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 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

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
 Navigation
 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:
 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
 NA41 Use a range of multiplicative strategies when operating on whole numbers.
 NA42 Understand addition and subtraction of fractions, decimals, and integers.
Patterns and relationships
 NA48 Generalise properties of multiplication and division with whole numbers.
 NA49 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Shape
 GM45 Identify classes of two and threedimensional shapes by their geometric properties.
 GM55 Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
 GM56 Create accurate nets for simple polyhedra and connect threedimensional solids with different twodimensional representations.
Position and orientation
 GM47 Communicate and interpret locations and directions, using compass directions, distances, and grid references.
 GM57 Construct and describe simple loci.
 GM58 Interpret points and lines on coordinate planes, including scales and bearings on maps.
Transformation
 GM48 Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
 GM59 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
 GM510 Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
Measurement
 GM41 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
 GM42 Convert between metric units, using whole numbers and commonly used decimals.
 GM44 Interpret and use scales, timetables, and charts.
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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

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
 NA41 Use a range of multiplicative strategies when operating on whole numbers.
 NA42 Understand addition and subtraction of fractions, decimals, and integers.
 NA44 Apply simple linear proportions, including ordering fractions.
Measurement
 GM41 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
 GM42 Convert between metric units, using whole numbers and commonly used decimals.
 GM44 Interpret and use scales, timetables, and charts.
Statistical investigation
 S41 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 timeseries data to detect patterns, variations, relationships, and trends
 C  comparing distributions visually
 D  communicating findings, using appropriate displays.
 S51 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 recategorising 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
 S42 Evaluate statements made by others about the findings of statistical investigations and probability activities.
 S52 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
Probability
 S43 Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
 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.
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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
 NA41 Use a range of multiplicative strategies when operating on whole numbers.
 NA42 Understand addition and subtraction of fractions, decimals, and integers.
 NA43 Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
 NA44 Apply simple linear proportions, including ordering fractions.
 NA45 Know the equivalent decimal and percentage forms for everyday fractions.
 NA46 Know the relative size and place value structure of positive and negative integers and decimals to three places.
 NA51 Reason with linear proportions.
 NA52 Use prime numbers, common factors and multiples, and powers (including square roots).
 NA53 Understand operations on fractions, decimals, percentages, and integers.
 NA54 Use rates and ratios.
 NA55 Know commonly used fraction, decimal, and percentage conversions.
 NA56 Know and apply standard form, significant figures, rounding, and decimal place value.
Equations and expressions
 NA47 Form and solve simple linear equations.
 NA57 Form and solve linear and simple quadratic equations.
Patterns and relationships
 NA48 Generalise properties of multiplication and division with whole numbers.
 NA49 Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
 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.
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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.
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
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