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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 Trigonometry book.
  • 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)
    • Sliding ladder (p. 175)
    • 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
    • Facebook
    • 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
    • YouTube clip
    • 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.

Ideas for teaching and learning activities

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.

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 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 April 28, 2016



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