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Maths

A deeper level of understanding

All our content is directly connected to subjects from the NSW Board of Studies. We begin by explaining the concepts, then we proceed to simpler questions and eventually tackle questions similar to those in exams.

A fun learning environment

Our classes are both interactive and enjoyable. We like to have group conversations and want students to feel free to ask lots of questions!

What Will You Get?

Personalised Homework Questions

At LOGOS Academia, we make homework personal. We customise student's questions to target each and every one of our student's weak spots. Weekly, they get a special booklet full of practice questions meant to tackle their unique challenges head-on

Answer Books

We start preparing you as early as Year 6 to structure your mathematical explanations. Just like organising paragraphs and sentences in English, we teach students to logically present their work in math using our effective answer book system

Our Proven Lessons Breakdown

15 MIN

We go through any homework related issues, and ensure all students are comfortable.

45 MIN

We teach new material, developing theory, and slowing move up in difficulty until we are answering exam-style questions.

Subject Details

Week 1

WHOLE NUMBERS

THE NUMBER LINE​

  • Investigate everyday situations that use integers locate and represent these numbers on a number line
  • Compare, order, add and subtract integers

Week 2

WHOLE NUMBERS

PRIME AND SQUARE NUMBERS​

  • Identify and describe properties of prime, composite, square and triangular numbers

Week 3

FRACTIONS AND DECIMALS

MENTAL STATEGIES​

  • Use efficient mental and written strategies and apply appropriate digital technologies to solve problems
  • Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers​

Week 4

MULTIPLICATION AND DIVISION

MENTAL STATEGIES​

  • Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies
  • Solve problems involving division by a one-digit number, including those that result in a remainder
  • Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers

Week 5

OPERATIONS

BODMAS​

  • Explore the use of brackets and the order of operations to write number sentences​

Week 6

FRACTIONS AND DECIMALS

OPERATIONS OF DECIMALS​

  • Recognise that the place value system can be extended beyond hundredths​
  • Compare, order and represent decimals
  • Compare fractions with related denominators and locate and represent them on a number line​
  • Multiply and divide decimals by powers of 10
  • Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers​
  • Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies​
  • Round decimals to a specified number of decimal places

Week 7

FRACTIONS AND DECIMALS

OPERATIONS OF FRACTIONS

  • Fractions, Decimals and Percenteges​

Week 8

FRACTIONS AND DECIMALS

PERCENTAGES

  • Make connections between equivalent fractions, decimals and percentages​
  • Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without the use of digital technologies​
  • Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologie​

Week 9

PATTERNS AND ALGEBRA

RECOGNISING AND CREATING PATTERNS​

  • Continue and create sequences involving whole numbers, fractions and decimals describe the rule used to create the sequence​

Week 10

POSITION

INTRODUCTION TO THE CARTESIAN PLANE​

  • Introduce the Cartesian coordinate system using all four quadrants​
  • Use a grid-reference system to describe locations
  • Describe routes using landmarks and directional language

Week 1

TIME 1

24HR TIME​

  • Compare 12- and 24-hour time systems and convert between them​
  • Determine and compare the duration of events
  • Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone​

Week 2

TIME 2

USING AND INTERPRETING TIMETABLES AND TIMEZONES​

  • Compare 12- and 24-hour time systems and convert between them
  • Interpret and use timetables
  • Draw and interpret timelines using a given scale
  • Solve problems involving international time zones

Week 3

ANGLES

TYPES OF ANGLES AND VERTICALLY OPPOSITE ANGLES​

  • Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles use the results to find unknown angles
  • Use the language, notation and conventions of geometry​
  • Recognise the geometrical properties of angles at a point

Week 4

LENGTH

IDENTIFYING SHAPES AND CALCULATING PERIMETER​

  • Calculate the perimeters of rectangles using familiar metric units​
  • Connect decimal representations to the metric system
  • Solve problems involving the comparison of lengths using appropriate units
  • Classify two-dimensional shapes and describe their features
  • Find perimeters of parallelograms, trapeziums, rhombuses and kites

Week 5

TWO-DIMENSIONAL SPACE

TRANSLATION AND SYMMETRY​

  • Describe translations, reflections and rotations of two-dimensional shapes​
  • Identify line and rotational symmetries
  • Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies​

Week 6

TWO-DIMENSIONAL SPACE

DIAGONALS AND THE CIRCLE​

  • Investigate the diagonals of two-dimensional shapes​
  • Identify and name parts of circles

Week 7

LENGTH

CIRCLES​​

  • Investigate the concept of irrational numbers, including π​
  • Investigate the relationship between features of circles, such as the circumference, radius and diameter use formulas to solve problems involving circumference​

Week 8

AREA

SQUARES, RECTANGLES, PARALLELOGRAMS, TRIANGLES​

  • Choose appropriate units of measurement for area and convert from one unit to another​
  • Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving​
  • Classify triangles according to their side and angle properties and describe quadrilaterals​

Week 9

AREA

KITES, RHOMBUSES AND TRAPEZIUMS​

  • Find areas of trapeziums, rhombuses and kites​

Week 10

AREA

CIRCLES​

  • Investigate the relationship between features of circles, such as the area and the radius use formulas to solve problems involving area​

Week 1

THREE-DIMENSIONAL SPACE

CONSTRUCT 3D FIGURES​

  • Compare, describe and name prisms and pyramids
  • Connect three-dimensional objects with their nets and other two-dimensional representations​
  • Construct simple prisms and pyramids

Week 2

VOLUME AND CAPACITY

VOLUME OF PRISMS​

  • Connect volume and capacity and their units of measurement​
  • Convert between common metric units of capacity
  • Calculate the volumes of rectangular prisms

Week 3

MASS

CONVERSIONS OF MASS​

  • Choose appropriate units of measurement for mass
  • Connect decimal representations to the metric system
  • Convert between common metric units of mass

Week 4

DATA

DISPLAY, DESCRIBE AND INTERPRET DATA​

  • Pose questions and collect categorical or numerical data by observation or survey​
  • Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies​
  • Describe and interpret different data sets in context
  • Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
  • Interpret secondary data presented in digital media and elsewhere​

Week 5

CHANCE 1

PROBABILITY

  • List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions​
  • Recognise that probabilities range from 0 to 1

Week 6

CHANCE 2

FREQUENCY AND EXPERIMENTS​

  • Compare observed frequencies across experiments with expected frequencies​
  • Describe probabilities using fractions, decimals and percentages
  • Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies​

Week 7

PROBABILITY

PROBABILITY

  • Construct sample spaces for single-step experiments with equally likely outcomes​
  • Assign probabilities to the outcomes of events and determine probabilities for events​

Week 8

PROBABILITY

COMPLEMENTARY EVENTS​

  • Identify complementary events and use the sum of probabilities to solve problems​

Week 9

COMPUTATIONS WITH INTEGERS​

  • Apply the associative, commutative and distributive laws to aid mental and written computation​
  • Compare, order, add and subtract integers
  • Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies​

Week 10

FRACTIONS, DECIMALS, PERCENTAGES​

  • Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line​
  • Multiply and divide fractions and decimals using efficient written strategies and digital technologies​
  • Express one quantity as a fraction of another, with and without the use of digital technologies​
  • Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies​
  • Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologie​

Week 1

ALGEBRA

INTRODUCTION TO ALGEBRA​

  • Introduce the concept of variables as a way of representing numbers using letters​
  • Extend and apply the laws and properties of arithmetic to algebraic terms and expressions​

Week 2

ALGEBRA

EXPANDING

  • Simplify algebraic expressions involving the four operations​
  • Create algebraic expressions and evaluate them by substituting a given value for each variable​
  • Extend and apply the distributive law to the expansion of algebraic expressions​

Week 3

ALGEBRA

FACTORISATION​

  • Factorise algebraic expressions by identifying numerical factors​

Week 4

EQUATIONS

SOLVING LINEAR EQUATIONS​

  • Investigate and use square roots of perfect square numbers​

Week 5

INDICES

SQUARE ROOT, CUBE ROOT AND SOLVING QUADRATIC EQUATIONS​

  • Solve simple linear equations
  • Solve linear equations using algebraic techniques and verify solutions by substitution​
  • Solve simple quadratic equations

Week 6

LINEAR RELATIONSHIPS​

CARTESIAN PLANE

  • Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point​
  • Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates​
  • Plot linear relationships on the Cartesian plane, with and without the use of digital technologies​

Week 7

LINEAR RELATIONSHIPS​

NUMBER PATTERNS AND DERIVING THE RULE​

  • Plot linear relationships on the Cartesian plane, with and without the use of digital technologies​
  • Solve linear equations using graphical techniques​

Week 8

PYTHAGORAS' THEOREM

C2=A2+B2

  • Investigate Pythagoras' theorem and its application to solving simple problems involving right-angled triangles​

Week 9

PYTHAGORAS' THEOREM

PROVING A TRIANGLE IS RIGHT-ANGLED​

  • Investigate Pythagoras' theorem and its application to solving simple problems involving right-angled triangles​
  • Investigate the concept of irrational numbers​

Week 10

PROPERTIES OF GEOMETRICAL FIGURES:​

TRIANGLES

  • Classify triangles according to their side and angle properties and describe quadrilaterals​
  • Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral​
  • Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning​

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