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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.

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.

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.

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 September 9, 2018