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:
- 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.
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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:
- 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.
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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
- 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.
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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
- 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.
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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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