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# Level 4 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
• Mapping and orienteering:
• Field trips – link to geography
• Geocaching
• Trigonometry – trig points on hills
• Landscaping – link with technology
• Mapping and orienteering – link with health and PE
• Satellite and astronomy – link with science and physics
• Matariki – link with languages, especially Māori
• Waka ama
• The Pacific
• GPS trails around the school
• 2D and 3D shapes – links with technology and visual arts:
• Modelling
• Scale diagrams
• Transformational geometry:
• Interactive websites
• Geometric patterns in different cultures – from a geometric and algebraic sense
• Kōwhaiwhai
• Islamic art
• Siapo
• Escher
• Penrose tiles
• Mosaics
• Friezes
• Describing linear patterns:
• Perimeter fences, areas and volumes, for example, stacking sugar cubes
• Tukutuku patterns
• Kaleidoscopes
• Telescopes and microscopes – link with science and physics

### Suggested achievement objectives

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

#### Number strategies and knowledge

• NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
• NA4-2 Understand addition and subtraction of fractions, decimals, and integers.

#### Patterns and relationships

• NA4-8 Generalise properties of multiplication and division with whole numbers.
• NA4-9 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.

#### Shape

• GM4-5 Identify classes of two- and three-dimensional shapes by their geometric properties.
• GM5-5 Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
• GM5-6 Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.

#### Position and orientation

• GM4-7 Communicate and interpret locations and directions, using compass directions, distances, and grid references.
• GM5-7 Construct and describe simple loci.
• GM5-8 Interpret points and lines on co-ordinate planes, including scales and bearings on maps.

#### Transformation

• GM4-8 Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
• GM5-9 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
• GM5-10 Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.

#### Measurement

• GM4-1 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
• GM4-2 Convert between metric units, using whole numbers and commonly used decimals.
• GM4-4 Interpret and use scales, timetables, and charts.

## 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 4/5:
• Rumbling tummy
• Chocolicious
• Armspans
• Speedster
• Which average?
• Scatter it
• Time flies
• The case of the missing cake
• Bear hugs 1, Bear hugs 2, Bear hugs 3
• Nosey parker 1, Nosey parker 2
• Are you getting enough zzz?
• 8 glasses per day
• Who wants to be a millionaire?
• Big foot
• A tall tale
• Tell it like it is!
• Masterpiece 1, Masterpiece 2, Masterpiece 3
• Posing summary investigative questions
• Using data cards
• Analysis tools
• Cleaning data

### Suggested achievement objectives

#### Number strategies and knowledge

• NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
• NA4-2 Understand addition and subtraction of fractions, decimals, and integers.
• NA4-4 Apply simple linear proportions, including ordering fractions.

#### Measurement

• GM4-1 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
• GM4-2 Convert between metric units, using whole numbers and commonly used decimals.
• GM4-4 Interpret and use scales, timetables, and charts.

#### Statistical investigation

• S4-1 Plan and conduct investigations using the statistical enquiry cycle:
• A - determining appropriate variables and data collection methods
• B - gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends
• C - comparing distributions visually
• D - communicating findings, using appropriate displays.
• 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

• S4-2 Evaluate statements made by others about the findings of statistical investigations and probability activities.
• S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.

#### Probability

• S4-3 Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
• 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.

## Term 3 – Graphical focus

• Patterns:
• Growth and patterns in nature
• Triangular numbers, square numbers, pentagonal numbers
• Multiple representations, tables, graphs, equations
• Using experiment and data from other learning areas:
• Time related data
• Temperature related data
• Linear relationship data, for example, springs and weights
• Links to Technology, Science, Social Science
• Graphs tell stories:
• A picture tells a thousand words; write the thousand words for the graph as a class, five groups of five – 200 words per group. Be descriptive, one page per group, one paragraph each.
• Links to literacy, numeracy, concepts of gradient, interpreting graphs, focus on features of graphs, relationships.

### Suggested achievement objectives

#### Number strategies and knowledge

• NA4-1 Use a range of multiplicative strategies when operating on whole numbers.
• NA4-2 Understand addition and subtraction of fractions, decimals, and integers.
• NA4-3 Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
• NA4-4 Apply simple linear proportions, including ordering fractions.
• NA4-5 Know the equivalent decimal and percentage forms for everyday fractions.
• NA4-6 Know the relative size and place value structure of positive and negative integers and decimals to three places.
• 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.

#### Equations and expressions

• NA4-7 Form and solve simple linear equations.
• NA5-7 Form and solve linear and simple quadratic equations.

#### Patterns and relationships

• NA4-8 Generalise properties of multiplication and division with whole numbers.
• NA4-9 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
• 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.

• 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 programme

Most likely these students will be working with the three numeracy unit standards.

• US26623 Use number to solve problems – 4 credits; Internal
• US26627 Use measurement to solve problems – 3 credits; Internal
• US26626 Interpret statistical information for a purpose – 3 credits; Internal

In addition, complementary achievement standards may be offered if students are working at a suitable level. Some of the following maybe appropriate:

• 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
• 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

Last updated September 9, 2018