Semester 1 (Unit 1)
Topic 1: Calculations, percentages and rates
Examples in context
Calculations – for example:
- creating a budget for living at home and for living independently
- using timesheets, which include overtime, to calculate weekly wages
- converting between weekly, fortnightly and yearly incomes.
Percentages – for example:
- expressing ingredients of packaged food as percentages of the total quantity, or per serving size, or per 100 grams
- comparing the quantities, both numerically and in percentage terms, of additives within a product or between similar products, such as flavours
- calculating commissions, including retainers from sales information.
Rates – for example:
- using rates to compare and evaluate nutritional information, such as quantity per serve and quantity per 100g
- calculating heart rates as beats per minute, given the number of beats and different time periods
- applying rates to calculate the energy used in various activities over different time periods
- completing calculations with rates, including solving problems involving direct proportion in terms of rate; for example, if a person works for 3 weeks at a rate of $300 per week, how much do they earn?
- analysing and interpreting tables and graphs that compare body ratios such as hip height versus stride length, foot length versus height.
Calculations:
solve practical problems requiring basic number operations (ACMEM001)
apply arithmetic operations according to their correct order (ACMEM002)
ascertain the reasonableness of answers to arithmetic calculations (ACMEM003)
use leading-digit approximation to obtain estimates of calculations (ACMEM004)
use a calculator for multi-step calculations (ACMEM005)
check results of calculations for accuracy (ACMEM006)
recognise the significance of place value after the decimal point (ACMEM007)
evaluate decimal fractions to the required number of decimal places (ACMEM008)
round up or round down numbers to the required number of decimal places (ACMEM009)
apply approximation strategies for calculations. (ACMEM010)
Percentages:
calculate a percentage of a given amount (ACMEM011)
determine one amount expressed as a percentage of another (ACMEM012)
apply percentage increases and decreases in situations; for example, mark-ups, discounts and GST. (ACMEM013)
Rates:
identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse (ACMEM014)
convert units of rates occurring in practical situations to solve problems (ACMEM015)
use rates to make comparisons; for example, using unit prices to compare best buys, comparing heart rates after exercise. (ACMEM016)
Topic 2: Measurement
Examples in context
Length – for example:
- determining the dimensions/measurements of food packaging
- determining the length of the lines on a sporting field to find the cost of marking it.
Mass – for example:
- comparing and discussing the components of different food types for the components of packaged food expressed as grams.
Area and volume – for example:
- determining the area of the walls of a room for the purpose of painting
- finding the volume of water collected from a roof under different conditions
- finding the volume of various cereal boxes.
Linear measure:
use metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy and choice of units (ACMEM017)
estimate lengths (ACMEM018)
convert between metric units of length and other length units (ACMEM019)
calculate perimeters of familiar shapes, including triangles, squares, rectangles, and composites of these. (ACMEM020)
Area measure:
use metric units of area, their abbreviations, conversions between them, and appropriate choices of units (ACMEM021)
estimate the areas of different shapes (ACMEM022)
convert between metric units of area and other area units (ACMEM023)
calculate areas of rectangles and triangles. (ACMEM024)
Mass:
use metric units of mass, their abbreviations, conversions between them, and appropriate choices of units (ACMEM025)
estimate the mass of different objects. (ACMEM026)
Volume and capacity:
use metric units of volume, their abbreviations, conversions between them, and appropriate choices of units (ACMEM027)
understand the relationship between volume and capacity (ACMEM028)
estimate volume and capacity of various objects (ACMEM029)
calculate the volume of objects, such as cubes and rectangular and triangular prisms. (ACMEM030)
Units of energy:
use units of energy to describe consumption of electricity, such as kilowatt hours (ACMEM031)
use units of energy used for foods, including calories (ACMEM032)
use units of energy to describe the amount of energy in activity, such as kilojoules (ACMEM033)
convert from one unit of energy to another. (ACMEM034)
Topic 3: Algebra
Examples in context
Formula substitution – for example:
- using formulas to calculate the volumes of various packaging
- using formulas to find the height of a male (H) given the bone radius (r)
- find weekly wage (W) given base wage (b) and overtime hours(h) at 1.5 times rate (r) W = b + 1.5 × h × r.
Single substitution:
substitute numerical values into algebraic expressions; for example, substitute different values of xx to evaluate the expressions 3×5,5(2x−4)3×5,5(2x−4) (ACMEM035)
General substitution:
substitute given values for the other pronumerals in a mathematical formula to find the value of the subject of the formula. (ACMEM036)
Topic 4: Graphs
Examples in context
Reading and interpreting graphs – for example:
- analysing and interpreting a range of graphical information about global weather patterns that affect food growth
- interpreting a range of graphical information provided on gas and electricity bills.
Drawing graphs – for example:
- expressing ingredients of particular food types as percentages of the total quantity, or per serving size, or per 100 grams, and presenting the information in different formats; for example, column graphs, and pie graphs
- creating graphs to show the deductions from gross wages such as tax, the Medicare levy and superannuation.
Reading and interpreting graphs:
interpret information presented in graphs, such as conversion graphs, line graphs, step graphs, column graphs and picture graphs (ACMEM037)
interpret information presented in two-way tables (ACMEM038)
discuss and interpret graphs found in the media and in factual texts. (ACMEM039)
Drawing graphs:
determine which type of graph is best used to display a dataset (ACMEM040)
use spreadsheets to tabulate and graph data (ACMEM041)
draw a line graph to represent any data that demonstrate a continuous change, such as hourly temperature. (ACMEM042)
Semester 2 (Unit 2)
Topic 1: Representing and comparing data
Examples in context
- analysing and interpreting a range of statistical information related to car theft, car accidents and driver behaviour
- using statistics and graphs to find the number of people in each blood type, given the population percentages of blood types in different countries
- using blood usage statistics to predict the amount of blood needed at different times of the year
- using blood donation statistics to predict how much blood will be needed and when.
Classifying data:
identify examples of categorical data (ACMEM043)
identify examples of numerical data. (ACMEM044)
Data presentation and interpretation:
display categorical data in tables and column graphs (ACMEM045)
display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms (ACMEM046)
recognise and identify outliers (ACMEM047)
compare the suitability of different methods of data presentation in real-world contexts. (ACMEM048)
Summarising and interpreting data:
identify the mode (ACMEM049)
calculate measures of central tendency, the arithmetic mean and the median (ACMEM050)
investigate the suitability of measures of central tendency in various real-world contexts (ACMEM051)
investigate the effect of outliers on the mean and the median (ACMEM052)
calculate and interpret quartiles, deciles and percentiles (ACMEM053)
use informal ways of describing spread, such as spread out/dispersed, tightly packed, clusters, gaps, more/less dense regions, outliers (ACMEM054)
calculate and interpret statistical measures of spread, such as the range, interquartile range and standard deviation (ACMEM055)
investigate real-world examples from the media illustrating inappropriate uses, or misuses, of measures of central tendency and spread. (ACMEM056)
Comparing data sets:
compare back-to-back stem plots for different data-sets (ACMEM057)
complete a five number summary for different datasets (ACMEM058)
construct box plots using a five number summary (ACMEM059)
compare the characteristics of the shape of histograms using symmetry, skewness and bimodality. (ACMEM060)
Topic 2: Percentages
Examples in context
- calculating stamp duty costs involved in buying a car, using percentages and tables
- calculating depreciation of a vehicle over time
- using statistics and graphs to find the number of people in each blood type, given the population percentages of blood types in different countries.
Percentage calculations:
review calculating a percentage of a given amount (ACMEM061)
review one amount expressed as a percentage of another. (ACMEM062)
Applications of percentages:
determine the overall change in a quantity following repeated percentage changes; for example, an increase of 10% followed by a decrease of 10% (ACMEM063)
calculate simple interest for different rates and periods. (ACMEM064)
Topic 3: Rates and ratios
Examples in context
Rates – for example:
- using rates to find fuel consumption for different vehicles under different driving conditions
- calculating food, clothing, transport costs per day, week or month using tables, spreadsheets, and estimation
- calculating clothing costs per week or month using tables, spreadsheets, and estimation.
Ratios – for example:
- discussing various ratios used in bicycle gears
- comparing ratios such as people per household.
Ratios:
demonstrate an understanding of the elementary ideas and notation of ratio (ACMEM065)
understand the relationship between fractions and ratio (ACMEM066)
express a ratio in simplest form (ACMEM067)
find the ratio of two quantities (ACMEM068)
divide a quantity in a given ratio (ACMEM069)
use ratio to describe simple scales. (ACMEM070)
Rates:
review identifying common usage of rates such as km/h (ACMEM071)
convert between units for rates; for example, km/h to m/s, mL/min to L/h (ACMEM072)
complete calculations with rates, including solving problems involving direct proportion in terms of rate (ACMEM073)
use rates to make comparisons (ACMEM074)
use rates to determine costs; for example, calculating the cost of a tradesman using rates per hour, call-out fees. (ACMEM075)
Topic 4: Time and motion
Examples in context
Time – for example:
- calculating reaction times through experiments.
Distance – for example:
- calculating distances travelled to school and the time taken, considering different average speeds.
Speed – for example:
- calculating stopping distances for different speeds by using formulas for different conditions such as road type, tyre conditions and vehicle type.
Time:
use units of time, conversions between units, fractional, digital and decimal representations (ACMEM076)
represent time using 12-hour and 24-hour clocks (ACMEM077)
calculate time intervals, such as time between, time ahead, time behind (ACMEM078)
interpret timetables, such as bus, train and ferry timetables (ACMEM079)
use several timetables and electronic technologies to plan the most time-efficient routes (ACMEM080)
interpret complex timetables, such as tide charts, sunrise charts and moon phases (ACMEM081)
compare the time taken to travel a specific distance with various modes of transport (ACMEM082)
Distance:
use scales to find distances, such as on maps; for example, road maps, street maps, bushwalking maps, online maps and cadastral maps (ACMEM083)
optimise distances through trial-and-error and systematic methods; for example, shortest path, routes to visit all towns, and routes to use all roads. (ACMEM084)
Speed:
identify the appropriate units for different activities, such as walking, running, swimming and flying (ACMEM085)
calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
calculate the time or costs for a journey from distances estimated from maps (ACMEM087)
interpret distance-versus-time graphs (ACMEM088)
calculate and interpret average speed; for example, a 4-hour trip covering 250 km. (ACMEM089)