# year 7-10 MAths

## What our Year 7-10 Maths students will develop

### A deeper level of understanding

All of our material is directly linked to topics from the NSW Board of studies. We start with explaining theory, then start with easier questions and move onto exam style questions

### A fun learning environment

Our lessons are fun, engaging and relaxed. We encourage group discussions, and students are encouraged to ask as many questions as possible!

## What you will recieve

#### Each student at PLATO receives three different books each week which are personalised to each individual!

### Weekly books

We design, print and hand out new books to all students each week. We do not bulk print our materials at the start of each term! Our materials evolve week-to-week, learning from the mistakes of all students and automatically refine to become the ultimate learning tools!

###
Class theory book

The theory books contain the class common questions and notes. There is also a weekly report at the front which is jam-packed with details about each student.

### Personalised homework book

These books contain homework questions which are unique to each student based on their weaknesses or special requests. To learn more about the homework system at PLATO, click here.

### Answer books

At PLATO, we get you ready from as early as Year 6 to organise your mathematical arguments. In English, we learn how to organise text with paragraphs and sentences, and maths is no different! We teach students how to logically present their work, with our proven answer book system!

## What ouR PARENTS recieve

### Weekly reports

Our parents and studnets receive a weekly email report letting them know how their progress has changed, and which topics they are struggling with at the moment

### DIRECT COMMUNICATION

You can contact us directly by SMS or phone call, and speak to your child's tutor directly. No emails, no help desk! Just straight to the point communication!

### Our proven lesson breakdown

### 10 weekly lessons in the school term

## 15 min

###### Weekly quiz

**Weekly quiz on content from the previous week.**

## 30 min

###### Homework help

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

## 75 min

###### Lesson

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

# Maths years 7-10 details

- Year 7
- Year 8
- Year 9
- Year 10

### Year 7 Details

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Integers

##### Operations and BODMAS

- 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 2

#### Integers

##### HCF and LCM

- Identify and describe factors and multiples of whole numbers and use them to solve problems
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line

## week 3

#### Angles

##### Types of Angles

- Construct angles using a protractor
- 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
- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal

## week 4

#### Angles

##### Angles on Parallel Lines

- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
- Investigate conditions for two lines to be parallel
- Solve simple numerical problems using reasoning

## week 5

#### Fractions, Decimals and Percenteges

##### Operations of Decimals

- 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
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Round decimals to a specified number of decimal places

## week 6

#### Fractions, Decimals and Percenteges

##### Operations of Fractions

- Solve problems involving addition and subtraction of fractions with the same or related denominators
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies

## week 7

#### Fractions, Decimals and Percenteges

##### Converting Fractions and Decimals

- 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

## week 8

#### Fractions, Decimals and Percenteges

##### Terminating and Reccuring Decimals

- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals
- Connect fractions, decimals and percentages and carry out simple conversions

## week 9

#### Fractions, Decimals and Percenteges

##### 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
- Connect fractions, decimals and percentages and carry out simple conversions

## week 10

#### Fractions, Decimals and Percenteges

##### Calcullating Percentages of Quantities

- Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, 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

*OPERATIONS AND BODMAS*

- 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

*HCF AND LCM*

- Identify and describe factors and multiples of whole numbers and use them to solve problems
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line

*TYPES OF ANGLES*

- Construct angles using a protractor
- 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
- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal

*ANGLES ON PARALLEL LINES*

- Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
- Investigate conditions for two lines to be parallel
- Solve simple numerical problems using reasoning

*OPERATIONS OF DECIMALS*

- 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
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies
- Round decimals to a specified number of decimal places

*OPERATIONS OF FRACTIONS*

- Solve problems involving addition and subtraction of fractions with the same or related denominators
- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- Multiply and divide fractions and decimals using efficient written strategies and digital technologies

*CONVERTING FRACTIONS AND DECIMALS*

- 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

*TERMINATING AND RECCURING DECIMALS*

- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals
- Connect fractions, decimals and percentages and carry out simple conversions

*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
- Connect fractions, decimals and percentages and carry out simple conversions

*CALCULLATING PERCENTAGES OF QUANTITIES*

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

##### WHAT IS A VARIABLE?

- Introduce the concept of variables as a way of representing numbers using letters

## week 2

#### ALGEBRA

##### COLLECTING LIKE-TERMS

- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
- Simplify algebraic expressions involving the four operations

## week 3

#### ALGEBRA

##### EXPANDING

- Extend and apply the distributive law to the expansion of algebraic expressions

## week 4

#### ALGEBRA

##### FACTORISING

- Factorise algebraic expressions by identifying algebraic factors

## week 5

#### ALGEBRA

##### SUBSTITUTION

- Create algebraic expressions and evaluate them by substituting a given value for each variable

## week 6

#### EQUATIONS

##### SOLVING LINEAR EQUATIONS

- Solve simple linear equations
- Solve linear equations using algebraic techniques and verify solutions by substitution

## week 7

#### LINEAR RELATIONSHIPS

##### AN INTRODUCTION TO LINEAR RELATIONSHIPS

- 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

## week 8

#### LINEAR RELATIONSHIPS

##### PLOT LINEAR RELATIONSHIPS ON THE CARTESIAN PLANE, WITH AND WITHOUT THE USE OF DIGITAL TECHNOLOGIES 1

- Plot linear relationships on the Cartesian plane, with and without the use of digital technologies

## week 9

#### LINEAR RELATIONSHIPS

##### SOLVE LINEAR QUEATIONS USING GRAPHICAL TECHNIQUES

- Solve linear equations using graphical techniques

## week 10

#### CONGRUENCY

##### CONGRUENCY

- Define congruence of plane shapes using transformations
- Develop the conditions for congruence of triangles
- Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning

*WHAT IS A VARIABLE?*

- Introduce the concept of variables as a way of representing numbers using letters

*COLLECTING LIKE-TERMS*

- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
- Simplify algebraic expressions involving the four operations

*EXPANDING*

- Extend and apply the distributive law to the expansion of algebraic expressions

*FACTORISING*

- Factorise algebraic expressions by identifying algebraic factors

*SUBSTITUTION*

- Create algebraic expressions and evaluate them by substituting a given value for each variable

*SOLVING LINEAR EQUATIONS*

- Solve simple linear equations
- Solve linear equations using algebraic techniques and verify solutions by substitution

*AN INTRODUCTION TO LINEAR RELATIONSHIPS*

- 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 1*

- Plot linear relationships on the Cartesian plane, with and without the use of digital technologies

*SOLVE LINEAR QUEATIONS USING GRAPHICAL TECHNIQUES*

- Solve linear equations using graphical techniques

*CONGRUENCY*

- Define congruence of plane shapes using transformations
- Develop the conditions for congruence of triangles
- Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning

## week 1

#### INDICES

##### WHAT ARE INDICES?

- Investigate index notation and represent whole numbers as products of powers of prime numbers

## week 2

#### INDICES

##### SQUARE ROOTS AND PERFECT SQUARES

- Investigate and use square roots of perfect square numbers

## week 3

#### LENGTH

##### PERIMETER

- Find perimeters of parallelograms, trapeziums, rhombuses and kites

## week 4

#### LENGTH

##### CIRCLES AND CIRCUMFERENCE

- 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 5

#### AREA

##### SQUARES, RECTANGLES, PARALLELOGRAMS, AND 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

## week 6

#### AREA

##### TRAPEZIUMS, KITES AND RHOMBUSES

- Find areas of trapeziums, rhombuses and kites

## week 7

#### AREA

##### CIRCLES

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

## week 8

#### VOLUME

##### UNITS OF MEASUREMENT FOR VOLUME

- Draw different views of prisms and solids formed from combinations of prisms
- Choose appropriate units of measurement for volume and convert from one unit to another

## week 9

#### VOLUME

##### CALCULATING VOLUME OF PRISMS AND CYLIINDERS

- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general use formulas to solve problems involving volume
- Calculate the volumes of cylinders and solve related problems

## week 10

#### TIME

##### DURATION

- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone
- Solve problems involving international time zones

*WHAT ARE INDICES?*

- Investigate index notation and represent whole numbers as products of powers of prime numbers

*SQUARE ROOTS AND PERFECT SQUARES*

- Investigate and use square roots of perfect square numbers
- Use index notation with numbers to establish the index laws with positive-integer indices and the zero index
- Solve simple quadratic equations

*PERIMETER*

- Find perimeters of parallelograms, trapeziums, rhombuses and kites

*CIRCLES AND CIRCUMFERENCE*

- 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

*SQUARES, RECTANGLES, PARALLELOGRAMS, AND 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

*TRAPEZIUMS, KITES AND RHOMBUSES*

- Find areas of trapeziums, rhombuses and kites

*CIRCLES*

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

*UNITS OF MEASUREMENT FOR VOLUME*

- Draw different views of prisms and solids formed from combinations of prisms
- Choose appropriate units of measurement for volume and convert from one unit to another

*CALCULATING VOLUME OF PRISMS AND CYLIINDERS*

- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general use formulas to solve problems involving volume
- Calculate the volumes of cylinders and solve related problems

*DURATION*

- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone
- Solve problems involving international time zones

## week 1

#### PROBABILITY

##### CALCULATING PROBABILITIES OF OUTCOMES

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

## week 2

#### PROBABILITY

##### COMPLEMENTARY EVENTS

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

## week 3

#### DATA

##### AN INTRODUCTION TO STATISTICS AND DATA ANALYSIS

- Construct and compare a range of data displays, including stem-and-leaf plots and dot plots

## week 4

#### DATA

##### MEAN, MODE, MEDIAN, RANGE

- Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data
- Describe and interpret data displays using mean, median and range

## week 5

#### PYTHAGORA'S THEOREM

##### c^{2}=a^{2}+b^{2}

- Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles

## week 6

#### PYTHAGORA'S THEOREM

##### SOLVE PROBLEMS INVOLVING PYTHAGORA'S THEOREM

- Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles

## week 7

#### PROPERTIES OF GEOMTRICAL FIGURE

##### TRIANGLES AND QUADRILATERALS

- Classify triangles according to their side and angle properties and describe quadrilaterals

## week 8

#### PROPERTIES OF GEOMTRICAL FIGURE

##### ANGLE SUM OF TRIANGLE AND QUADRILATERAL

- Identify line and rotational symmetries
- Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral

## week 9

#### ALGEBRA

##### EXPANDING, SIMPLIFYING AND SOLVING

- Apply the four operations to simple algebraic fractions with numerical denominators
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Solve linear equations

## week 10

#### ALGEBRA

##### FACTORISING AND HARDER EQUATIONS

- Factorise algebraic expressions by taking out a common algebraic factor
- Solve linear equations involving simple algebraic fractions

*CALCULATING PROBABILITIES OF OUTCOMES*

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

*COMPLEMENTARY EVENTS*

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

*AN INTRODUCTION TO STATISTICS AND DATA ANALYSIS*

- Construct and compare a range of data displays, including stem-and-leaf plots and dot plots

*MEAN, MODE, MEDIAN, RANGE*

- Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data
- Describe and interpret data displays using mean, median and range

*C*

^{2}=A^{2}+B^{2}Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles

*SOLVE PROBLEMS INVOLVING PYTHAGORA'S THEOREM*

Investigate Pythagora's theorem and its application to solving simple problems involving right-angled triangles

*TRIANGLES AND QUADRILATERALS*

- Classify triangles according to their side and angle properties and describe quadrilaterals

*ANGLE SUM OF TRIANGLE AND QUADRILATERAL*

- Identify line and rotational symmetries
- Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral

*EXPANDING, SIMPLIFYING AND SOLVING*

- Apply the four operations to simple algebraic fractions with numerical denominators
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Solve linear equations

*FACTORISING AND HARDER EQUATIONS*

- Factorise algebraic expressions by taking out a common algebraic factor
- Solve linear equations involving simple algebraic fractions

### Year 8 Details

- Term 1
- Term 2
- Term 3
- Term 4

## week 1

#### Algebra

##### Simplifying Algebraic Expressions

- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
- Simplify algebraic expressions involving the four operations
- Create algebraic expressions and evaluate them by substituting a given value for each variable

## week 2

#### Algebra

##### Expansion and Factorisation

- 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
- Factorise algebraic expressions by identifying numerical factors
- Factorise algebraic expressions by identifying algebraic factors
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Expand binomial products using a variety of strategies

## week 3

#### Right-Angled Triangles (Pythagoras)

##### Applications of Pythagoras' Theorem

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

## week 4

#### Fractions, Decimals and Percenteges

##### FRACTIONS AND DECIMALS (REVIEW)

- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- Express one quantity as a fraction of another, with and without the use of digital technologies
- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals

## week 5

#### FRACTIONS, DECIMALS AND PERCENTEGES

##### PERCENTEGES

- Connect fractions, decimals and percentages and carry out simple conversions
- Represent events in two-way tables and Venn diagrams and solve related problems
- Investigate the concept of irrational numbers, including π
- 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 6

#### Probability

##### Probability

- Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'
- Represent events in two-way tables and Venn diagrams and solve related problems

## week 7

#### Area

##### CIRCLE

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

## week 8

#### REVISION

##### REVISION

- Exam Revision

## week 9

#### Area and Surface Area

##### Area

- 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
- Find areas of trapeziums, rhombuses and kites

## week 10

#### Time

##### Time

- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone
- Solve problems involving international time zones

*SIMPLIFYING ALGEBRAIC EXPRESSIONS*

- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
- Simplify algebraic expressions involving the four operations
- Create algebraic expressions and evaluate them by substituting a given value for each variable

*EXPANSION AND FACTORISATION*

- 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
- Factorise algebraic expressions by identifying numerical factors
- Factorise algebraic expressions by identifying algebraic factors
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Expand binomial products using a variety of strategies

*APPLICATIONS OF PYTHAGORAS' THEOREM*

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

*FRACTIONS AND DECIMALS (REVIEW)*

- Compare fractions using equivalence locate and represent positive and negative fractions and mixed numerals on a number line
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
- 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
- Round decimals to a specified number of decimal places
- Investigate terminating and recurring decimals

*PERCENTEGES*

- Connect fractions, decimals and percentages and carry out simple conversions
- Represent events in two-way tables and Venn diagrams and solve related problems
- Investigate the concept of irrational numbers, including π
- 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

*PROBABILITY*

- Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'
- Represent events in two-way tables and Venn diagrams and solve related problems

*CIRCLE*

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

*REVISION*

- Exam Revision

*AREA*

- 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
- Find areas of trapeziums, rhombuses and kites

*TIME*

- Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone

- Solve problems involving international time zones