Mathematics Learning Area

Year 8

Western Australian Curriculum

General Capabilities:

• Literacy

• Numeracy

• ICT

• Critical and Creative Thinking

• Ethical Behaviour

• Personal and Social Competence

• Intercultural Understanding

Resources: Cambridge Essential Mathematics Year 8

Outcomes:

1. Students recognise that everyone has the right to feel valued and safe, and, in this regard, understand their

rights and obligations and behave responsibly.

2. Students are self-motivated and confident in their approach to learning and are able to work individually and

collaboratively.

3. Students appreciate the role mathematics has had, and continues to have, in their own and other communities.

4. Students use mathematics thinking processes and skills in interpreting and dealing with mathematical and non-

mathematical situations.

Cross-Curriculum Priorities

Aboriginal and Torres Strait Islander histories and cultures

Students will explore connections between representations of number and pattern and how they relate to aspects of Aboriginal and Torres Strait Islander cultures. They will investigate time, place, relationships

and measurement concepts in Aboriginal and Torres Strait Islander contexts. Students will deepen their understanding of the lives of Aboriginal and Torres Strait Islander Peoples through the application and evaluation of statistical data.

Asia and Australia’s engagement with Asia

Students investigate the concept of chance using Asian games. They explore the way Asian societies apply other mathematical concepts such as patterns and symmetry in art and architecture. Investigations involving data collection and representation can be used to examine issues pertinent to the Asia region.

Sustainability

Mathematical understandings and skills are necessary to monitor and quantify both the impact of human activity on ecosystems and changes to conditions in the biosphere. Actions to improve sustainability involve students in processes such as auditing, reading measures

and gauges, and interpreting data on invoices and accounts. Mathematical and statistical analysis enables informed decision making about present and future action.

Year 8 Syllabus

Year Level Description

The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level:

• understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area

• fluency includes calculating accurately with simple decimals, indices and integers; recognising equivalence of common decimals and fractions including recurring decimals; factorising and simplifying basic algebraic expressions and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects

• problem-solving includes formulating and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes and using two-way tables and Venn diagrams to calculate probabilities

• reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.

Year 8 Achievement Standard

Number and Algebra

At Standard, students solve everyday problems involving rates, ratios and percentages. They describe index laws and apply them to whole numbers. Students describe rational and irrational numbers. They solve problems involving profit and loss. Students make connections between expanding and factorising algebraic expressions. They use efficient mental and written strategies to carry out the four operations with integers. Students simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane.

Measurement and Geometry

Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. Students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. They convert between units of measurement for area and volume. Students perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles.

Statistics and probability

Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. Students explain issues related to the collection of data and the effect of outliers on means and medians in that data. They determine the probabilities of complementary events and calculate the sum of probabilities.

Week Western Australian

Curriculum

Content Description

At the end of this section of work the student

should be able to

Literacy words Resources Assessment

1 Revise number skills from Year 7 course

2 Carry out the four operations

with rational numbers and

integers, using efficient mental

and written strategies and

appropriate digital technologies

(ACMNA183)

Integers

• Evaluate using whole numbers and the four

operations

• Calculate multiples of numbers

• Find the HCF and LCM of pairs of numbers

Integer

Multiples

Number

Factor

Ex 1A, 1B, 1C

3 Compare, order, add and

subtract integers (ACMNA280)

Carry out the four operations

with integers, using efficient

mental and written strategies

and appropriate digital

technologies (ACMNA183)

• Test for divisibility

• Find the prime factors of numbers

• Add and subtract negative numbers

Prime

Subtract

Negative

Divisibility

Ex 1D, 1E, 1F

4 Compare, order, add and

subtract integers (ACMNA280)

Carry out the four operations

with integers, using efficient

mental and written strategies

and appropriate digital

technologies (ACMNA183)

• Multiply and divide using integers

• Use order of operations to evaluate

problems

Order

Multiply

Divide

Evaluate

Operation

Ex 1G, 1H Test Chapter 1

5

Lines, shapes and solids

• Find angles at a point

• Find sizes of angles within parallel lines

Angle

Parallel

Ex 2A, 2B

6 • Find sizes of angles within triangles

• Test for similarity in triangles

Triangle

Similarity

Ex 2C, 2D

7 Establish properties of

quadrilaterals using congruent

triangles and angle properties,

and solve related numerical

problems using reasoning

(ACMMG202)

• Find the size of angles in a quadrilateral

• Find the size of angles in various polygons

Quadrilateral

Polygon

Ex 2E, 2F

8 • Develop and use Euler’s rule Euler Ex 2G Test Chapter 2

9 Compare fractions using

equivalence. Locate and

represent fractions and mixed

numerals on a number line

(ACMNA152)

Investigate terminating and

recurring decimals

(ACMNA184)

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)

Fractions, Decimals and Percentages

• Write equivalent fractions

• Use the four operations with fractions

Fraction

Decimal

Percentage

Equivalent

Ex 3A, 3B

10 Compare fractions using

equivalence. Locate and

represent fractions and mixed

numerals on a number line

(ACMNA152)

Investigate terminating and

recurring decimals

(ACMNA184)

• Use the four operations with negative

fractions

• Compare and convert fractions and decimals

Compare

Fraction

Decimal

Ex 3C, 3D

11 Compare fractions using

equivalence. Locate and

represent fractions and mixed

numerals on a number line

• Use the four operations with decimals

• Understand and use terminating, recurring

and rounding decimals

Terminating

Recurring

Rounding

Ex 3E, 3F

(ACMNA152)

Investigate terminating and

recurring decimals

(ACMNA184)

12 Express one quantity as a

fraction of another with and

without the use of digital

technologies (ACMNA155)

Solve problems involving the

use of percentages, including

percentage increases and

decreases, with and without

digital technologies

(ACMNA187)

• Convert percentages to fractions and

decimals and vice versa

• Express one quantity as a percentage of

another and find the percentage of quantity

Quantity

Percentage

Convert

Ex 3G, Ex 3H

13

Solve problems involving the

use of percentages, including

percentage increases and

decreases, with and without

digital technologies

(ACMNA187)

• Decrease and increase amounts by a

percentage

• Calculate percentage change

• Calculate percentage using the unitary

method

FA1 – The right to be safe

Topic 2: Warning signs and emergencies

2.4 Explore a range of emergencies, research

statistics and percentages, discuss strategies to

solve problems (P56)

2.5 As above (P57)

FA2 - Relationships

Topic 3: Bullying as an abuse of power

3.1 Research bullying statistics and

percentages, discuss strategies to solve

problems (P68) (display as data – see bottom

cell)

3.2 As above (P68)

FA3 – Recognising and reporting abuse

Topic 2: Identifying abuse and neglect

2.1 Research abuse statistics and percentages,

discuss strategies to solve problems (P78)

2.3 Sexual abuse – as above (P81)

2.5 Domestic violence – as above (P84)

Decrease

Increase

Unitary

Ex 3I, 3J, 3K Test Chapter 3

FA4 – Protective strategies

Topic 1: Problem – solving strategies

1.1 Use trust, take, control problem solving

strategy (P93) for activities FA1: 2.2, 2.5 FA2:

3.1, 3.2 FA3: 2.1, 2.3, 2.5

14 Find perimeters and areas of

parallelograms, rhombuses and

kites (ACMMG196)

Measurement and Pythagoras’ Theorem

• Convert between measures of length and

calculate perimeter of shapes

• Calculate the circumference of a circle

Length

Perimeter

Circumference

Circle

Ex 4A, 4B

15 Find perimeters and areas of

parallelograms, rhombuses and

kites (ACMMG196)

• Convert between area measurements and

calculate the area of shapes

• Calculate the area of special quadrilaterals

Area

Measurement

Quadrilateral

Ex 4C, 4D

16 Investigate the relationship

between features of circles such

as circumference, area, radius

and diameter. Use formulas to

solve problems involving

circumference and area

(ACMMG197)

• Calculate the area of a circle

• Calculate the area of sectors and composite

shapes

Sector

Composite

Shape

Ex 4E, 4F

17 Choose appropriate units of

measurement for area and

volume and convert from one

unit to another (ACMMG195)

Develop the formulas for

volumes of rectangular and

triangular prisms and prisms in

general. Use formulas to solve

problems involving volume

(ACMMG198)

• Calculate the surface area of a prism

• Calculate the volume and capacity of

rectangular prisms

• Calculate the volume of other prisms,

including cylinders

Surface

Volume

Rectangular

Prism

Cylinder

Ex 4G, 4H, 4I

18 Solve problems involving

duration, including using 12-

and 24-hour time within a single

• Convert between units of time

• Understand the rule of Pythagoras

Convert

Unit

Time

Ex 4J, 4K

time zone (ACMMG199)

Pythagoras

19 • Use Pythagoras’ theorem to calculate the

length of the hypotenuse and one of the

shorter sides

Theorem

Hypotenuse

Ex 4L, 4M Chapter 4 Test

20 Extend and apply the laws and

properties of arithmetic to

algebraic terms and expressions

(ACMNA177) Create algebraic

expressions and evaluate them

by substituting a given value for

each variable (ACMNA176))

Algebra

• Recognise terms, coefficients and algebraic

expressions

• Substitute numerical values into algebraic

expressions

• Add and subtract like terms

Term

Coefficient

Numerical

Ex 5A, 5B, 5C

21

Simplify algebraic expressions

involving the four operations

(ACMNA192)

• Multiply and divide algebraic terms

• Add and subtract algebraic fractions

Algebraic

Fractions

Ex 5D, 5E

22 Extend and apply the

distributive law to the expansion

of algebraic expressions

(ACMNA190)

• Multiply and divide algebraic fractions

• Expand brackets involving algebraic

expressions

Expand

Bracket

Expression

Ex 5F, 5G

23 Factorise algebraic expressions

by identifying numerical factors

(ACMNA191)

• Factorise algebraic expressions

• Applying algebra to various problems

Factorise

Algebra

Ex 5H, 5I

24 Use index notation with

numbers to establish the index

laws with positive integral

indices and the zero index

(ACMNA182)

• Multiply and divide terms with powers

• Simplify expressions using raising of

powers

Powers

Simplify

Ex 5J, 5K Chapter 5 Test

25 Recognise and solve problems

involving simple ratios

(ACMNA173)Investigate and

calculate 'best buys', with and

without digital technologies

(ACMNA174)

Rates and Ratios

• Understand basic ratios

• Simplify ratios

• Divide a quantity in a given ratio

Rate

Ratio

Ex 6A, 6B, 6C

26 Solve a range of problems

involving rates and ratios, with

and without digital technologies

(ACMNA188)

• Convert scale distance to actual distance and

vice versa

• Simplify rates

Distance

Rates

Convert

Ex 6D, 6E

27 Solve a range of problems

involving rates and ratios, with

and without digital technologies

(ACMNA188)

• Use the unitary method with ratios and rates

• Solve rate problems

• Convert speed into various units

Unitary

Speed

Unit

Ex 6F, 6G, 6H Chapter 6 Test

28 Solve linear equations using

algebraic and graphical

techniques. Verify solutions by

substitution (ACMNA194)

Equations

• Review equations

• Solve equations algebraically

Equation

Solve

Ex 7A, 7B

29 Solve linear equations using

algebraic and graphical

techniques. Verify solutions by

substitution (ACMNA194)

• Solve equations with fractions

• Solve equations with variables on both sides

• Solve equations with brackets

Variable

Bracket

Ex 7C, 7D, 7E

30 Solve linear equations using

algebraic and graphical

techniques. Verify solutions by

substitution (ACMNA194)

• Use formula in algebra

• Solve problems involving algebra

Formula

Problem

Algebra

Ex 7F, 7G Chapter 7 Test

31 Explore the practicalities and

implications of obtaining

representative data using a

variety of investigative

processes (ACMSP206)

Probability and Statistics

• Interpret graphs and tables

• Draw frequency tables

• Interpret histograms containing data

Probability

Statistics

Frequency

Histogram

Ex 8A, 8B, 8C

32 Explore the practicalities and

implications of obtaining

representative data using a

variety of investigative

processes (ACMSP206)

Investigate the effect of

individual data values ,

including outliers, on the mean

and median (ACMSP207)

• Calculate the mean, mode and median of

data

• Calculate the range and interquartile range

of data

FA2: Relationships

Topic 2: Power in relationships

2.1 Research powerful people and display

positive a negative effects (P64)

2.2 As above (P65)

FA2 - Relationships

Topic 3: Bullying as an abuse of power

3.1 Use bullying statistics and percentages

(from top cell) and display as data (P68)

3.2 As above (P68)

Mean

Mode

Median

Interquartile

Range

Ex 8D, 8E

FA4: Protective strategies

Topic 2: Network review and community

support

2.1 Display and investigate data using the

network review challenge (P98)

33 Explore the variation of means

and proportions in

representative data

(ACMSP293)

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)

• Understand and use surveying and sampling

• Calculate the probability of events

• Construct two-way tables of events

FA1 – The right to be safe

Topic 2: Warning signs and emergencies

2.4 Explore a range of emergencies, research

statistics and percentages, discuss strategies to

solve problems (P56)

2.5 As above (P57)

FA3 – Recognising and reporting abuse

Topic 2: Identifying abuse and neglect

2.1 Research abuse statistics and probabilities,

discuss strategies to solve problems (P78)

2.3 Sexual abuse – as above (P81)

2.5 Domestic violence – as above (P84)

Survey

Sample

Construct

Event

Ex 8F, 8G, 8H

34 Represent such events in two-

way tables and Venn diagrams

and solve related problems

(ACMSP292)

• Construct and interpret tree diagrams

• Interpret events using Venn diagrams and

two-way tables

• Calculate experimental probabilities

Construct

Interpret

Experimental

Ex 8I, 8J, 8K Chapter 8 Test

35 Plot linear relationships on the

Cartesian plane with and

without the use of digital

technologies (ACMNA193)

Straight Line Graphs

• Plot points on the number plane

• Draw tables from rules given

• Finding a rule from a graph and table

Plane

Rule

Graph

Ex 9A, 9B, 9C

36 Plot linear relationships on the

Cartesian plane with and

without the use of digital

technologies (ACMNA193)

• Calculate the gradient of a line

• Drawing graphs and finding equations using

gradient – intercept form

• Finding the x-intercept of a graph

Gradient

Intercept

Ex 9D, 9E, 9F

37 Plot linear relationships on the

Cartesian plane with and

without the use of digital

technologies (ACMNA193)

• Finding rules to applying linear graphs Linear

Ex 9G Chapter 9 Test

38 Transformations Reflection Ex 10A, 10B, 10C

• Draw images involving reflections,

translations and rotations

Translation

Rotation

transformation

Assessment Schedule

Assessment Week Weighting

Chapter 1 - Integers 4 1

Chapter 2 – Lines, shapes and

solids

8 1

Chapter 3 – Fractions, decimals

and percentages

13 1

Chapter 4 – Measurement and

Pythagoras’ Theorem

19 1

Chapter 5 – Algebra 24 1

Chapter 6 – Rates and ratios 27 1

Chapter 7 – Equations 30 1

Chapter 8 – Probability and

statistics

34 1

Chapter 9 – Straight line graphs 37 1