Working Mathematically  eTAP Lesson 

Communicating  
Uses appropriate terminology, diagrams and symbols in mathematical contexts
NSW.MA5.11WM 
Signs and Symbols in Mathematics 
Selects appropriate notations and conventions to communicate mathematical ideas and solutions
NSW.MA5.21WM 
Expressing More Relationships Between Numbers 
Uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures
NSW.MA5.31WM 

Problem Solving  
Selects and uses appropriate strategies to solve problems
NSW.MA5.12WM 
Changing Words into Math 
Iinterprets mathematical or reallife situations, systematically applying appropriate strategies to solve problems
NSW.MA5.22WM 
Areas of Triangles 
Generalises mathematical ideas and techniques to analyse and solve problems efficiently
NSW.MA5.32WM 
Setting Up and Solving Equations 
Reasoning  
Provides reasoning to support conclusions that are appropriate to the context
NSW.MA5.13WM 
Symbols of Logic Law of Contraposition 
Constructs arguments to prove and justify results
NSW.MA5.23WM 
Modus Tollens, Negation, Law of Syllogism 
Uses deductive reasoning in presenting arguments and formal proofs
NSW.MA5.33WM 
Direct Proofs Conditional Proof 
Number and Algebra  eTAP Lesson 
Financial Mathematics  
Solves financial problems involving earning, spending and investing money
NSW.MA5.14NA 
Investment Growth Over Time 
Solves financial problems involving compound interest
NSW.MA5.24NA 
Interest Rate and Loan Length 
Ratios and Rates  
Recognises direct and indirect proportion, and solves problems involving direct proportion
NSW.MA5.25NA 
Ratios and Proportions 
Draws, interprets and analyses graphs of physical phenomena
NSW.MA5.34NA 
Seeking Trends with Line Graphs 
Algebraic Techniques  
Simplifies algebraic fractions, and expands and factorises quadratic expressions
NSW.MA5.26NA 
Expanding and Reducing Fractions 
Selects and applies appropriate algebraic techniques to operate with algebraic expressions
NSW.MA5.35NA 

Indices  
Operates with algebraic expressions involving positiveinteger and zero indices, and establishes the meaning of negative indices for numerical bases
NSW.MA5.15NA 
Integers and the Number Line 
Applies index laws to operate with algebraic expressions involving integer indices
NSW.MA5.27NA 

Surds and Indices  
Performs operations with surds and indices
NSW.MA5.36NA 

Equations  
Solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques
NSW.MA5.28NA 
How to Use Graphs Graphing Systems of Equations Solving Quadratic Equations by Graphing 
Solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations
NSW.MA5.37NA 
Simultaneous Equations Simultaneous Equations With Strange Solutions 
Linear Relationships  
Determines the midpoint, gradient and length of an interval, and graphs linear relationships
NSW.MA5.16NA 
Slope of a Line Midpoint of a Line Segment 
Uses the gradientintercept form to interpret and graph linear relationships
NSW.MA5.29NA 
Slope Intercept Form of Equations 
Uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line
NSW.MA5.38NA 
Coordinate Axes and Negative Numbers 
NonLinear Relationships  
Graphs simple nonlinear relationships
NSW.MA5.17NA 
Graphing Systems of Equations 
Connects algebraic and graphical representations of simple nonlinear relationships
NSW.MA5.210NA 
Graphing Systems of Inequalities 
Sketches and interprets a variety of nonlinear relationships
NSW.MA5.39NA 
Substitution Elimination 
Polynomials  
Recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems
NSW.MA5.310NA 
Polynomials 
Logarithms  
Uses the definition of a logarithm to establish and apply the laws of logarithms
NSW.MA5.311NA 
Using Logarithms to Model Data 
Functions and Other Graphs  
Uses function notation to describe and sketch functions
NSW.MA5.312NA 
Function Notation 
Measurement and Geometry  eTAP Lesson 
Area and Surface Area  
Calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms
NSW.MA5.18MG 
Areas of Rectangles and Parallelograms Areas of Triangles, Trapezoids and Kites 
Calculates the surface areas of right prisms, cylinders and related composite solids
NSW.MA5.211MG 
Surface Area 
Applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids
NSW.MA5.313MG 
Areas of Regular Polygons Areas of Circles 
Volume  
Applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders
NSW.MA5.212MG 
Cylinders Polyhedrons, Prisms and Pyramids 
Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids
NSW.MA5.314MG 
Cones Solids with Curved Surfaces 
Numbers of Any Magnitude  
Interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures
NSW.MA5.19MG 
Base Ten Exponents 
RightAngled Triangles (Trigonometry)  
Applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression
NSW.MA5.110MG 
Measuring Angles 
Applies trigonometry to solve problems, including problems involving bearings
NSW.MA5.213MG 
Trigonometric Calculations 
Trigonometry and Pythagoras' Theorem  
Applies Pythagorasâ€™ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions
NSW.MA5.315MG 
Definitions  Sine and Cosine Law of Sines Law of Cosines 
Properties of Geometrical Figures  
Describes and applies the properties of similar figures and scale drawings
NSW.MA5.111MG 
Similar Triangles 
Calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar
NSW.MA5.214MG 
Indirect Measurement with Similar Triangles 
Proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals
NSW.MA5.316MG 
Corresponding Parts 
Circle Geometry  
Applies deductive reasoning to prove circle theorems and to solve related problems
NSW.MA5.317MG 
Tangent Properties 
Statistics and Probability  eTAP Lesson 
Single Variable Data Analysis  
Uses statistical displays to compare sets of data, and evaluates statistical claims made in the media
NSW.MA5.112SP 

Uses quartiles and box plots to compare sets of data, and evaluates sources of data
NSW.MA5.215SP 
Probability Data Plots 
Uses standard deviation to analyse data
NSW.MA5.318SP 
Normal Distributions 
Bivariate Data Analysis  
Investigates relationships between two statistical variables, including their relationship over time
NSW.MA5.216SP 
Standard Deviation of Random Variable 
Investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decisionmaking processes
NSW.MA5.319SP 
Dependent & Independent Variables 
Probability  
Calculates relative frequencies to estimate probabilities of simple and compound events
NSW.MA5.113SP 
Multiple Events 
Describes and calculates probabilities in multistep chance experiments
NSW.MA5.217SP 
Conditional Probability 