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 inclass 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
 NA61 Apply direct and inverse relationships with linear proportions.
Equations and expressions
 NA57 Form and solve linear and simple quadratic equations.
 NA65 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
Patterns and relationships
 NA67 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
Measurement
 GM52 Convert between metric units, using decimals.
 GM53 Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.
 GM54 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
 GM61 Measure at a level of precision appropriate to the task.
 GM62 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
 GM63 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.
Shape
 GM55 Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
 GM64 Deduce and apply the angle properties related to circles.
 GM65 Recognise when shapes are similar and use proportional reasoning to find an unknown length.
 GM66 Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.
Transformation
 GM59 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
 GM68 Compare and apply single and multiple transformations.
 GM69 Analyse symmetrical patterns by the transformations used to create them.
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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 S61:
 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 S62:
 Speed is the biggest killer on NZ roads
 ‘Dice’ throwing with nonintuitive 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 S63:
 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
 GM61 Measure at a level of precision appropriate to the task.
Statistical investigation
 S61 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
 S62 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
Probability
 S53 Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
 S54 Calculate probabilities, using fractions, percentages, and ratios.
 S63 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.
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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
 NA64 Find optimal solutions, using numerical approaches.
Patterns and relationships
 NA58 Generalise the properties of operations with fractional numbers and integers.
 NA59 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
 NA66 Generalise the properties of operations with rational numbers, including the properties of exponents.
 NA67 Relate graphs, tables, and equations to linear relationships found in number and spatial patterns.
 NA68 Relate rate of change to the gradient of a graph.
Equations and expressions
 NA57 Form and solve linear and simple quadratic equations.
 NA65 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
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Links
Resources

Lovitt, C., & Clarke, D. (1992). MCTP Professional development package: Activity bank volume 1. Carlton, Victoria: Curriculum Corporation

Lovitt, C., & Clarke, D. (1992). MCTP Professional development package: Activity bank volume 2. Carlton, Victoria: Curriculum Corporation

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 rightangled 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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