and statistics 1.5 Apply measurement in solving problem:**

- Convert between metric units, using decimals.
- Deduce and use formulae to find the perimeters and areas of polygons, and volumes of prisms.
- Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
- Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
- Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

**AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems:**

- Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
- Recognise when shapes are similar and use proportional reasoning to find an unknown length.
- Use trigonometric ratios and Pythagoras’ Theorem in two dimensions.
- Deduce and apply the angle properties related to circles.

**AS91032 Mathematics and statistics 1.7 Apply right angled triangles in solving measurement problems:**

- Use trigonometric ratios and Pythagoras’ Theorem in two and three dimensions.
- Recognise when shapes are similar and use proportional reasoning to find an unknown length.
- Select and use appropriate metric units for length and area.
- Measure at a level of precision appropriate to the task.

**AS91033 Mathematics and statistics 1.8 Apply knowledge of geometric representations in solving problems:**

- Construct and describe simple loci.
- Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
- Create accurate nets for simple polyhedra and connect three dimensional solids with different two dimensional representations.
- Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

**AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems:**

- Define and use transformations and describe invariant properties of figures and objects under these transformations.
- Compare and apply single and multiple transformations.
- Analyse symmetrical patterns by the transformations used to create them.

**Statistics
**

**AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle:**

- Plan and conduct surveys and experiments using the statistical enquiry cycle:
- determining appropriate variables
- cleaning data
- using multiple displays, and re-categorising data to find patterns, variations, in multivariate data sets
- comparing sample distributions visually, using measures of centre, spread, and proportion
- presenting a report of findings.

- Plan and conduct investigations using the statistical enquiry cycle:
- justifying the variables used
- identifying and communicating features in context (differences within and between distributions), using multiple displays
- making informal inferences about populations from sample data
- justifying findings, using displays and measures.

**AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle:**

- Plan and conduct surveys and experiments using the statistical enquiry cycle:
- determining appropriate variables and measures
- considering sources of variation
- gathering and cleaning data
- using multiple displays, and re-categorising data to find patterns and relationships, in multivariate data sets
- presenting a report of findings.

- Plan and conduct investigations using the statistical enquiry cycle:
- justifying the variables and measures used
- managing sources of variation including through the use of random sampling
- identifying and communicating features in context (relationships between variables), using multiple displays
- justifying findings, using displays and measures.

**AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data:**

- Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
- Calculate probabilities, using fractions, percentages, and ratios.
- Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
- Investigate situations that involve elements of chance: calculating probabilities in discrete situations.

**AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance:**

- Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
- Investigate situations that involve elements of chance:
- comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size

- calculating probabilities in discrete situations.

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Last updated March 1, 2012