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Short themes

Energy efficiency | Baking | Planes | Recycling | Links | Achievement standards

Energy efficiency

  • Wikipedia - Carbon credit:
    • Offsetting
    • Modelling
      • How much carbon can a tree absorb?
      • For different fuel rates, how much carbon produced per km?
      • How many trees for a flight, a car journey?
    • Global warming
    • Promoting NZ:
      • Takes less carbon to produce meat here.
  • Sources of energy:
    • Coal/wind/water/solar
    • Efficiency of solar panels – size, shape, start-up cost.
  • Price of petrol varies with price of oil:
    • Fuel tax
    • Comparison of fuel prices internationally.
    • Conversion from local currency to NZ currency.
  • Water:
    • 100ml of rain – how much in a reservoir?
    • Catchment area – how much is absorbed or not?
    • Filling rate
    • Coming out rate
    • Water usage tracking
  • Power bills:
    • Time series – usage, cost, gas, power.

Possible achievement objectives

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

Number strategies and knowledge

  • NA5-1 Reason with linear proportions.
  • 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.
  • NA6-1 Apply direct and inverse relationships with linear proportions.
  • NA6-3 Apply everyday compounding rates.
  • 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

  • NA5-9 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
  • NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
  • NA6-8 Relate rate of change to the gradient of a graph.

Measurement

  • GM5-2 Convert between metric units, using decimals.
  • 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.

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, and trends in multivariate data sets
    • F – presenting a report of findings.
  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • C – identifying and communicating features in context (trends), using multiple displays.

Baking

Compare and contrast different recipes for a particular favourite cake or biscuit, for example, ginger crunch.

  • Number of ingredients.
  • Quantity of flour, baking powder, ginger, butter, sugar etc.
  • Number of pieces it makes.
  • Temperature to cook at.
  • Time taken to cook.
  • Taste testing:
    • set-up criteria
    • get everyone to try cake and rank for each criteria
    • decide on a best ginger crunch using evidence from taste testing
    • does your class get the same best ginger crunch as the class next door?
  • Cost per slice (what size is a slice?).
  • Scale up to make for the whole class.
  • Cost for the whole class.
  • If your four-year-old cousin, who is cooking with you, puts in an extra cup of flour, what do you do now?
  • Comparing NZ recipes with US, Australian, German, etc.
  • Make packaging for the product, one piece, two pieces, the whole cake.

Possible 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.
  • NA6-1 Apply direct and inverse relationships with linear proportions.

Measurement

  • GM5-1Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
  • GM5-2 Convert between metric units, using decimals.
  • GM6-1 Measure at a level of precision appropriate to the task.

Shape

  • GM5-6 Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.

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.
  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • A – justifying the variables and measures used
    • B – managing sources of variation, including through the use of random sampling
    • C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
    • D – making informal inferences about populations from sample data
    • E – justifying findings, using displays and measures.

Planes

Make paper planes, different designs.

  • Throw the planes:
    • Find the direction it flies.
    • Measure the distance it flies.
    • What is the best design?
    • Stunts, distance, speed?

Possible achievement objectives

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

Measurement

  • GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
  • GM6-1 Measure at a level of precision appropriate to the task.

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.

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.
  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • A – justifying the variables and measures used
    • B – managing sources of variation, including through the use of random sampling
    • C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
    • D – making informal inferences about populations from sample data
    • E – justifying findings, using displays and measures.

Recycling

  • Products:
    • glass, paper, plastic
  • Variables:
    • volumes, cost

Links to:

Measurement

  • Containers
  • Recycling bins, home versus business versus school.

Statistics

  • Collect data.
  • Mean volumes per month.
  • Different proportions of the different types of products.
  • Recycled vs thrown out.
  • Organic waste recycling.

Probability

  • Simulation of quantities over a year, for example:
    • Christmas maybe 40% of year’s recycling due to mailers, presents=packaging to throw out, more food.

Number

  • Comparison of rates of recycling between countries.

Graphs

  •  Compare volumes and mixes of types of recycling within NZ, between countries.

Possible achievement objectives

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

Number strategies and knowledge

  • NA5-1 Reason with linear proportions.
  • NA5-4 Use rates and ratios.
  • NA5-5 Know commonly used fraction, decimal, and percentage conversions.
  • NA6-1 Apply direct and inverse relationships with linear proportions.

Patterns and relationships

  • NA5-9 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
  • NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.

Measurement

  • GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
  • GM5-2 Convert between metric units, using decimals.
  • GM6-1 Measure at a level of precision appropriate to the task.
  • GM6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.

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
    • E – comparing sample distributions visually, using measures of centre, spread, and proportion
    • F – presenting a report of findings.
  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • A – justifying the variables and measures used
    • B – managing sources of variation, including through the use of random sampling
    • C – identifying and communicating features in context, using multiple displays
    • D – making informal inferences about populations from sample data
    • E – justifying findings, using displays and measures.

Statistical literacy

  • S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
  • S6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.

Probability

  • S5-4 Calculate probabilities, using fractions, percentages, and ratios.
  • S6-3 Investigate situations that involve elements of chance:
    • B – calculating probabilities in discrete situations.

Links

Achievement standards

Learning from these short themes could potentially provide evidence towards the following achievement standards.

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – 4 credits; External
  • 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
  • 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
  • AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External
  • AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance – 3 credits; Internal

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Last updated May 31, 2017



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