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Achievement standards with achievement objectives

Level 1 Achievement standards

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • AS91027 Mathematics and statistics 1.2 Apply algebraic procedures in solving problems – 4 credits; External (CAT)
  • AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – 4 credits; External
  • AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems – 3 credits; Internal
  • AS91030 Mathematics and statistics 1.5 Apply measurement in solving problems – 3 credits; Internal
  • AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems – 4 credits; External
  • AS91032 Mathematics and statistics 1.7 Apply right-angled triangles in solving measurement problems – 3 credits; Internal
  • AS91033 Mathematics and statistics 1.8 Apply knowledge of geometric representations in solving problems – 3 credits; Internal
  • AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems – 2 credits; Internal
  • AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
  • AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle – 3 credits; Internal
  • AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External
  • AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance – 4 credits; External

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



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