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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
    • 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:
    • 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.

Links

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



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