Grade 10 Maths has two streams.  Core and Extension.  Extension is designed to prepare students for Methods maths in the senior years.

 

Grade 10 Core Maths

Number and Algebra

Money and financial mathematics

Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229 – Scootle )

Patterns and algebra

Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230 – Scootle )

Simplify algebraic products and quotients using index laws (ACMNA231 – Scootle )

Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232 – Scootle )

Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233 – Scootle )

Substitute values into formulas to determine an unknown (ACMNA234 – Scootle )

Linear and non-linear relationships

Solve problems involving linear equations, including those derived from formulas (ACMNA235 – Scootle )

Solve linear inequalities and graph their solutions on a number line (ACMNA236 – Scootle )

Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology (ACMNA237 – Scootle )

Solve problems involving parallel and perpendicular lines (ACMNA238 – Scootle )

Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239 – Scootle )

Solve linear equations involving simple algebraic fractions (ACMNA240 – Scootle )

Solve simple quadratic equations using a range of strategies (ACMNA241 – Scootle )

 

Measurement and Geometry

Using units of measurement

Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242 – Scootle )

Geometric reasoning

Formulate proofs involving congruent triangles and angle properties (ACMMG243 – Scootle )

Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244 – Scootle )

Pythagoras and trigonometry

Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245 – Scootle )

 

 

Statistics and Probability

Chance

Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246 – Scootle )

Use the language of ‘if ….then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (ACMSP247 – Scootle )

Data representation and interpretation

Determine quartiles and interquartile range (ACMSP248 – Scootle )

Construct and interpret box plots and use them to compare data sets (ACMSP249 – Scootle )

Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250 – Scootle )

Use scatter plots to investigate and comment on relationships between two numerical variables (ACMSP251 – Scootle )

Investigate and describe bivariate numerical data where the independent variable is time (ACMSP252 – Scootle )

Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253 – Scootle)

 

Year 10 Extension Maths

 

Number and Algebra

Real numbers

Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264 – Scootle )

Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265 – Scootle )

Patterns and algebra

Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266 – Scootle )

Linear and non-linear relationships

Solve simple exponential equations (ACMNA270 – Scootle )

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267 – Scootle )

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268 – Scootle )

Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269 – Scootle )

 

Measurement and Geometry

Using units of measurement

Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271 – Scootle )

Geometric reasoning

Prove and apply angle and chord properties of circles (ACMMG272 – Scootle )

Pythagoras and trigonometry

Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273 – Scootle )

Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274 – Scootle )

Solve simple trigonometric equations (ACMMG275 – Scootle )

Apply Pythagoras’ Theorem and trigonometry to solving three-dimensional problems in right-angled triangles (ACMMG276 – Scootle )

 

Statistics and Probability

Chance

Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (ACMSP277 – Scootle )

Data representation and interpretation

Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278 – Scootle )

Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279 – Scootle) 

Grade 12 General Maths

Semester 1 (Unit 3)

Topic 1: Bivariate data analysis

The statistical investigation process:

review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results. (ACMGM048)

Identifying and describing associations between two categorical variables:

construct two-way frequency tables and determine the associated row and column sums and percentages (ACMGM049)

use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association (ACMGM050)

describe an association in terms of differences observed in percentages across categories in a systematic and concise manner, and interpret this in the context of the data. (ACMGM051)

Identifying and describing associations between two numerical variables:

construct a scatterplot to identify patterns in the data suggesting the presence of an association (ACMGM052)

describe an association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak) (ACMGM053)

calculate and interpret the correlation coefficient (r) to quantify the strength of a linear association. (ACMGM054)

Fitting a linear model to numerical data:

identify the response variable and the explanatory variable (ACMGM055)

use a scatterplot to identify the nature of the relationship between variables (ACMGM056)

model a linear relationship by fitting a least-squares line to the data (ACMGM057)

use a residual plot to assess the appropriateness of fitting a linear model to the data (ACMGM058)

interpret the intercept and slope of the fitted line (ACMGM059)

use the coefficient of determination to assess the strength of a linear association in terms of the explained variation (ACMGM060)

use the equation of a fitted line to make predictions (ACMGM061)

distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation (ACMGM062)

write up the results of the above analysis in a systematic and concise manner. (ACMGM063)

Association and causation:

recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them (ACMGM064)

identify possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner. (ACMGM065)

The data investigation process:

implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables; for example, is there an association between attitude to capital punishment (agree with, no opinion, disagree with) and sex (male, female)? Is there an association between height and foot length? (ACMGM066)

 

Topic 2: Growth and decay in sequences

The arithmetic sequence:

use recursion to generate an arithmetic sequence (ACMGM067)

display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations (ACMGM068)

deduce a rule for the nth term of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions (ACMGM069)

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating the value of an office photocopier at the end of each year using the straight-line method or the unit cost method of depreciation. (ACMGM070)

The geometric sequence:

use recursion to generate a geometric sequence (ACMGM071)

display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations (ACMGM072)

deduce a rule for the nth term of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions (ACMGM073)

use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour, the decreasing height of the bounce of a ball at each bounce; or calculating the value of office furniture at the end of each year using the declining (reducing) balance method to depreciate. (ACMGM074)

Sequences generated by first-order linear recurrence relations:

use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form (ACMGM075)

recognise that a sequence generated by a first-order linear recurrence relation can have a long term increasing, decreasing or steady-state solution (ACMGM076)

use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems; for example, investigating the growth of a trout population in a lake recorded at the end of each year and where limited recreational fishing is permitted, or the amount owing on a reducing balance loan after each payment is made. (ACMGM077)

 

Topic 3: Graphs and networks

The definition of a graph and associated terminology:

explain the meanings of the terms: graph, edge, vertex, loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), arc, weighted graph, and network (ACMGM078)

identify practical situations that can be represented by a network, and construct such networks; for example, trails connecting camp sites in a National Park, a social network, a transport network with one-way streets, a food web, the results of a round-robin sporting competition (ACMGM079)

construct an adjacency matrix from a given graph or digraph. (ACMGM080)

Planar graphs:

explain the meaning of the terms: planar graph, and face (ACMGM081)

apply Euler’s formula, v+f−e=2v+f−e=2, to solve problems relating to planar graphs. (ACMGM082)

Paths and cycles:

explain the meaning of the terms: walk, trail, path, closed walk, closed trail, cycle, connected graph, and bridge (ACMGM083)

investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only) (ACMGM084)

explain the meaning of the terms: Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems; for example, the Königsberg Bridge problem, planning a garbage bin collection route (ACMGM085)

explain the meaning of the terms: Hamiltonian graph and semi-Hamiltonian graph, and use these concepts to investigate and solve practical problems; for example, planning a sight-seeing tourist route around a city, the travelling-salesman problem (by trial-and-error methods only). (ACMGM086)

Semester 2 (Unit 4)

Topic 1: Time series analysis

Describing and interpreting patterns in time series data:

construct time series plots (ACMGM087)

describe time series plots by identifying features such as trend (long term direction), seasonality (systematic, calendar-related movements), and irregular fluctuations (unsystematic, short term fluctuations), and recognise when there are outliers; for example, one-off unanticipated events. (ACMGM088)

Analysing time series data:

smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process (ACMGM089)

calculate seasonal indices by using the average percentage method (ACMGM090)

deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process (ACMGM091)

fit a least-squares line to model long-term trends in time series data. (ACMGM092)

The data investigation process:

implement the statistical investigation process to answer questions that involve the analysis of time series data. (ACMGM093)

 

Topic 2: Loans, investments and annuities

Compound interest loans and investments:

use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment (ACMGM094)

calculate the effective annual rate of interest and use the results to compare investment returns and cost of loans when interest is paid or charged daily, monthly, quarterly or six-monthly (ACMGM095)

with the aid of a calculator or computer-based financial software, solve problems involving compound interest loans or investments; for example, determining the future value of a loan, the number of compounding periods for an investment to exceed a given value, the interest rate needed for an investment to exceed a given value. (ACMGM096)

Reducing balance loans (compound interest loans with periodic repayments):

use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan (ACMGM097)

with the aid of a financial calculator or computer-based financial software, solve problems involving reducing balance loans; for example, determining the monthly repayments required to pay off a housing loan. (ACMGM098)

Annuities and perpetuities (compound interest investments with periodic payments made from the investment):

use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity (ACMGM099)

with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case); for example, determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount. (ACMGM100)

 

Topic 3: Networks and decision mathematics

Trees and minimum connector problems:

explain the meaning of the terms tree and spanning tree identify practical examples (ACMGM101)

identify a minimum spanning tree in a weighted connected graph either by inspection or by using Prim’s algorithm (ACMGM102)

use minimal spanning trees to solve minimal connector problems; for example, minimising the length of cable needed to provide power from a single power station to substations in several towns. (ACMGM103)

Project planning and scheduling using critical path analysis (CPA):

construct a network to represent the durations and interdependencies of activities that must be completed during the project; for example, preparing a meal (ACMGM104)

use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project (ACMGM105)

use ESTs and LSTs to locate the critical path(s) for the project (ACMGM106)

use the critical path to determine the minimum time for a project to be completed (ACMGM107)

calculate float times for non-critical activities. (ACMGM108)

Flow networks:

solve small-scale network flow problems including the use of the ‘maximum-flow minimum- cut’ theorem; for example, determining the maximum volume of oil that can flow through a network of pipes from an oil storage tank (the source) to a terminal (the sink). (ACMGM109)

Assignment problems:

use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem; for example, assigning four swimmers to the four places in a medley relay team to maximise the team’s chances of winning (ACMGM110)

determine the optimum assignment(s), by inspection for small-scale problems, or by use of the Hungarian algorithm for larger problems. (ACMGM111)

Grade 11 General Maths

Semester 1 (Unit 1)

Topic 1: Consumer arithmetic

Applications of rates and percentages:

review rates and percentages (ACMGM001)

calculate weekly or monthly wage from an annual salary, wages from an hourly rate including situations involving overtime and other allowances and earnings based on commission or piecework (ACMGM002)

calculate payments based on government allowances and pensions (ACMGM003)

prepare a personal budget for a given income taking into account fixed and discretionary spending (ACMGM004)

compare prices and values using the unit cost method (ACMGM005)

apply percentage increase or decrease in various contexts; for example, determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest (ACMGM006)

use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, such as US$1500, or the value of a given amount of foreign currency when converted to Australian dollars, such as the value of €2050 in Australian dollars (ACMGM007)

calculate the dividend paid on a portfolio of shares, given the percentage dividend or dividend paid per share, for each share; and compare share values by calculating a price-to-earnings ratio. (ACMGM008)

Use of spreadsheets:

use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, preparing a wage-sheet displaying the weekly earnings of workers in a fast food store where hours of employment and hourly rates of pay may differ, preparing a budget, or investigating the potential cost of owning and operating a car over a year. (ACMGM009)

 

Topic 2: Algebra and matrices

Linear and non-linear expressions:

substitute numerical values into linear algebraic and simple non-linear algebraic expressions, and evaluate (ACMGM010)

find the value of the subject of the formula, given the values of the other pronumerals in the formula (ACMGM011)

use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities; for example, a table displaying the body mass index (BMI) of people of different weights and heights. (ACMGM012)

Matrices and matrix arithmetic:

use matrices for storing and displaying information that can be presented in rows and columns; for example, databases, links in social or road networks (ACMGM013)

recognise different types of matrices (row, column, square, zero, identity) and determine their size (ACMGM014)

perform matrix addition, subtraction, multiplication by a scalar, and matrix multiplication, including determining the power of a matrix using technology with matrix arithmetic capabilities when appropriate (ACMGM015)

use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each other via a third person. (ACMGM016)

 

Topic 3: Shape and measurement

Pythagoras Theorem:

review Pythagoras’ Theorem and use it to solve practical problems in two dimensions and for simple applications in three dimensions. (ACMGM017)

Mensuration:

solve practical problems requiring the calculation of perimeters and areas of circles, sectors of circles, triangles, rectangles, parallelograms and composites (ACMGM018)

calculate the volumes of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the volume of water contained in a swimming pool (ACMGM019)

calculate the surface areas of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the surface area of a cylindrical food container. (ACMGM020)

Similar figures and scale factors:

review the conditions for similarity of two-dimensional figures including similar triangles (ACMGM021)

use the scale factor for two similar figures to solve linear scaling problems (ACMGM022)

obtain measurements from scale drawings, such as maps or building plans, to solve problems (ACMGM023)

obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures (ACMGM024)

obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids. (ACMGM025)

 

Unit 2

Topic 1: Univariate data analysis and the statistical investigation process

The statistical investigation process:

review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results. (ACMGM026)

Making sense of data relating to a single statistical variable:

classify a categorical variable as ordinal, such as income level (high, medium, low), or nominal, such as place of birth (Australia, overseas), and use tables and bar charts to organise and display the data (ACMGM027)

classify a numerical variable as discrete, such as the number of rooms in a house, or continuous, such as the temperature in degrees Celsius (ACMGM028)

with the aid of an appropriate graphical display (chosen from dot plot, stem plot, bar chart or histogram), describe the distribution of a numerical dataset in terms of modality (uni or multimodal), shape (symmetric versus positively or negatively skewed), location and spread and outliers, and interpret this information in the context of the data (ACMGM029)

determine the mean and standard deviation of a dataset and use these statistics as measures of location and spread of a data distribution, being aware of their limitations. (ACMGM030)

Comparing data for a numerical variable across two or more groups:

construct and use parallel box plots (including the use of the ‘Q1 – 1.5 x IQR’ and ‘Q3 + 1.5 x IQR’ criteria for identifying possible outliers) to compare groups in terms of location (median), spread (IQR and range) and outliers and to interpret and communicate the differences observed in the context of the data (ACMGM031)

compare groups on a single numerical variable using medians, means, IQRs, ranges or standard deviations, as appropriate; interpret the differences observed in the context of the data; and report the findings in a systematic and concise manner (ACMGM032)

implement the statistical investigation process to answer questions that involve comparing the data for a numerical variable across two or more groups; for example, are Year 11 students the fittest in the school? (ACMGM033)

 

Topic 2: Applications of trigonometry

Applications of trigonometry:

review the use of the trigonometric ratios to find the length of an unknown side or the size of an unknown angle in a right-angled triangle (ACMGM034)

determine the area of a triangle given two sides and an included angle by using the rule Area=12absinCArea=12absin⁡C, or given three sides by using Heron’s rule, and solve related practical problems (ACMGM035)

solve problems involving non-right-angled triangles using the sine rule (ambiguous case excluded) and the cosine rule (ACMGM036)

solve practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation. (ACMGM037)

Topic 3: Linear equations and their graphs

Linear equations:

identify and solve linear equations (ACMGM038)

develop a linear formula from a word description (ACMGM039)

Straight-line graphs and their applications:

construct straight-line graphs both with and without the aid of technology (ACMGM040)

determine the slope and intercepts of a straight-line graph from both its equation and its plot (ACMGM041)

interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation (ACMGM042)

construct and analyse a straight-line graph to model a given linear relationship; for example, modelling the cost of filling a fuel tank of a car against the number of litres of petrol required. (ACMGM043)

Simultaneous linear equations and their applications:

solve a pair of simultaneous linear equations, using technology when appropriate (ACMGM044)

solve practical problems that involve finding the point of intersection of two straight-line graphs; for example, determining the break-even point where cost and revenue are represented by linear equations. (ACMGM045)

Piece-wise linear graphs and step graphs:

sketch piece-wise linear graphs and step graphs, using technology when appropriate (ACMGM046)

interpret piece-wise linear and step graphs used to model practical situations; for example, the tax paid as income increases, the change in the level of water in a tank over time when water is drawn off at different intervals and for different periods of time, the charging scheme for sending parcels of different weights through the post. (ACMGM047)

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 1cm3=1mL1cm3=1mL and 1m3=1kL1m3=1kL (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 xx (ACMEM122)

graph linear functions for all values of xx 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)

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)

Number and Algebra

Real numbers

Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208 – Scootle )

Apply index laws to numerical expressions with integer indices (ACMNA209 – Scootle )

Express numbers in scientific notation (ACMNA210 – Scootle )

Money and financial mathematics

Solve problems involving simple interest (ACMNA211 – Scootle )

Patterns and algebra

Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212 – Scootle )

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213 – Scootle )

Linear and non-linear relationships

Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214 – Scootle )

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294 – Scootle )

Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215 – Scootle )

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296 – Scootle )

 

Measurement and Geometry

Using units of measurement

Calculate areas of composite shapes (ACMMG216 – Scootle )

Calculate the surface area and volume of cylinders and solve related problems (ACMMG217 – Scootle )

Solve problems involving the surface area and volume of right prisms (ACMMG218 – Scootle )

Investigate very small and very large time scales and intervals (ACMMG219 – Scootle )

Geometric reasoning

Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220 – Scootle )

Solve problems using ratio and scale factors in similar figures (ACMMG221 – Scootle )

Pythagoras and trigonometry

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222 – Scootle )

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223 – Scootle )

Apply trigonometry to solve right-angled triangle problems (ACMMG224 – Scootle )

 

Statistics and Probability

Chance

List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225 – Scootle )

Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’ (ACMSP226 – Scootle )

Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (ACMSP227 – Scootle )

Data representation and interpretation

Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources (ACMSP228 – Scootle )

Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282 – Scootle )

Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283 – Scootle )

Number and Algebra

Number and place value

Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182 – Scootle )

Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183 – Scootle )

Real numbers

Investigate terminating and recurring decimals (ACMNA184 – Scootle )

Investigate the concept of irrational numbers, including π (ACMNA186 – Scootle )

Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187 – Scootle )

Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188 – Scootle )

Money and financial mathematics

Solve problems involving profit and loss, with and without digital technologies (ACMNA189 – Scootle )

Patterns and algebra

Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190 – Scootle )

Factorise algebraic expressions by identifying numerical factors (ACMNA191 – Scootle )

Simplify algebraic expressions involving the four operations (ACMNA192 – Scootle )

Linear and non-linear relationships

Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193 – Scootle )

Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194 – Scootle )

Measurement and Geometry

Using units of measurement

Choose appropriate units of measurement for area and volume and convert from one unit to another (ACMMG195 – Scootle )

Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (ACMMG196 – Scootle )

Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area (ACMMG197 – Scootle )

Develop formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (ACMMG198 – Scootle )

Solve problems involving duration, including using 12- and 24-hour time within a single time zone (ACMMG199 – Scootle )

Geometric reasoning

Define congruence of plane shapes using transformations (ACMMG200 – Scootle )

Develop the conditions for congruence of triangles (ACMMG201 – Scootle )

Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202 – Scootle )

Statistics and Probability

Chance

Identify complementary events and use the sum of probabilities to solve problems (ACMSP204 – Scootle )

Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’. (ACMSP205 – Scootle )

Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292 – Scootle )

Data representation and interpretation

Investigate techniques for collecting data, including census, sampling and observation (ACMSP284 – Scootle )

Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (ACMSP206 – Scootle )

Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293 – Scootle )

Investigate the effect of individual data values, including outliers, on the mean and median (ACMSP207 – Scootle )

Number and Algebra

Number and place value

Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149 – Scootle )

Investigate and use square roots of perfect square numbers (ACMNA150 – Scootle )

Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151 – Scootle )

Compare, order, add and subtract integers (ACMNA280 – Scootle )

Real numbers

Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152 – Scootle )

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153 – Scootle )

Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154 – Scootle )

Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155 – Scootle )

Round decimals to a specified number of decimal places (ACMNA156 – Scootle )

Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157 – Scootle )

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158 – Scootle )

Recognise and solve problems involving simple ratios (ACMNA173 – Scootle )

Money and financial mathematics

Investigate and calculate ‘best buys’, with and without digital technologies (ACMNA174 – Scootle )

Patterns and algebra

Introduce the concept of variables as a way of representing numbers using letters (ACMNA175 – Scootle )

Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176 – Scootle )

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177 – Scootle )

Linear and non-linear relationships

Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178 – Scootle )

Solve simple linear equations (ACMNA179 – Scootle )

Investigate, interpret and analyse graphs from authentic data (ACMNA180 – Scootle )

 

Measurement and Geometry

Using units of measurement

Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159 – Scootle )

Calculate volumes of rectangular prisms (ACMMG160 – Scootle )

Shape

Draw different views of prisms and solids formed from combinations of prisms (ACMMG161 – Scootle )

Location and transformation

Describe translations, reflections in an axis and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181 – Scootle )

Geometric reasoning

Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165 – Scootle )

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166 – Scootle )

Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163 – Scootle )

Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164 – Scootle )

 

Statistics and Probability

Chance

Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167 – Scootle )

Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168 – Scootle )

Data representation and interpretation

Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169 – Scootle )

Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSP170 – Scootle )

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171 – Scootle )

Describe and interpret data displays using median, mean and range (ACMSP172 – Scootle )

Number and Algebra

Number and place value

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122 – Scootle )

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123 – Scootle )

Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124 – Scootle )

Fractions and decimals

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125 – Scootle )

Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126 – Scootle )

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127 – Scootle )

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128 – Scootle )

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129 – Scootle )

Multiply and divide decimals by powers of 10 (ACMNA130 – Scootle )

Make connections between equivalent fractions, decimals and percentages (ACMNA131 – Scootle )

Money and financial mathematics

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132 – Scootle )

Patterns and algebra

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133 – Scootle )

Explore the use of brackets and order of operations to write number sentences (ACMNA134 – Scootle )

Measurement and Geometry

Using units of measurement

Connect decimal representations to the metric system (ACMMG135 – Scootle )

Convert between common metric units of length, mass and capacity (ACMMG136 – Scootle )

Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137 – Scootle )

Connect volume and capacity and their units of measurement (ACMMG138 – Scootle )

Interpret and use timetables (ACMMG139 – Scootle )

Shape

Construct simple prisms and pyramids (ACMMG140 – Scootle )

Location and transformation

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142 – Scootle )

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143 – Scootle )

Geometric reasoning

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141 – Scootle )

Statistics and Probability

Chance

Describe probabilities using fractions, decimals and percentages (ACMSP144 – Scootle )

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145 – Scootle )

Compare observed frequencies across experiments with expected frequencies (ACMSP146 – Scootle )

Data representation and interpretation

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147 – Scootle )

Interpret secondary data presented in digital media and elsewhere (ACMSP148 – Scootle )

Number and Algebra

Number and place value

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026 – Scootle )

Recognise, model, represent and order numbers to at least 1000 (ACMNA027 – Scootle )

Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028 – Scootle )

Explore the connection between addition and subtraction (ACMNA029 – Scootle )

Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030 – Scootle )

Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031 – Scootle )

Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032 – Scootle )

Fractions and decimals

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033 – Scootle )

Money and financial mathematics

Count and order small collections of Australian coins and notes according to their value (ACMNA034 – Scootle )

Patterns and algebra

Describe patterns with numbers and identify missing elements (ACMNA035 – Scootle )

Solve problems by using number sentences for addition or subtraction (ACMNA036 – Scootle )

Measurement and Geometry

Using units of measurement

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037 – Scootle )

Compare masses of objects using balance scales (ACMMG038 – Scootle )

Tell time to the quarter-hour, using the language of ‘past’ and ‘to’ (ACMMG039 – Scootle )

Name and order months and seasons (ACMMG040 – Scootle )

Use a calendar to identify the date and determine the number of days in each month (ACMMG041 – Scootle )

Shape

Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042 – Scootle )

Describe the features of three-dimensional objects (ACMMG043 – Scootle )

Location and transformation

Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044 – Scootle )

Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045 – Scootle )

Identify and describe half and quarter turns (ACMMG046 – Scootle )

Statistics and Probability

Chance

Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047 – Scootle )

Data representation and interpretation

Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048 – Scootle )

Collect, check and classify data (ACMSP049 – Scootle )

Create displays of data using lists, table and picture graphs and interpret them (ACMSP050 – Scootle )