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Year 11 General Mathematics Scope and Sequence -2015

TERM 1

1 2 3 4 5 6 7 8 9 10

Collecting and PresentingData

MGP-1,2,7,10

Algebra and equations MGP-1,2,3,9,10

+

FOCUS STUDY: Driving Safely MGP-1,2,3,7,9,10

Similar Figures and TrigonometryMGP-2,3,4,5

TASK 1 – 20%

TERM 2

1 2 3 4 5 6 7 8 9 10

Earning Money and Taxation MGP1,2,3,6,9,10

ProbabilityMGP-2,8,10

Measurement MGP-2,3,4,5

+FOCUS STUDY: Phone Plans and Downloading Data

MGP-2,3,5,6,7,9,10TASK 2 – 40%

TERM 3

1 2 3 4 5 6 7 8 9 10

Linear FunctionsMGP-1,2,3,9,10

+FOCUS STUDY: Buying a Car

MGP-1,2,5,6,7,8,9

Analysing data MGP-1,2,7,9,10

Investing Money MGP-1,2,3,6,9,10

TASK 3 – 40%

NEW CENTURY MATHS 11 MATHEMATICS GENERAL (PATHWAY 2) | Preliminary Course | Teaching program 1

www.boardofstudies.com.au


http://www.boardofstudies.com.au/

1. COLLECTING AND PRESENTING DATATime: 3 weeks .Text: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 1, p. 1.Syllabus reference: Data and Statistics

DS1 Statistics and society, data collection and sampling (p.32)DS2 Displaying and interpreting single data sets (p.34)

INTRODUCTIONThis Data and Statistics topic examines the different types of statistical samples and displays, consolidating concepts and skills introduced at Stages 4 and 5. The new content includes classifying categorical data, types of samples, bias and radar charts. The Analysing data topic will cover cumulative frequency graphs, box-and-whisker plots and the various measures of location and spread.

CONTENT

1 Interpreting graphs DS2

o interpret the various displays of single data sets

2 Misleading graphs DS2

o identify the misrepresentation of data

3 Types of data DS1

o classify data as quantitative (either discrete or continuous) or categorical (either nominal or ordinal)

4 Statistics in society DS1

o investigate the process of statistical inquiry, and describe the following steps: posing questions, collecting data, organising data, summarising and displaying data, analysing data and drawing conclusions, and writing a report

5 Sampling techniques DS1

o identify the target population to be investigated

o determine whether data for the whole population is available (for example the results of a round of a sporting competition), or if sampling is necessary

o describe a random sample as a sample in which every member of the population has an equal chance of being included in the sample

o distinguish between the following sample types: random, stratified and systematic, and determine the appropriateness of each type for a given situation

o describe a method of choosing each type of sample in a given situation

o relate sample selection to population characteristics

o identify possible sources of bias in the collection of a sample

6 Constructing graphs DS2

o create statistical displays using a spreadsheet or appropriate software

7 Frequency histograms and polygons DS2

8 Dot plots and stem-and-leaf plots DS2

o construct a dot plot from a small data set and interpret the dot plot

9 Radar charts DS2

o draw a radar chart to display datao link type of data with an appropriate

display, for example continuous data with a histogram, or categorical data with a divided bar graph or sector graph (pie chart)

10 Revision and mixed problems

RELATED TOPICSPreliminary: Analysing data, Probability, Buying a car, Phone plans and downloading data, Driving safely, HSC: Statistical distributions, Sampling and the normal distribution.

EXTENSION ACTIVITIESo Investigate the history and activities of the

Australian Bureau of Statistics , the United Nations and the World Health Organization.


TEACHING NOTES AND IDEASo Resources: Statistical graphs from

newspapers, magazines and the Internet, statistical yearbooks and Census data from the Australian Bureau of Statistics: www.abs.gov.au, including CensusAtSchool, weather and climate data from the Bureau of Meteorology: www.bom.gov.au, spreadsheets, graphics calculators, and statistical graphing software.

o Statisticians collect and organise data and analyse them to give them meaning. They predict outcomes, make decisions and draw conclusions based on the features of a sample (for example customer demand, road use, opinion polls, television ratings, economic trends, weather, psychology experiments, newspaper circulation, CD album sales, and marketing).

o Tables and graphs can be collected from newspapers and magazines and their data discussed in class. Examine the use and misuse of graphs, particularly in advertising and the media.

o A questionnaire of personal details could be given to students at the start of the topic and the data analysed in subsequent lessons and topics. See Worksheet ‘Student survey form’. Examine the issues of privacy and ethics when collecting information.

o A good sample is large, random and representative. Students should be able to judge when a sample is biased (for example a street poll, a phone poll, or a door knock).

o Syllabus, p.31: ‘The Australian Bureau of Statistics publishes notes about graph types. Teachers may find these notes useful when giving students experience in the presentation of data displays’.

o Experiment with different types of graphs on the same set of data. Every graph should have a title and key or scale.

ASSESSMENT ACTIVITIESo Assignment illustrating and evaluating the

use and misuse of graphs in the mass media.

o Evaluate the strengths and weaknesses of a particular type of graph.

o Conduct and report on a sampling activity or statistical investigation.

o Design a questionnaire.

TECHNOLOGYInvestigate the graphing capabilities of spreadsheet software, graphics calculators or statistical software. Random numbers can be generated on a calculator or spreadsheet.

LANGUAGEo ‘Data’ is the plural of ‘datum’, so it is

correct to say ‘The data represent …’, not ‘The data represents …’

o In some subjects, such as science and geography, a horizontal column graph is sometimes called a bar graph.

o ‘Nominal’ means ‘having a name’, ‘ordinal’ means ‘having an order’.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

o TEACHER’S SIGNATURE___________________________

o DATE___ / /_____


http://www.abs.gov.au/

2. ALGEBRA AND EQUATIONSTime: 2 weeks (Term 1, Week 4)Text: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 2, p. ??Syllabus reference: Algebra and Modelling

AM1 Algebraic manipulation (p.52)

INTRODUCTIONThe aim of this revision topic is to provide a foundation in basic algebra skills. Students should appreciate how formulas and equations are practical ways of representing the mathematical patterns that occur in nature, society and industry. Syllabus, p.51: ‘Algebraic skills should be developed through practical and vocational contexts … and consolidated further in Focus Studies’.

CONTENT

1 Linear number patterns AM1

2 Simplifying algebraic expressions AM1

o add, subtract, multiply and divide algebraic terms

o simplify algebraic expressions involving multiplication and division

3 Expanding algebraic expressions AM1

o expand and simplify algebraic expressions

4 Formulas AM1

o substitute numerical values into algebraic expressions

o substitute given values for the other pronumerals in a mathematical formula to find the value of the subject of the formula

5 Solving equations AM1

o solve linear equations involving two steps

6 (HSC course) Formulas and equations AM3

o solve equations following substitution of values


RELATED TOPICSPreliminary: Linear functions, HSC: Equations and linear functions.

EXTENSION ACTIVITIESo Equations involving powers and rootso Algebraic fractions, changing the subject of

a formula, simultaneous equations (HSC course)

TEACHING NOTES AND IDEASo Even though this entire topic is revision, do

not rush through it. Skills in areas such as expansion and solving equations need to be consolidated. Solutions to equations should be checked by substitution (if practical).

o Syllabus, p.53: ‘Substitution into expressions should include substitution into expressions containing multiple variables, positive and negative values, powers and square roots’. See the syllabus for more examples of formulas.

o Keep formulas as practical and relevant as possible [for example

perimeter, area and volume formulas; simple and compound interest formulas, Pythagoras’ theorem, Fried’s rule for medicine dosage

and the body-mass index

formula (healthy range is 21 to 25)]. TAFE handbooks may be consulted for trade formulas.

o Students could calculate their own BMI (body-mass index) and determine their healthy mass range for a healthy BMI.

ASSESSMENT ACTIVITIESo Practical applications of formulas

TECHNOLOGYUse spreadsheets to evaluate algebraic expressions and formulas.


LANGUAGEo Common mistake in substitution: students

often mistakenly believe that 2a2 means (2a)2, not 2(a2).

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


3. SIMILAR FIGURES AND TRIGONOMETRYText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 3, p. ??Syllabus reference: Measurement

MM3 Similarity of two-dimensional figures, right-angled triangles (p. 44)

INTRODUCTIONThis Measurement topic revises Pythagoras’ theorem, similar figures and right-angled trigonometry (the sine and cosine rules will be taught in the HSC course). There is plenty of scope for practical and outdoor work here. The properties of similar figures are examined, then applied to scale drawings and building plans. Examining similarity with right-angled triangles leads to work on trigonometry. Although trigonometry was introduced in Stage 5, this topic focuses upon applying trigonometric skills to practical situations. Spend considerable time teaching precisely the concepts of bearings and angles of elevation/depression, as these are areas in which students often experience difficulty.

CONTENT

1 Pythagoras’ theorem MM3

2 Similar figures and scale factors MM3

o calculate scale factors of similar figureso use scale factors to solve problems

involving similar figures

3 Scale diagrams MM3

o calculate measurements from scale diagrams

4 House plans MM3

o solve practical problems using scale diagrams and factors

5 The sine, cosine and tangent ratios MM3

o recognise that the ratio of matching sides in similar right-angled triangles is constant for equal angles

o calculate sine, cosine and tangent ratioso (HSC course) round angle sizes to the

nearest minute

6 Finding an unknown side MM3

o use trigonometric ratios to find an unknown side-length in a right-angled triangle

o solve practical problems using trigonometry

o determine whether an answer seems reasonable by considering proportions within the triangle under consideration

7 Finding an unknown angle MM3

o use trigonometric ratios to find the size of an unknown angle in a right-angled triangle

8 (HSC course) Bearings MM5

9 (HSC course) Problems involving bearings MM5

o use compass bearings (eight points only) and true bearings (three-figure bearings) in problem-solving related to maps and charts

10 Angles of elevation and depression MM3

o calculate angles of elevation and depression, given the appropriate diagram


RELATED TOPICSPreliminary: Measurement, HSC: The sine and cosine rules, Geometry of the Earth.

EXTENSION ACTIVITIESo Constructing scale drawings and house

plans. Construct an accurate floor plan of the classroom.

o Design an office, home extension, holiday apartment, granny flat or car park according to specifications.

o Syllabus, p.45: ‘Online maps are readily available (with measurement tools) for extension activities.


o What happens to the area of a plane shape when its dimensions are doubled?

o Trigonometry problems where the diagram is not given.

o (HSC course) Problems involving two connected right-angled triangles.

o Investigate the maximum and minimum values of each trigonometric ratio.

o (HSC course) Trigonometric ratios for obtuse angles.

TEACHING NOTES AND IDEASo Resources: house and building plans (from

newspapers, home exhibition centres and TAS faculty), metre ruler, shadow stick, tape measure, trundle wheel, scale drawings, maps, directional compass, clinometer.

o The following concepts are strictly not part of the Preliminary course but have been included in this topic for Pathway 2 students: trigonometric equations where the unknown side is in the denominator, giving angle answers to the nearest minute, bearings.

o Why are measurements on house plans always given in millimetres?

o Students should be able to interpret floor plans, to visualise the look of the building. Use house plans to solve problems involving carpeting, painting, tiling. When ordering tiles or carpet, allow for offcuts and wastage.

o When solving problems, check that answers sound reasonable. Check that the hypotenuse is in fact the longest side and a shorter side is not longer than the hypotenuse. Use the known measurements and draw a rough diagram to verify.

o Syllabus, p. 45: ‘Investigate the trigonometric ratios for angles of, say, 30°, 45°, 60° in a number of similar right-angled triangles.’

o When solving angle of depression problems, there are two possible approaches: complementary angle or alternate angle. Compare both methods. Similarly, with bearings problems, two triangle diagrams are possible.

o Use a shadow stick and trigonometry to calculate the altitude (angle of elevation) of the Sun.

o Syllabus, p. 39: ‘Plan and carry out an orienteering event at the school.’

ASSESSMENT ACTIVITIESo Outdoor project: calculating heights of

flagpoles, trees, school buildings, etc. using angle of elevation, angle of depression or the fact that tan 45° = 1.

o Practical assignment or test.o Design a map or scale drawing, such as a

floor plan of the classroom or school.

TECHNOLOGYEnsure that calculators are set to degrees mode. Investigate sides, angles and areas of triangles using GeoGebra.

LANGUAGEo Mnemonics for trigonometry ratios: ‘Sun

Over Head Caused A Huge Tan On Arm’, or ‘Only Half An Hour Of Algebra (in the) School Certificate Test’.

o With compass bearings, stress the terminology: ‘the bearing of P from O’.

o ‘Elevated’ = feeling happy = looking up, ‘depressed’ = feeling sad = looking down.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


4. EARNING MONEY AND TAXATIONText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 4, p. ??Syllabus reference: Financial Mathematics

FM1 Earning money (p. 24)FM3 Taxation (p. 28)

INTRODUCTIONThis Financial Mathematics topic examines the mathematics of earning an income and paying taxes. Some of the content has been met in Stage 5 but it is revised here in greater detail. Students will become competent in calculating wages, salaries, overtime, allowances, income tax and GST. Aim to use current pay rates, tax rates and prices in this topic. As well as the mathematics, pay attention to the amount of financial terminology to be learned, especially related to taxation. The other Financial mathematics topic for this year is Investing money.

CONTENT

1 Wages, salaries and overtime FM1

o calculate monthly, fortnightly, weekly, daily and hourly pay rates from a given salary

o calculate wages involving hourly rates and penalty rates, for example overtime

2 Commission, piecework and royalties FM1

o describe the differences between salaries, wages and commission

o calculate earnings based on commission (including commission based on a sliding scale), piecework and royalties

o compare different ways of earning

3 Bonuses, allowances and annual leave loading FM1

o calculate special allowances, including allowances for wet work, confined spaces, toxic substances, heat, heights

o calculate annual leave loading

4 Government allowances and pensions FM1

o calculate payments based on government allowances and pensions, for example allowances based on youth, tertiary study and travel

5 Gross and net pay FM1

o determine deductions from income, for example tax instalments, superannuation contributions, health fund instalments, union fees and HECS repayments

o calculate net pay following deductions from gross pay

6 Budgeting FM1

o prepare a budget for a given income, taking into account fixed and discretionary spending

o evaluate a prepared budget

7 Income tax and Medicare levy FM3

o calculate the amount of allowable (tax) deductions from gross income, to calculate taxable income

o calculate income tax payable and Medicare levy (basic levy only)

8 PAYG and tax returns FM3

o calculate the amount of Pay As You Go (PAYG) tax payable or refund owing, using current tax scales

9 GST and VAT FM3

o calculate the goods and services tax (GST) payable on a range of goods and services

10 Graphs of tax rates FM3

o create and interpret graphs to illustrate and describe different tax rates


RELATED TOPICSPreliminary: Buying a car, Phone plans and downloading data, Investing money, HSC: Loans and annuities.

EXTENSION ACTIVITIES


o Double-time-and-a-half and triple time.o Investigate the GST and which essential

items are exempt from it.

TEACHING NOTES AND IDEASo Resources: current wage awards, Tax Pack,

employment section of newspapers, PAYG tax rates from the post office, the Australian Tax Office website www.ato.gov.au, Centrelink website www.centrelink.gov.au, Australian Bureau of Statistics website www.abs.gov.au, pay slips, spreadsheets.

o Consult the HSIE faculty for information and resources.

o Syllabus, p. 25: ‘Review a previously prepared budget to reallocate funds for a sudden contingency.’

o Compare various ways of earning money, for example, a wage of $x per hour compared to a salary of $y.

o Examples of budget expenses: board, food, union fees, health fund, life and car insurance, transport fees, council rates, medical bills, car service, petrol, entertainment, clothes, loan repayments, and savings.

o Analyse the costs of sharing accommodation in a house or flat in the local area.

o Taxable incomes are rounded down to the nearest dollar.

ASSESSMENT ACTIVITIESo Research assignment or case study of a

particular type of income or on calculating income tax.

o Students could survey and compare incomes of different occupations. Collect advertisements from newspapers and categorise according to ways of earning.

o Prepare a personal or business budget on paper or using a spreadsheet.

TECHNOLOGYUse a spreadsheet to calculate incomes (gross and net), taxes and budgets. Investigate the effects of changing values in the cells of the spreadsheet. Syllabus, p.29: ‘Students use an online tax calculator’.

LANGUAGEo Pay attention to the amount of terminology

involved in this topic, especially related to taxation. Promote literacy activities and word puzzles.

o A group certificate is now called a ‘PAYG payment summary’.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


5. PROBABILITYText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 5, p. ??Syllabus reference: Probability

PB1 Relative frequency and probability (p. 48)

INTRODUCTIONThis topic revises and extends chance concepts learned in Stage 5. More formal treatment of probability theory, such as tree diagrams and counting techniques for ordered and unordered selections, will be examined in the HSC topic Probability next year. The practical component of this topic allows for comparisons to be made between experimental and theoretical probability. Probability is often a difficult concept for students to grasp. Better understanding can be reinforced through careful practice with a variety of applied problems. Reliance upon formal theory and formulas should be kept to a minimum.

CONTENT

1 Probability of simple events PB1

o identify events with equally likely outcomes

o use the following definition of the probability of an event where outcomes are equally likely:

o recognise that o express probabilities as fractions, decimals

and percentageso comment critically on the validity of simple

probability statements

2 Multi-stage events PB1

o verify the total number of outcomes for simple multi-stage experiments by systematic listing

3 The multiplication principle for counting PB1

o determine the number of outcomes for a multi-stage experiment by multiplying the number of choices at each stage

4 Complementary events PB1

o calculate the probability of the complement of an event using the relationship P(an event does not occur) = 1 P(the event does occur)

5 Experimental probability PB1

o perform simple experiments and use recorded results to obtain relative frequencies

o estimate the relative frequencies of events from recorded data

o use relative frequencies to obtain approximate probabilities

o illustrate the results of experiments through statistical graphs and displays

6 Comparing calculated and experimental probabilities PB1

o compare theoretical probabilities with experimental estimates


RELATED TOPICSPreliminary: Collecting and presenting data, HSC: Probability.

EXTENSION ACTIVITIESo Factorial notationo (HSC) Tree diagrams, ordered and

unordered selections

TEACHING NOTES AND IDEASo Resources: dice, coins, counters, playing

cards, spreadsheets, probability simulation software.

o Do not assume that all students have had experience with the properties of playing cards: suits, colours, deck of 52, etc. Be


sensitive to religious and cultural attitudes towards games of chance.

o Syllabus, p.49: ‘Comment critically on statements involving probability, such as: “Since it either rains or is fine, the probability of a fine day us 50-50”’.

o The total number of ways to place three different letters in three envelopes is 3 × 2 ×1. Note, however, that factorial notation is not required for this course.

o Count the number of possible car registration number plates, telephone numbers, radio station call signs, combination locks, security codes and PINs.

o Syllabus, p. 49: ‘Investigate the number of different meals that can be chosen from a menu. Determine the number of combinations of raised dots that are possible in the Braille system for reading and writing. Investigate whether or not all the possible combinations are used. (Could undertake a similar study for Morse code).’

o Examples of probability situations: dice, coins, cards, coloured balls, counters, traffic lights, gender of children, and selecting committees randomly.

o In reality, the chance of a newborn baby being a boy is slightly higher than that of a girl.

o Syllabus, p. 49: ‘Experiments could be carried out in which the probability is not intuitively obvious, for example the probability of a drawing pin landing point up’.

o The greater the number of trials, the closer the experimental probability is to the theoretical probability. However, every trial is still independent (for example, with coin tosses, if five heads come up in a row, on the sixth toss there is still an even chance of heads or tails because a coin does not have ‘memory’). Explain how gamblers often misunderstand the law of averages.

o Biased situations should also be considered.

ASSESSMENT ACTIVITIESo Plan, implement and report on a probability

experiment.o Vocabulary test.

TECHNOLOGYUse computers to simulate probability situations. Random numbers can be generated on a calculator, graphics calculator and spreadsheet.

LANGUAGEo Syllabus, p. 49: ‘Investigate expressions

used in other disciplines and in everyday life to describe likely or unlikely events, for example ‘once in a blue moon,’ ‘a one in 300-year flood.’ Or ‘a 75% chance of recovery following a medical operation’.

o What is the everyday meaning of the word ‘complement’? How does this relate to its meaning in probability?

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


6. MEASUREMENTText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 6, p. ??Syllabus reference: Measurement

MM1 Units of measurement and applications (p. 40)MM2 Applications of perimeter, area and volume (p. 42)

INTRODUCTIONThis topic extends concepts in measurement and number, including significant figures, percentage error, repeated percentage change, converting rates and offset surveys. This is not a revision topic but the application of measurement skills to practical problems. Students will be exposed to a variety of situations in which they will rely upon their measurement knowledge. There will be a more advanced ‘Area and volume’ topic in Year 12.

CONTENT

1 Metric units MM1

o use standard prefixes in the context of measurement

2 Error in measurement MM1

o repeat and average measurements to reduce the likelihood of error

o (HSC) calculate the percentage error in a measurement

3 Significant figures MM1

o investigate the degree of accuracy of reported measurements, including the use of significant figures where appropriate

4 Scientific notation MM1

o use scientific notation in the context of measurement

o express measurements in scientific notation

5 Ratio problems MM1

o calculate with ratios, including finding the ratio of two quantities and using the unitary method to solve problems

6 Dividing a quantity in a given ratio MM1

o divide quantities in a given ratio

7 Rate problems MM1

o calculate rates, including pay rates, rates of flow and rates of speed

8 Converting rates MM1

o convert between units for rates, for example km/h to m/s, mL/min to L/h

9 Percentage change MM1

o determine the overall change in a quantity following repeated percentage changes, for example an increase of 20% followed by a decrease of 20%

10 Perimeters of composite shapes MM2

o calculate the perimeter of simple figures, including right-angled triangles, circles, semi-circles and quadrants

o calculate the perimeter of simple composite figures consisting of two shapes, including semi-circles and quadrants

11 Area MM1, MM2

o convert between common units for areao identify and use the correct formula to

solve practical area problemso calculate the area of simple composite

figures consisting of two shapes, including semi-circles and quadrants

12 Offset surveys MM2

o calculate the perimeter and area of irregularly-shaped blocks of land using a field diagram

13 Volume MM1, MM2

o convert between common units for volumeo estimate areas and volumeso calculate the volume of right prisms and

cylinders using appropriate formulas

14 Volume and capacity MM2


o convert between units of volume and capacity


RELATED TOPICSPreliminary: Similar figures and trigonometry, Phone plans and downloading data, Driving safely, HSC: Area and volume, The sine and cosine rules, Water usage, Health and medicine

EXTENSION ACTIVITIESo Research the use of ratios, rates and

percentage change in careers such as nursing or veterinary science.

o Engineering notation as an extension of scientific notation.

o Syllabus, p. 43: ‘Investigate the dimensions that maximise the area for a given shape and perimeter, such as in the design of playpens and stock paddocks.’

o Radial surveys (HSC course) and other types of land surveying.

TEACHING NOTES AND IDEASo Resources: rulers and other measuring

instruments, measuring cylinders and jugs for capacity, field diagrams, nets of solid shapes, poster of formulas.

o The number of significant figures in a calculated answer should be (at most) the same as the number of significant figures given in the original measurements.

o Applications of ratios: concrete, lawnmower fuel, shares in rent or prize money, cordial, cake recipes, paste (flour and water), tyres, eye chart, telescope/microscope, fertiliser, gears, gradients of hills, betting odds, and scale drawings.

o Problems involving ratios and rates should not be covered lightly. They are often tested in HSC exams.

o Encourage students to develop a ‘number sense’ rather than rely on the calculator too much. Check that answers make sense. Estimate first.

o Rate problems should include meaningful applications, for example filling a water tank, population growth, speed, birth and death rates, telephone charges, typing

speed, heartbeat rate, cricket strike and run rates, and population density.

o Applications of concentration: nursing and medicine, agriculture, pesticides, feed additives, vitamin supplements, and fertiliser.

o Syllabus, p. 41: ‘A patient needs 3 litres of fluid per day. One millilitre of fluid contains approximately 15 drops. Find the rate at which the intravenous drip must run, expressing the answer in the form: number of drops fed to the patient per minute.’

o Syllabus, p. 41: ‘Calculate rates of application of chemicals used in agriculture, such as rates for pesticides and feed additives.’

o When calculating areas and volumes, it is easier to convert scaled lengths from millimetres to metres first rather than convert areas and volumes from mm2 or mm3 to m2 or m3 respectively.

o Applications of area, volume and surface area should involve realistic problems (for example the cost of materials needed [paint, wood, carpet, fencing, soil] for a home renovation or gardening job).

o Field diagrams are new to students, so spend considerable time going over the detail and processes. Survey an irregular area using offsets and then calculate its approximate area.

ASSESSMENT ACTIVITIESo Practical test or assignment (for example

offset survey).o Research assignment.

TECHNOLOGYRatios can be entered into the calculator using the

fraction key. However, when simplifying

‘improper ratios,’ to avoid having mixed numeral

answers, use the key to convert them.

LANGUAGEo Syllabus, p. 41: ‘Standard prefixes need to

include nano-, micro-, milli-, centi-, kilo-, mega-, giga- and tera-.


o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____o


7. LINEAR FUNCTIONSText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 7, p. ??Syllabus reference: Algebra and Modelling

AM2 Interpreting linear relationships (p. 46)

INTRODUCTIONThis Algebra and Modelling topic involves much graphing work and analysis of practical situations that can be modelled by linear functions. Students should appreciate how formulas and graphs are practical ways of describing the mathematical patterns that occur in society, industry and nature. Algebra can be a difficult topic for Mathematics General students, so spend considerable time covering each concept and skill precisely.

CONTENT

1 Graphing linear functions AM2

o generate tables of values from a linear equation

o graph linear functions with pencil and paper, and with technology, given an equation or a table of values

o determine the y-intercept for a given grapho sketch graphs of linear functions expressed

in the form y = mx b without the use of tables

2 The gradient formula AM2

o calculate the gradient of a straight line from a graph

3 Linear modelling AM2

o identify independent and dependent variables in practical contexts

o establish a meaning for the intercept on the vertical axis in a given context

o use linear equations to model practical situations, for example simple interest

o describe the limitations of linear models in practical contexts

4 (HSC) Linear variation AM4

o develop graphs of linear equations of the form y = mx from descriptions of situations in which one quantity varies directly with another, and use the graph to establish the value of m (the gradient) and solve problems related to the given variation context

o develop linear equations from descriptions of situations in which one quantity varies directly with another

5 Conversion graphs AM2

o use graphs to make conversions, for example, Australian dollars to euros

6 Intersection of lines AM2

o sketch the graphs of a pair of linear equations to find the point of intersection

o find the solution of a pair of simultaneous linear equations from a given graph

o solve practical problems using graphs of simultaneous linear equations

7 Stepwise linear functions AM2

o use stepwise linear functions to model and interpret practical situations, for example parking charges, taxi fares, tax payments and freight charges


RELATED TOPICSPreliminary: Algebra and equations, Buying a car, Phone plans and downloading data. Driving safely, HSC: Health and medicine, Non-linear functions.

EXTENSION ACTIVITIESo (HSC) Inverse linear variation, solving

simultaneous equations algebraically.

TEACHING NOTES AND IDEASo Resources: grid paper, graphing software or

graphics calculators, spreadsheets, conversion graphs.

o An algebraic model approximates a real-life situation using a formula, table of values or graph.


o Students are required only to use the gradient-intercept form of a straight line (y = mx b), not the general form or any other form.

o For linear cost functions, discuss fixed costs versus variable costs. Examples: printing costs, taxi fares, and catering costs.

o Syllabus, p.55: ‘Students should recognise the limitations of linear models in practical contexts, for example a person’s height as a function of age may be approximated by a straight line for a limited number of years. Students should be aware that models may apply only over a particular domain’.

o With linear variation, when x doubles, y doubles. When x is halved, y is halved. Applications: distance versus speed, cost versus time, cost versus number of people.

o Examples of stepwise linear functions: parking costs, speeding fines, and postage costs

o Non-linear functions, their graphs and other types of variation will be covered next year in the HSC topic Non-linear functions.

ASSESSMENT ACTIVITIESo Practical graphing test or assignment, with

or without technology.

TECHNOLOGYInvestigate the features of graphing software, a graphics calculator or spreadsheet to graph a line, to locate points and intercepts, and to find the point of intersection of two lines.

LANGUAGEo Students should not only know the

meanings of gradient and vertical intercept as they relate to a linear graph, but also their meanings with respect to a linear function. Gradient = rate of change of y, vertical intercept = (initial) value of y when x = 0.

o Syllabus, p. 51: ‘Students should develop an understanding of a function as input, processing, output. (It is not intended that students learn a formal definition of a function).’

o With variation, students are sometimes confused that x and y can take on different values while k stays the same. Stress that,

for different problems, x and y are variable but k is a constant.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


FOCUS STUDY: BUYING A CARText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 8, p. ??Syllabus reference: Mathematics and Driving

FSDr1 Costs of purchase and insurance (p. 64)FSDr2 Running costs and depreciation (p. 66)

INTRODUCTIONThis focus study looks at the costs of purchasing and maintaining a car, applying skills from the Financial Mathematics, Data and Statistics, and Measurement strands. Linear modelling is also examined again in the context of stamp duty and straight-line depreciation. This is a practical topic in which students can role-play the processes and decisions involved in buying a car. The financial and statistical data to be used should be as authentic as possible—there is much opportunity for visiting websites and online calculators.

CONTENT

1 Motor insurance FSDr1

o describe the different types of insurance available, including compulsory and non-compulsory third-party insurance, and comprehensive insurance

o compare regional theft statistics and the related cost of insurance

o analyse theft and accident statistics in relation to insurance costs

2 Stamp duty FSDr1

o calculate the cost of stamp duty payable using current rates

o create a line graph showing the stamp duty payable on vehicles of various prices, for example create a line graph for vehicles priced from $1000 to $80 000

3 Car loans FSDr1

o determine the monthly repayments on a reducing balance personal loan using tables or an online calculator

o compare the sale price of a car and the total amount paid over the period of the loan

4 Purchasing costs FSDr1

o compare the cost of purchase of different motor vehicles (cars and motorcycles only), including finance, transfer of registration and insurance

5 Fuel consumption and prices FSDr2

o identify fuel consumption measures as rateso calculate the amount of fuel used on a tripo compare fuel consumption statistics for

various vehicleso compare the amount of fuel needed and

associated costs for various sizes, makes and models of vehicles, over different distances

o collect and present data on the price of fuel over time to identify trends

6 Straight-line depreciation FSDr2

o calculate the percentage decrease in the value of a new vehicle after one year

o calculate the depreciation of a vehicle using the straight-line method S = V0 – Dn

o create a depreciation graph based on the straight-line method of depreciation (graphs to be produced from formulas and tables)

o use prepared graphs and tables of straight-line depreciation to solve problems

7 Declining balance depreciation FSDr2

o calculate the depreciation of a vehicle using the declining balance method S = V0(1 – r)n

o use prepared graphs and tables of declining balance depreciation to solve problems


RELATED TOPICSPreliminary: Measurement, Linear functions, Analysing data, Investing money, Driving safely, HSC: Credit and annuities, Equations and linear functions.

EXTENSION ACTIVITIES


o Investigate insurance, the role of actuaries, and the probabilities of accidents and thefts.

o Investigate the cost of petrol in other states or other countries. Where can the cheapest fuel be found?

TEACHING NOTES AND IDEASo Resources: Websites such as RTA, NRMA,

MAA, Money Smart, car-purchasing sites and insurance companies.

o Syllabus, p.65: ‘Teachers should be sensitive to the situations and experiences of students when discussing accident statistics’.

o What factors directly affect the size of car insurance premiums? Why? Discuss in class how and why insurance companies determine premiums.

o Students should investigate what effect increasing the excess has on the size of a premium.

o Like income tax and some forms of commission, stamp duty is an example of a piecewise linear function, calculated according to a sliding scale.

o Syllabus, p.67: ‘Calculate and compare running costs for similar vehicles using different types of fuel, for example calculate and compare the running costs of a particular vehicle using petrol, diesel, or liquefied petroleum gas (LPG) ... Students could investigate the ‘break-even’ cost of installing LPG. A graph would be an appropriate method for displaying the results’.

o Explain why there are usually two fuel consumption rates quoted for a model of car.

o Why is petrol cheaper in Queensland?o Syllabus, p.67: ‘Actual running costs could

be calculated from a logbook, which includes, date, location, cost and amount of petrol purchased, and odometer reading’.

o Syllabus, p.67: ‘Investigate cycles in the price of unleaded petrol (ULP) and evaluate saving strategies over time ... Compare country fuel prices to metropolitan fuel prices over time, and compare different fuel-type prices over time. Students can obtain data from the Internet and present the data graphically’.

o Syllabus, p.67: ‘The depreciation in the first year of a new car can exceed 35%. For many vehicles, depreciation levels out to between 7% and 10% per annum after the first three years’.

o In the depreciation formulas, V0 is the ‘Value of the car at time 0’, or the initial value of the car. Note that these formulas actually calculate the salvage value, not the depreciation (in the same way the compound interest formula does not calculate the compound interest). To find the depreciation, the salvage value must be subtracted from the initial value.

o The declining balance formula for depreciation is actually a ‘negative’ version of the compound interest formula. The graph of this formula shows the rapid drop in the value of the car straight after it is bought.

ASSESSMENT ACTIVITIESo See the syllabus, p.65, for possible

investigations involving insurance premiums or the costs of buying a car.

TECHNOLOGYUse spreadsheets to calculate stamp duty, car loans, purchasing costs and depreciation. The MAA website www.maa.nsw.gov.au features a calculator for the CTP insurance premiums of all the major insurance companies.

LANGUAGEo Be wary of the amount of jargon related to

insurance, for example premium, excess, no-claim discount, third party.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


http://www.maa.nsw.gov.au/


o DATE___ / /_____

9. ANALYSING DATAText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 9, p. ??Syllabus reference: Data and Statistics

DS2 Displaying and interpreting single data sets (p. 34)DS3 Summary statistics (p. 36)

INTRODUCTIONThis topic examines statistical calculations and the measures of location and spread. Students will use pen-and paper techniques and the calculator’s statistical functions to determine the summary statistics of data sets presented in different forms. New content includes interquartile range, box-and-whisker plots, cumulative frequency graphs, deciles, percentiles and standard deviation. This is a fairly technical topic, so spend a considerable amount of teaching time going over the detail and statistical skills.

CONTENT

1 The mean DS3

o calculate the mean for grouped data presented in table or graphical form

o determine the mean for larger data sets of either ungrouped or grouped data using the statistical functions of a calculator

2 The median and mode DS3

o calculate the median, including from stem-and-leaf plots

o calculate the measures of location – mean, mode and median – for grouped data presented in table or graphical form

3 Comparing measures of location DS3

o select and use the appropriate statistic (mean, median or mode) to describe features of a data set, for example median house prices, or modal shirt size

o assess the effect of outlying values on summary statistics for small data sets

4 Quartiles, deciles and percentiles DS2

o divide large sets of data into deciles, quartiles and percentiles and interpret displays

5 The range and interquartile range DS2

o calculate and interpret the range and interquartile range as measures of the spread of a data set

6 Cumulative frequency graphs DS2, DS3

o calculate the median from cumulative frequency polygons

o construct frequency tables for grouped data from cumulative frequency graphs (histograms and polygons)

o estimate the median and upper and lower quartiles of a data set from a cumulative frequency polygon for grouped data

7 Box-and-whisker plots DS2

o establish a five-number summary for a data set (lower extreme, lower quartile, median, upper quartile and upper extreme)

o determine the five-number summary from a stem-and-leaf plot

o develop a box-and-whisker plot from a five-number summary

8 Standard deviation DS3

o describe (population) standard deviation informally as a measure of the spread of data in relation to the mean

o calculate summary statistics using

spreadsheet formulas

9 Comparing samples and populations DS3

o compare summary statistics of various samples from the same population



RELATED TOPICSPreliminary: Collecting and presenting data, Buying a car, Phone plans and downloading data, Driving safely, HSC: Statistical distributions, Water usage, Health and medicine, Sampling and the normal distribution, Energy and sustainability.

EXTENSION ACTIVITIESo The formula and method for calculating

standard deviation. A spreadsheet could be set up to calculate standard deviation.

TEACHING NOTES AND IDEASo Resources: statistical data, including those

collected from the Collecting and presenting data topic, graphics calculator, spreadsheet, statistical software, Australian Bureau of Statistics website www.abs.gov.au, including CensusAtSchool, and Bureau of Meteorology website www.bom.gov.au.

o Syllabus, p.32: ‘Students could collect, display and analyse data related to a course of study in another key learning area, for example fitness data in PDHPE or attitude data in Geography, or results from a scientific experiment’.

o Collect different ‘averages’ from newspapers and determine which is most appropriate. The mean can be affected by extreme scores, the mode is appropriate for categorical data or if many scores are common, the median is unsuitable if scores are clumped. Which is lower: the mean or median house price in Sydney?

o Investigate the effects of adding a typical score or an extreme score to a data set.

o The formal definition of an outlier, as well as comparing data from two different distributions, will be met in the HSC topic, Statistical distributions.

o Include problems in which students need to find the value of a new score that will make a data set have a given mean, because this is commonly tested in the HSC exam.

o Students are not required to calculate standard deviation from first principles. The emphasis is upon knowing that it is a measure of spread about the mean and being able to calculate it using a

calculator’s statistical functions. The

sample standard deviation is no longer part of this course: use the

population standard deviation only.o Sample size affects the reliability of the

statistics obtained from a sample. The sample mean approaches the population mean as the size of the sample increases. Calculate and compare the means (and other statistics) of different samples from the same population. Compare the heartbeat rate of a Year 11 class of students to that of the whole of Year 11.

ASSESSMENT ACTIVITIESo Statistical investigation.o Spreadsheet or graphics calculator test.

TECHNOLOGYInvestigate the statistical functions of a calculator, graphics calculator, spreadsheet or statistical software. The STDEVP() function on a

spreadsheet calculates . Be wary of the individual differences in the statistical modes of calculators, especially when inputing data from a frequency table.

LANGUAGEo Reinforce the collective terms ‘measures of

location’ and ‘measures of spread’.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


FOCUS STUDY: PHONE PLANS AND DOWNLOADING DATAText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 10, p. ??Syllabus reference: Mathematics and Communication

FSCo1 Mobile phone plans (p. 58)FSCo2 Digital download and file storage (p. 60)

INTRODUCTIONThis focus study looks at the measurement and financial mathematics behind downloading data from the Internet and using a mobile phone plan. It is a practical topic that is extremely relevant and useful to young people today, examining issues such as download times, illegal downloading and the usage and costs of mobile phones. The Internet is a rich source of up-to-date information for this topic, from online calculators that calculate download times to comparison websites that allow you to find the best mobile phone plan.

CONTENT

1 Bits and bytes FSCo2

o use prefixes to describe the size of units of storage, for example mega-, giga-, tera-

o convert units of storage from bits to bytes, and vice-versa

o convert between units for measuring memory size, file size and secondary storage on devices such as USB drives and external hard drives

2 Download speed FSCo2

o calculate the time to download or upload a file, given a download or upload speed in bits per second, or kilobits per second, where a kilobit is defined as 1000 bits

3 Downloading music and video FSCo2

o collect, display and analyse data on the downloading of music and videos

o calculate the probabilities of songs being played using the random selection mode

o interpret statistics related to the effect of downloading audio files and video files, legally and illegally, on the sales of media companies

4 Mobile phone plans FSCo1

o read and interpret mobile phone billso read and interpret mobile phone planso calculate the cost of calls, given the time

and duration, based on different mobile phone plans

o calculate the cost of sending and receiving messages, given the details of the mobile phone plan

o calculate the cost of data usage, given the details of the mobile phone plan

5 Call costs and usage FSCo1

o construct and interpret tables and graphs of mobile phone usage and the cost of making mobile phone calls (graphs should include stepwise linear functions)

o investigate patterns of usage for a given phone bill

6 Comparing phone plans FSCo1

o determine a suitable mobile phone plan using calculations based on a typical usage pattern


RELATED TOPICSPreliminary: Collecting and presenting data, Measurement, Linear functions, Analysing data.

EXTENSION ACTIVITIESo Investigate other types of phone calls (for

example video calls) and downloadable apps, and their costs.

o Syllabus, p.61: ‘As an extension activity, students could consider the costs and calculations associated with integrated


plans that bundle landline services, mobile phones and Internet access’.

TEACHING NOTES AND IDEASo Resources: mobile phone plans and bills,

graphs and statistics on mobile phone use and download of music and video.

o Students should be wary of what happens when they go over the included credit and data of their mobile phone plan.

o There is some inconsistency in the use of ‘kilo-‘ to mean 1024 in ‘kilobytes’ when it means 1000 everywhere else, including in ‘kilobits’. Kilo- is the metric prefix meaning one thousand, but it has also been applied to mean 1024 bytes in ‘kilobytes’ because 1024 is close to 1000. This imprecision has caused confusion and disagreement in the computing industry.

o For download times and file sizes, students should obtain rough estimates of their answers first, then check that their calculated answers sound sensible and feasible.

o Syllabus, p.59: ‘With teacher direction, students should brainstorm a list of the attributes of a mobile phone use who is making effective use of a mobile phone plan. Some of these attributes are knowing and understanding the plan, maximising the use of free-time and off-peak rates, keeping usage within the allowances of the plan.’ Note, however, that most phone plans today do not have ‘off-peak’ periods.

o Syllabus, p.59: ‘Students calculate excess usage charges and consider initial setup costs and fees and/or the costs of switching from one provider to another’.

ASSESSMENT ACTIVITIESo Assignment on selecting the best mobile

phone plan.

TECHNOLOGYOnline calculators and comparison websites, statistical and graphing software.

LANGUAGEo Be wary of the amount of jargon associated

with mobile phones and downloading data. The class could generate a glossary of terminology as a project.

o ‘Bits’ and ‘bytes’ are easy to confuse because they sound so similar, but keep in mind that ‘bit’ is abbreviated with a lower-case ‘b’, while ‘byte’ is abbreviated by an upper-case ‘B’.

o Syllabus, p.61: ‘In this course, the kilobyte is taken to be synonymous with kibibyte’. A kibibyte (KiB) is 1024 bytes where ‘kibi’ stands for ‘kilo-binary’. This word was invented because the kilobyte is often interpreted ambiguously as being either 1000 bytes or 1024 bytes. However, ‘kibibyte’ has not achieved widespread acceptance.

o Explain what the phrase ‘or part thereof’ means when it comes to describing phone call or data charges.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


11. INVESTING MONEYText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 11, p. ??Syllabus reference: Financial Mathematics

FM2 Investing money (p. 26)

INTRODUCTIONThis topic investigates the mathematics of investing money in financial institutions and the share market. The methods and formulas for calculating simple and compound interest introduced in Stage 5 are analysed, followed by the costs and procedures involved in buying shares. There will be many opportunities for students to perform financial calculations, learn new terminology and interpret information presented in tables and graphs.

CONTENT

1 Simple interest FM2

o calculate simple interest using I = Prno calculate monthly, quarterly and six-

monthly interest rates based on quoted rates per annum (pa)

2 Simple interest graphs FM2

o use tables of values for fixed values of P, and hence draw and describe graphs of I against n for different values of r

3 Compound interest FM2o calculate the final amount, interest and

principal using the compound interest formula A = P(1 r)n, where A (amount) represents the final amount, P (principal) represents the initial amount, n is the number of compounding periods, and r is the interest rate per compounding period expressed as a decimal

o compare different investment strategies

4 Compound interest tables FM2

o calculate and compare the final amount, interest and principal using a table of compounded values of one dollar

5 Account fees and charges FM2

o compare costs associated with maintaining accounts with financial institutions

6 Inflation and appreciation FM2

o calculate the price of goods following inflation

o investigate the effect of inflation on priceso calculate the appreciated value of items, for

example stamp collections and other memorabilia

7 Investing in shares FM2

o calculate the dividend paid on a shareholding and the dividend yield (excluding franked dividends)

8 Share tables and graphs FM2

o record and graph the price of a share over time


RELATED TOPICSPreliminary: Earning money and taxation, Buying a car, HSC: Loans and annuities.

EXTENSION ACTIVITIESo Investigate the share market and the figures

involved, such as P/E ratio.

TEACHING NOTES AND IDEASo Resources: interest rates, brochures and

websites from banks and credit unions, The Australian Stock Exchange website www.asx.com.au, Money magazine and Shares magazine, finance sections of newspapers, the Australian Financial Review, spreadsheets, graphics calculators.

o Compare interest rates of different financial institutions.


o Encourage students to mentally convert interest rates from percentages to decimals before putting them into formulas.

o Graphics calculators, financial calculators and spreadsheets have financial functions for calculating simple and compound interest.

o Include back-to-front problems where the final value is given and the principal must be found.

o Compound interest is an application of repeated percentage increase from the Measurement topic.

o Stress that the compound interest formula gives the final amount of an investment, not the compound interest earned. Students who have learned about compound interest at Stage 5.1 have not met its formula yet.

o Investigate the effect of increasing the number of compounding periods over the term of an investment (for example interest calculated monthly rather than yearly).

o Students will meet annuities (investments involving regular equal payments) in the HSC topic Loans and annuities.

o Investigate a selection of companies listed on the Australian Stock Exchange, preferably from different industries. Investigate the All Ordinaries Index or the Consumer Price Index.

o Simulate investing in a portfolio of shares over a period of time and calculate profits and losses. Play the ASX Game on the Australian Stock Exchange website. Link with the ‘Stock Market Game’ run for Economics students.

o Find out the current inflation rate and, if possible, find out the prices of items five or ten years ago.

ASSESSMENT ACTIVITIESo Investigate the different types of

investments in financial institutions.o Simulate investing in a share portfolio and

tracking the changes in share prices.o Vocabulary test.

TECHNOLOGYUse the graphing capabilities of a spreadsheet or graphics calculator to chart the growth of an investment under compound interest. Variables:

interest rate, compounding period, length of term, size of principal. There is much scope for using spreadsheets and graphics calculators to calculate and graph simple and compound interest. The Internet is a valuable source of interest rates and share prices.

LANGUAGEo What does ‘compound’ mean?o Syllabus, p. 27: ‘The ‘compounded’ value

of a dollar is also known as the ‘future value’ of a dollar. In the financial world, the compound interest formula A = P(1 r)n is known as the future value formula and is expressed as FV = PV(1 r)n’.

o Students can compile a glossary of share market jargon.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


o DATE___ / /_____


FOCUS STUDY: DRIVING SAFELYText: New Century Maths 11 Mathematics General (Pathway 2) Preliminary Course Chapter 12, p. ??Syllabus reference: Mathematics and Driving

FSDr3 Safety (p. 68)

INTRODUCTIONThis short focus study topic investigates road safety, in particular, the influence of speed, alcohol and driver fatigue on road accidents, applying skills from the Data and Statistics, Algebra and Modelling, and Measurement strands. Blood alcohol content is calculated using complex formulas, tables and graphs, then statistical data and displays of road accidents are analysed. Finally, problems involving speed and stopping distance are solved, using formulas, modelling and measurement.

CONTENT

1 Blood alcohol content (BAC)

o calculate and interpret blood alcohol content (BAC) based on drink consumption and body mass, including:

- using formulas, both in word form and algebraic form, to calculate an estimate for BAC

- use tables and graphs to estimate BAC

- determining the number of hours required for a person who stops consuming alcohol to reach zero BAC

- describing limitations of methods of estimating BAC

o construct and interpret graphs that illustrate the level of blood alcohol over time

2 Accident statistics

o construct and interpret tables and graphs relating to motor vehicles and motor vehicle accidents

o collect, represent and interpret data relating to driver behaviour and accident statistics

3 Speed, distance and time

o calculate distance, speed and time, given two of the three quantities (with change of units of measurement as required), using D

= ST,

4 Stopping distance

o calculate stopping distance, including by substitution of values into suitable formulas


RELATED TOPICSPreliminary: Collecting and presenting data, Algebra and equations, Measurement, Probability, Linear functions, Buying a car, Analysing data, HSC: Health and medicine.

EXTENSION ACTIVITIESo Syllabus, p.69: ‘Students could investigate

and make comparisons of legal blood alcohol limits in different countries’.

o Investigate the effect of road surface and other conditions on stopping distance.

TEACHING NOTES AND IDEASo Resources: road accident statistics, the

RTA and NRMA websites. Every state government has websites and resources on road safety, covering advice and statistics on speeding, drink driving and driver fatigue.

o Liaise with the PDHPE faculty for resources on alcohol and drink-driving.

o A BAC of 0.05 means that there is 0.05 g of alcohol in 100 mL of blood. In Australia and many other countries, it is illegal to drive with a BAC of 0.05 or over.

o Syllabus, p.69: ‘The following are limitations to the estimation of BAC: formulas and tables are based on average values and will not apply equally to everyone, factors (variables) that affect BAC include gender, weight, fitness, health and liver function’.

o A ‘standard drink’ contains 10 grams of alcohol, for example a middy of beer or a small (100 mL) glass of wine.


o Syllabus, p.69: ‘Zero BAC is an important consideration for young drivers in NSW, as the state’s laws require a zero BAC limit for all learner and provisional drivers’.

o After drinking, the human body can only reduce the BAC by between 0.015 and 0.02 per hour. The following formula for calculating the time taken for a BAC to

return to zero, Number of hours =

,

assumes the 0.015 rate.o Syllabus, p.69: ‘Calculate by formula the

difference in stopping distance if travelling 5 km/h over the speed limit ... (investigate) stopping distances for different speeds, road conditions and weather conditions’.

o For students who have difficulty working with rates, with speed problems you could introduce the D-S-T triangle, where covering one of the variables gives you the formula for it involving the other two variables. The only limitation of this method is that it does not promote conceptual understanding of why this method works.

o Plan an itinerary for a road trip to another capital city or major town, taking road distances and travelling times into account.

ASSESSMENT ACTIVITIESo Research assignment.

TECHNOLOGYUse an online calculator that measures reaction time, stopping distance and BAC.

LANGUAGEo Emphasise the difference between stopping

distance, reaction-time distance and braking distance.

o BAC stands for ‘blood alcohol content’ or ‘blood alcohol concentration,’ the 0.05 limit is called the ‘prescribed concentration of alcohol’ (PCA), DUI means ‘Driving Under the Influence of alcohol or drugs’.

o COMMENTS_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

o TEACHER’SSIGNATURE___________________________

o DATE___ / /_____


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