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# Level 4/5 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

• Activity: Culturally locating our students in the class
• Activity: How does your cell phone measure up
• Activity: Water woes
• Exploring practical situations, for example:
• Supermarket display and planning package/container to fit more on supermarket shelves.
• Swimming pool at home or spa:
• How big does it have to be to be practical?
• How much water?
• What is a good shape to fit the section?
• What would the water charges be to fill it up?
• How much chlorine is needed?
• Snowboards – what shape?
• What is the surface area?
• How does this compare with skis for same size person?
• Planning playground, adventure area, climbing wall. See activities such as environmental engineer in the EQUALS Towards Better Trigonometry Teaching.
• Orienteering
• Patterns in different cultures
• Kowhaiwhai
• Tukutuku patterns
• Islamic art
• Frieze patterns
• Escher tessellations
• Penrose tiles
• Pinwheel tiling
• MCTP Professional development package: Activity bank 1
• Danger distance (p. 100)
• Baby in the car (p. 105)
• Platonic Solids (p. 203)
• Trigonometry walk (p. 219)
• Regular polygons (p. 232)
• MCTP Professional development package: Activity bank 2
• Introductory Pythagoras (p. 323)
• Mental Map (p. 340)
• How far can you go? (p. 344)
• Estimation (p. 411)
• How many people can stand in your classroom? (p. 445)

### Suggested achievement objectives

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

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.

#### 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.
• GM6-2 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.

#### Position and orientation

• GM5-7 Construct and describe simple loci.
• GM5-8 Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
• GM6-7 Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

#### 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.

#### Statistical investigation

• S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
• A – determining appropriate variables and measures
• D – using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets.

#### Probability

• S5-4 Calculate probabilities, using fractions, percentages, and ratios.

## 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

• CensusAtSchool activities – level 5:
• Chocolicious
• Arm spans
• Speedster
• Which average?
• Time flies
• Bear hugs 1, Bear hugs 2, Bear hugs 3
• Nosey parker 1, Nosey parker 2
• Are you getting enough zzz?
• Big foot
• A tall tale
• Tell it like it is!
• Masterpiece 1, Masterpiece 2, Masterpiece 3
• Cleaning data
• Sources of data:
• School census
• Texting
• Computer games, for example, Tetris
• Games of chance, for example, black jack
• Lotto
• Students presenting their findings other than as a written report, for example:
• PowerPoint presentation
• Orally
• Other innovative means of presentation

### Suggested achievement objectives

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

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.
• NA5-3 Understand operations on fractions, decimals, percentages, and integers.
• NA5-4 Use rates and ratios.

#### Measurement

• GM4-4 Interpret and use scales, timetables, and charts.
• GM5-2 Convert between metric units, using decimals.

#### Statistical investigation

• S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
• A – determining appropriate variables and measures
• B – considering sources of variation
• C – gathering and cleaning data
• D – using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets
• E – comparing sample distributions visually, using measures of centre, spread, and proportion
• F – presenting a report of findings.

#### Statistical literacy

• S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.

#### 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

• NA5-1 Reason with linear proportions.
• NA5-2 Use prime numbers, common factors and multiples, and powers (including square roots).
• NA5-3 Understand operations on fractions, decimals, percentages, and integers.
• NA5-4 Use rates and ratios.
• NA5-5 Know commonly used fraction, decimal, and percentage conversions.
• NA5-6 Know and apply standard form, significant figures, rounding, and decimal place value.
• NA6-4 Find optimal solutions, using numerical approaches.

#### 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

• 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.

#### Statistical investigation

• S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
• C – gathering and cleaning data
• D – using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets.

• Penrose tiles:
• Kōwhaiwhai:

## 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

## Possible assessment programmes

• 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
• 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
• 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
• 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
• AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems – 2 credits; Internal
• AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle – 3 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
• AS91030 Mathematics and statistics 1.5 Apply measurement in solving problems – 3 credits; Internal
• AS91032 Mathematics and statistics 1.7 Apply right-angled triangles in solving measurement 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
• 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
• AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems – 3 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
• AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance – 3 credits; Internal

Last updated September 9, 2018