Semester 1 (Unit 3)
Topic 1: Measurement
Examples in context
- calculating and interpreting dosages for children and adults from dosage panels on medicines, given age or weight
- calculating and interpreting dosages for children from adults’ medication using various formulas (Fried, Young, Clark) in milligrams or millilitres
- calculating surface areas of various buildings to compare costs of external painting.
Linear measure:
review metric units of length, their abbreviations, conversions between them, estimation of lengths, and appropriate choices of units
(ACMEM090)
calculate perimeters of familiar shapes, including triangles, squares, rectangles, polygons, circles, arc lengths, and composites of these.
(ACMEM091)
find the area of irregular figures by decomposition into regular shapes (ACMEM094)
Area measure:
review metric units of area, their abbreviations, and conversions between them (ACMEM092)
use formulas to calculate areas of regular shapes, including triangles, squares, rectangles, parallelograms, trapeziums, circles and sectors (ACMEM093)
find the surface area of familiar solids, including cubes, rectangular and triangular prisms, spheres and cylinders (ACMEM095)
find the surface area of pyramids, such as rectangular- and triangular-based pyramids (ACMEM096)
use addition of the area of the faces of solids to find the surface area of irregular solids. (ACMEM097)
Mass:
review metric units of mass (and weight), their abbreviations, conversions between them, and appropriate choices of units (ACMEM098)
recognise the need for milligrams (ACMEM099)
convert between grams and milligrams. (ACMEM100)
Volume and capacity:
review metric units of volume, their abbreviations, conversions between them, and appropriate choices of units (ACMEM101)
recognise relations between volume and capacity, recognising that and (ACMEM102)
use formulas to find the volume and capacity of regular objects such as cubes, rectangular and triangular prisms and cylinders (ACMEM103)
use formulas to find the volume of pyramids and spheres. (ACMEM104)
Topic 2: Scales, plans and models
Examples in context
- drawing scale diagrams of everyday two-dimensional shapes
- interpreting common symbols and abbreviations used on house plans
- using the scale on a plan to calculate actual external or internal dimensions, the lengths of the house and the dimensions of? particular rooms
- using technology to translate two-dimensional house plans into three-dimensional buildings
- creating landscape designs using technology.
Geometry:
recognise the properties of common two-dimensional geometric shapes and three-dimensional solids (ACMEM105)
interpret different forms of two-dimensional representations of three-dimensional objects, including nets and perspective diagrams (ACMEM106)
use symbols and conventions for the representation of geometric information; for example, point, line, ray, angle, diagonal, edge, curve, face and vertex. (ACMEM107)
Interpret scale drawings:
interpret commonly used symbols and abbreviations in scale drawings (ACMEM108)
find actual measurements from scale drawings, such as lengths, perimeters and areas (ACMEM109)
estimate and compare quantities, materials and costs using actual measurements from scale drawings; for example, using measurements for packaging, clothes, painting, bricklaying and landscaping. (ACMEM110)
Creating scale drawings:
understand and apply drawing conventions of scale drawings, such as scales in ratio, clear indications of dimensions, and clear labelling (ACMEM111)
construct scale drawings by hand and by using software packages. (ACMEM112)
Three dimensional objects:
interpret plans and elevation views of models (ACMEM113)
sketch elevation views of different models (ACMEM114)
interpret diagrams of three-dimensional objects. (ACMEM115)
Right-angled triangles:
apply Pythagoras’ theorem to solve problems (ACMEM116)
apply the tangent ratio to find unknown angles and sides in right-angled triangles (ACMEM117)
work with the concepts of angle of elevation and angle of depression (ACMEM118)
apply the cosine and sine ratios to find unknown angles and sides in right-angled triangles (ACMEM119)
solve problems involving bearings. (ACMEM120)
Topic 3: Graphs
Examples in context
- interpreting graphs showing growth ranges for children (height or weight or head circumference versus age)
- interpreting hourly hospital charts showing temperature and pulse
- interpreting graphs showing life expectancy with different variables.
Cartesian plane:
demonstrate familiarity with Cartesian coordinates in two dimensions by plotting points on the Cartesian plane (ACMEM121)
generate tables of values for linear functions, including for negative values of (ACMEM122)
graph linear functions for all values of with pencil and paper and with graphing software. (ACMEM123)
Using graphs:
interpret and use graphs in practical situations, including travel graphs and conversion graphs (ACMEM124)
draw graphs from given data to represent practical situations (ACMEM125)
interpret the point of intersection and other important features of given graphs of two linear functions drawn from practical contexts; for example, the ‘break-even’ point. (ACMEM126)
Topic 4: Data collection
Examples in context
- analysing data obtained from medical sources, including bivariate data.
Census:
investigate the procedure for conducting a census (ACMEM127)
investigate the advantages and disadvantages of conducting a census. (ACMEM128)
Surveys:
understand the purpose of sampling to provide an estimate of population values when a census is not used (ACMEM129)
investigate the different kinds of samples; for example, systematic samples, self-selected samples, simple random samples (ACMEM130)
investigate the advantages and disadvantages of these kinds of samples; for example, comparing simple random samples with self-selected samples. (ACMEM131)
Simple survey procedure:
identify the target population to be surveyed (ACMEM132)
investigate questionnaire design principles; for example, simple language, unambiguous questions, consideration of number of choices, issues of privacy and ethics, and freedom from bias. (ACMEM133)
Sources of bias:
describe the faults in the collection of data process (ACMEM134)
describe sources of error in surveys; for example, sampling error and measurement error (ACMEM135)
investigate the possible misrepresentation of the results of a survey due to misunderstanding the procedure, or misunderstanding the reliability of generalising the survey findings to the entire population (ACMEM136)
investigate errors and misrepresentation in surveys, including examples of media misrepresentations of surveys. (ACMEM137)
Bivariate scatterplots:
describe the patterns and features of bivariate data (ACMEM138)
describe the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak). (ACMEM139)
Line of best fit:
identify the dependent and independent variable (ACMEM140)
find the line of best fit by eye (ACMEM141)
use technology to find the line of best fit (ACMEM142)
interpret relationships in terms of the variables (ACMEM143)
use technology to find the correlation coefficient (an indicator of the strength of linear association) (ACMEM144)
use the line of best fit to make predictions, both by interpolation and extrapolation (ACMEM145)
recognise the dangers of extrapolation (ACMEM146)
distinguish between causality and correlation through examples. (ACMEM147)
Semester 2 (Unit 4)
Topic 1: Probability and relative frequencies
Examples in context
- using data to calculate the relative frequencies of the different countries of origin of visitors to a particular tourist venue or country
- using data to calculate the relative frequencies of the amounts of household expenditure is this sentence incomplete?
Probability expressions:
interpret commonly used probability statements, including ‘possible’, ‘probable’, ‘likely’, ‘certain’ (ACMEM148)
describe ways of expressing probabilities formally using fractions, decimals, ratios, and percentages. (ACMEM149)Simulations:
perform simulations of experiments using technology (ACMEM150)
recognise that the repetition of chance events is likely to produce different results (ACMEM151)
identify relative frequency as probability (ACMEM152)
identify factors that could complicate the simulation of real-world events. (ACMEM153)
Simple probabilities:
construct a sample space for an experiment (ACMEM154)
use a sample space to determine the probability of outcomes for an experiment (ACMEM155)
use arrays or tree diagrams to determine the outcomes and the probabilities for experiments. (ACMEM156)
Probability applications:
determine the probabilities associated with simple games (ACMEM157)
determine the probabilities of occurrence of simple traffic-light problems. (ACMEM158)
Topic 2: Earth geometry and time zones
Location:
locate positions on Earth’s surface given latitude and longitude using GPS, a globe, an atlas, and digital technologies (ACMEM159)
find distances between two places on Earth on the same longitude (ACMEM160)
find distances between two places on Earth using appropriate technology. (ACMEM161)
Time:
understand the link between longitude and time (ACMEM162)
solve problems involving time zones in Australia and in neighbouring nations, making any necessary allowances for daylight saving (ACMEM163)
solve problems involving Greenwich Mean Time and the International Date Line (ACMEM164)
find time differences between two places on Earth (ACMEM165)
solve problems associated with time zones; for example, internet and phone usage (ACMEM166)
solve problems relating to travelling east and west, incorporating time zone changes. (ACMEM167)
Topic 3: Loans and compound interest
Examples in context
- using formula, graphs and spreadsheets to calculate the outcomes of investment accounts with compound interest
- using percentages, rates and spreadsheets to investigate personal loan calculations
- calculating and analysing the costs, hidden traps, advantages and disadvantages of payment plans with interest free periods, using rates and percentages.
Compound interest:
review the principles of simple interest (ACMEM168)
understand the concept of compound interest as a recurrence relation (ACMEM169)
consider similar problems involving compounding; for example, population growth (ACMEM170)
use technology to calculate the future value of a compound interest loan or investment and the total interest paid or earned (ACMEM171)
use technology to compare, numerically and graphically, the growth of simple interest and compound interest loans and investments (ACMEM172)
use technology to investigate the effect of the interest rate and the number of compounding periods on the future value of a loan or investment. (ACMEM173)
Reducing balance loans (compound interest loans with periodic repayments):
use technology and a recurrence relation to model a reducing balance loan (ACMEM174)
investigate the effect of the interest rate and repayment amount on the time taken to repay a loan. (ACMEM175)