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, startup cost.
 Price of petrol varies with price of oil:
 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
 NA51 Reason with linear proportions.
 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.
 NA61 Apply direct and inverse relationships with linear proportions.
 NA63 Apply everyday compounding rates.
 NA64 Find optimal solutions, using numerical approaches.
Equations and expressions
 NA57 Form and solve linear and simple quadratic equations.
 NA65 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
Patterns and relationships
 NA59 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
 NA67 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
 NA68 Relate rate of change to the gradient of a graph.
Measurement
 GM52 Convert between metric units, using decimals.
 GM54 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
 GM62 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
 GM63 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.
Statistical investigation
 S51 Plan and conduct surveys and experiments using the statistical enquiry cycle:
 C – gathering and cleaning data
 D – using multiple displays, and recategorising data to find patterns, and trends in multivariate data sets
 F – presenting a report of findings.
 S61 Plan and conduct investigations using the statistical enquiry cycle:
 C – identifying and communicating features in context (trends), using multiple displays.
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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:
 setup 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 fouryearold 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
 NA51 Reason with linear proportions.
 NA53 Understand operations on fractions, decimals, percentages, and integers.
 NA54 Use rates and ratios.
 NA61 Apply direct and inverse relationships with linear proportions.
Measurement
 GM51Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
 GM52 Convert between metric units, using decimals.
 GM61 Measure at a level of precision appropriate to the task.
Shape
 GM56 Create accurate nets for simple polyhedra and connect threedimensional solids with different twodimensional representations.
Statistical investigation
 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.
 S61 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.
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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
 GM51 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
 GM61 Measure at a level of precision appropriate to the task.
Position and orientation
 GM57 Construct and describe simple loci.
 GM58 Interpret points and lines on coordinate planes, including scales and bearings on maps.
 GM67 Use a coordinate plane or map to show points in common and areas contained by two or more loci.
Statistical investigation
 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.
 S61 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.
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Recycling
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
 NA51 Reason with linear proportions.
 NA54 Use rates and ratios.
 NA55 Know commonly used fraction, decimal, and percentage conversions.
 NA61 Apply direct and inverse relationships with linear proportions.
Patterns and relationships
 NA59 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
 NA67 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
Measurement
 GM51 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
 GM52 Convert between metric units, using decimals.
 GM61 Measure at a level of precision appropriate to the task.
 GM62 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
Statistical investigation
 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
 E – comparing sample distributions visually, using measures of centre, spread, and proportion
 F – presenting a report of findings.
 S61 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
 S52 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
 S62 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
Probability
 S54 Calculate probabilities, using fractions, percentages, and ratios.
 S63 Investigate situations that involve elements of chance:
 B – calculating probabilities in discrete situations.
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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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