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Level 5 learning programme example

  • The learning programme examples are divided into three terms of work. Each term has an overarching mathematical and statistical focus to support the learning.
  • Possible teaching and learning activities are given, from which teachers could select activities that best meet the needs of the students in their class/school. In addition teachers could select teaching and learning activities that they currently use, or source others that would meet student needs and address the focus.
  • Each term has a list of possible achievement objectives to select from, the choice of which will depend on the teaching and learning activities selected.
  • The intent is to be more holistic in the selection of achievement objects to allow for natural connections between and within strands.
  • Some achievement objectives could be summatively assessed directly through achievement or unit standards; others could be assessed through in-class formative or summative assessment. Not all achievement objectives need to be assessed.

Term 1 – Geometrical focus

The focus for this term is to place a geometrical lens over the teaching and learning of mathematics and statistics.

Ideas for teaching and learning activities

Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Number strategies and knowledge

  • NA6-1 Apply direct and inverse relationships with linear proportions.

Equations and expressions

  • NA5-7 Form and solve linear and simple quadratic equations.
  • NA6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

Patterns and relationships

  • NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.

Measurement

  • GM5-2 Convert between metric units, using decimals.
  • GM5-3 Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.
  • GM5-4 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
  • GM6-1 Measure at a level of precision appropriate to the task.
  • GM6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
  • GM6-3 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

Shape

  • GM5-5 Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
  • GM6-4 Deduce and apply the angle properties related to circles.
  • GM6-5 Recognise when shapes are similar and use proportional reasoning to find an unknown length.
  • GM6-6 Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.

Transformation

  • GM5-9 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
  • GM6-8 Compare and apply single and multiple transformations.
  • GM6-9 Analyse symmetrical patterns by the transformations used to create them.

Term 2 – Statistical focus

The focus for this term is to place a statistical lens over the teaching and learning of mathematics and statistics.

Ideas for teaching and learning activities

  • Activity: 100m sprint times
  • Possible context elaborations for AO S6-1:
    • Growing scatterplots
    • Sleeping sheep
    • Do boy babies tend to be heavier than girl babies?
    • Does practice make perfect?
    • You can’t fool me by giving me a cheap cola
  • Possible context elaborations for AO S6-2:
    • Speed is the biggest killer on NZ roads
    • Figure this activities
  • ‘Dice’ throwing with non-intuitive objects, for example, plastic dinosaurs or pass the pigs.
  • Probabilities associated with Weetbix cards, for example, getting the whole All Black team.
  • Possible context elaborations for AO S6-3:
    • Is this die fair?
    • Exploring paper, scissors or rock
    • Quiz or no quiz
    • Exploring spinners
    • Sum of two dice

Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Measurement

  • GM6-1 Measure at a level of precision appropriate to the task.

Statistical investigation

  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • A - justifying the variables and measures used
    • B - managing sources of variation, including through the use of random sampling
    • C - identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
    • D - making informal inferences about populations from sample data
    • E - justifying findings, using displays and measures.

Statistical literacy

  • S6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.

Probability

  • S5-3 Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
  • S5-4 Calculate probabilities, using fractions, percentages, and ratios.
  • S6-3 Investigate situations that involve elements of chance:
    • A - comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
    • B - calculating probabilities in discrete situations.

Term 3 – Graphical focus

The focus for this term is to place a graphical lens over the teaching and learning of mathematics and statistics.

Ideas for teaching and learning activities

Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Number strategies and knowledge

  • NA6-4 Find optimal solutions, using numerical approaches.

Patterns and relationships

  • NA5-8 Generalise the properties of operations with fractional numbers and integers.
  • NA5-9 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
  • NA6-6 Generalise the properties of operations with rational numbers, including the properties of exponents.
  • NA6-7 Relate graphs, tables, and equations to linear relationships found in number and spatial patterns.
  • NA6-8 Relate rate of change to the gradient of a graph.

Equations and expressions

  • NA5-7 Form and solve linear and simple quadratic equations.
  • NA6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

Links

Resources

  1. Lovitt, C., & Clarke, D. (1992). MCTP Professional development package: Activity bank volume 1. Carlton, Victoria: Curriculum Corporation
  2. Lovitt, C., & Clarke, D. (1992). MCTP Professional development package: Activity bank volume 2. Carlton, Victoria: Curriculum Corporation
  3. Drake, M., MacEwan, L., Romana, H., McIntyre, R., & Harvey, R. (1995). Learning experiences for level 6 mathematics. Teacher Support Services, Wellington.

Possible assessment programme

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – credits; External
  • AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems – 4 credits; External
  • AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
  • AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance – 3 credits; Internal

OR

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – 4 credits; External
  • AS91032 Mathematics and statistics 1.7 Apply right-angled triangles in solving measurement problems – 3 credits; Internal
  • AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
  • AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External

OR

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems – 3 credits; Internal
  • AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems – 4 credits; External
  • AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
  • AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External

Last updated October 3, 2012



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