How Does Education Perfect Maths Align to the NSW Syllabus?
Education Perfect Maths is an online learning resources with scaffolded Smart Lessons aligned to the NSW Syllabus
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Number and Algebra
Computation with Integers (MA44NA)
Compares, orders and calculates with integers, applying a range of strategies to aid computation
Compares, orders and calculates with integers, applying a range of strategies to aid computation
Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)

Education Perfect Lessons

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

Integers
Integer Addition Integer Subtraction Negative Integer Addition and Subtraction Multiplication Division Long Division Order of Operations Negative Integer Multiplication and Division Rational Numbers on the Number Line Adding and Subtracting Decimals on a Number Line Multiplying Decimals Dividing Decimals Extra Resources: Multiplying & Dividing Negative Numbers Extra Resources: Using the Four Operations & Rounding Extra Resources: Divisibility Tests Extra Resources: Prime Numbers Extra Resources: Highest Common Factor and Lowest Common Multiple 
Compare fractions using equivalence; locate and represent positive and negative fractions and mixed numerals on a number line (ACMNA152)

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

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

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

Investigate terminating and recurring decimals (ACMNA184)

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

Investigate the concept of irrational numbers, including pi (ACMNA186)

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

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

Investigate and calculate the Goods and Services Tax (GST), with and without the use of digital technologies

Investigate and calculate 'best buys', with and without the use of digital technologies (ACMNA174)

Solve problems involving profit and loss, with and without the use of digital technologies (ACMNA189)

Ratios and Rates (MA47NA)
Operates with ratios and rates, and explores their graphical representation
Operates with ratios and rates, and explores their graphical representation
Solve a range of problems involving ratios and rates, with and without the use of digital technologies (ACMNA188)

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

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

Simplify algebraic expressions involving the four operations (ACMNA192)

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

Evaluating Algebraic Expressions
Relating Words to Algebra Translating Between Word Descriptions and Algebraic Expressions Translating Between Authentic Situations and Algebraic Expressions Writing and Evaluating Algebraic Expressions Translating Between Situations and Algebraic Expressions Extra Resources: Algebraic Applications Revision: Evaluating Expressions and Using Formulas 
Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)

Factorise algebraic expressions by identifying numerical factors (ACMNA191)

Factorise algebraic expressions by identifying algebraic factors

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

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

Use index notation with numbers to establish the index laws with positiveinteger indices and the zero index (ACMNA182)

Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194)

Solve simple quadratic equations

Linear Relationships (MA411NA)
Creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane
Creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane
Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)

Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates (ACMMG181)

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

Solve linear equations using graphical techniques (ACMNA194)

Measurement and Geometry
Find perimeters of parallelograms, trapeziums, rhombuses and kites (ACMMG196)

Investigate the concept of irrational numbers, including pi (ACMNA186)

Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference (ACMMG197)

Area (MA413MG)
Uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area
Uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area
Choose appropriate units of measurement for area and convert from one unit to another (ACMMG195)

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

Find areas of trapeziums, rhombuses and kites (ACMMG196)

Investigate the relationship between features of circles, such as the area and the radius; use formulas to solve problems involving area (ACMMG197)

Volume (MA414MG)
Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume
Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume
Choose appropriate units of measurement for volume and convert from one unit to another (ACMMG195)

Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general; use formulas to solve problems involving volume (ACMMG198)

Calculate the volumes of cylinders and solve related problems (ACMMG217)

Solve problems involving international time zones

RightAngled Triangles (Pythagoras) (MA416MG)
Applies Pythagoras’ theorem to calculate side lengths in rightangled triangles, and solves related problems
Applies Pythagoras’ theorem to calculate side lengths in rightangled triangles, and solves related problems
Investigate Pythagoras' theorem and its application to solving simple problems involving rightangled triangles (ACMMG222)

Pythagoras’ Theorem
Parts of a Triangle and the Hypotenuse Calculating Unknown Lengths Using Pythagoras’ Theorem Solving Practical Problems Using Pythagoras’ Theorem Pythagoras’ Theorem Proofs Revision: Angles Revision: Triangles Revision: Ratios Revision: Algebraic Substitution and Evaluation Revision: Solving Equations 
Investigate the concept of irrational numbers (ACMNA186)

Properties of Geometrical Figures (MA417MG)
classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)

Identify line and rotational symmetries (ACMMG181)

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

Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning

Define congruence of plane shapes using transformations (ACMMG200)

Develop the conditions for congruence of triangles (ACMMG201)

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

Properties of Geometrical Figures II: Angle Relationships (MA418MG)
identifies and uses angle relationships, including those related to transversals on sets of parallel lines
identifies and uses angle relationships, including those related to transversals on sets of parallel lines
Use the language, notation and conventions of geometry

Recognise the geometrical properties of angles at a point

Identify corresponding, alternate and cointerior angles when two straight lines are crossed by a transversal (ACMMG163)

Solve simple numerical problems using reasoning

Statistics and Probability
Data Collection and Representation (MA419SP)
collects, represents and interprets single sets of data, using appropriate statistical displays
collects, represents and interprets single sets of data, using appropriate statistical displays
Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)

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

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

Single Variable Data Analysis (MA420SP)
analyses single sets of data using measures of location, and range
analyses single sets of data using measures of location, and range
Investigate the effect of individual data values, including outliers, on the mean and median (ACMSP207)

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

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

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

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)

Represent events in twoway tables and Venn diagrams and solve related problems (ACMSP292)
