AUSTRALIA MATH YEAR 8 – EDmama Australia

A. Integers

A.01. Represent integers on horizontal and vertical number lines
A.02. Compare and order integers using number lines and symbols
A.03. Define integers and their relationship to whole numbers
A.04. Graph integers on horizontal and vertical number lines
A.05. Solve real-world problems involving ordering of integers
A.06. Explain the importance of integers in real-world contexts

B. Rational Numbers

B.01. Define rational numbers and differentiate them from irrational numbers
B.02. Write fractions in their lowest terms
B.03. Identify the lowest common denominator of fractions
B.04. Convert between decimals, fractions, and mixed numbers
B.05. Recognise and represent repeating decimals as fractions
B.06. Round decimals and mixed numbers to specified places
B.07. Compare and order rational numbers using various strategies
B.08. Place rational numbers in order from least to greatest and vice versa
B.09. Explore the significance and application of rational numbers in various fields

C. Number Theory

C.01. Identify factors of a given number
C.02. Apply divisibility rules to determine if a number is divisible by another
C.03. Differentiate between prime and composite numbers
C.04. Determine the prime factorisation of a number
C.05. Find the highest common factor (HCF) of two or more numbers
C.06. Determine the lowest common multiple (LCM) of two or more numbers
C.07. Solve word problems involving HCF and LCM
C.08. Classify numbers based on their properties (e.g., square, cube)
C.09. Convert numbers into scientific notation and vice versa
C.10. Apply number theory concepts to solve mathematical puzzles and challenges
C.11. Investigate historical developments and contributions to number theory

D. Operations with Integers

D.01. State and apply the rules for integer addition and subtraction
D.02. Add and subtract integers using visual aids such as counters and number lines
D.03. Calculate sums and differences of integers
D.04. Add and subtract three or more integers in a single expression
D.05. Translate and solve word problems involving integer addition and subtraction
D.06. State and apply the rules for integer multiplication
D.07. Multiply integers, including positive and negative numbers
D.08. State and apply the rules for integer division
D.09. Identify equal quotients of integers
D.10. Divide integers, including positive and negative numbers
D.11. Summarise and apply the rules for integer multiplication and division
D.12. Perform both multiplication and division operations with integers
D.13. Complete multiplication and division equations with integers
D.14. Perform addition, subtraction, multiplication, and division with integers
D.15. Evaluate numerical expressions involving integers using the order of operations
D.16. Develop strategies for checking the reasonableness of calculations with integers

E. Operations with Rational Numbers

E.01. Determine reciprocals and multiplicative inverses of rational numbers
E.02. Add and subtract rational numbers, expressing answers in simplest form
E.03. Solve word problems involving addition and subtraction of rational numbers
E.04. Apply addition and subtraction rules to solve problems with rational numbers
E.05. Multiply and divide rational numbers, expressing answers in simplest form
E.06. Solve word problems involving multiplication and division of rational numbers
E.07. Apply multiplication and division rules to solve problems with rational numbers
E.08. Apply addition, subtraction, multiplication, and division rules to solve multi-step problems with rational numbers
E.09. Evaluate numerical expressions involving rational numbers, using the order of operations
E.10. Create and solve real-world problems involving multiple operations with rational numbers

F. Exponents and Roots

F.01. Understand the definition and notation of exponents
F.02. Evaluate powers of integers, decimals, and fractions
F.03. Solve simple equations with variable exponents
F.04. Evaluate powers with negative bases
F.05. Evaluate powers with decimal and fractional bases
F.06. Simplify expressions involving multiplication with exponents
F.07. Simplify expressions involving division with exponents
F.08. Simplify expressions involving both multiplication and division with exponents
F.09. Apply the power rule to simplify expressions with exponents
F.10. Evaluate expressions using multiple properties of exponents
F.11. Identify equivalent expressions involving exponents (Part I)
F.12. Identify equivalent expressions involving exponents (Part II)
F.13. Determine the square roots of perfect squares
F.14. Estimate square roots of non-perfect squares
F.15. Understand the relationship between squares and square roots
F.16. Solve equations involving squares and square roots
F.17. Determine the cube roots of perfect cubes
F.18. Estimate cube roots of non-perfect cubes
F.19. Solve equations involving cubes and cube roots
F.20. Apply exponential and radical expressions in geometric and scientific contexts
F.21. Explore the connection between exponents, roots, and logarithmic functions

G. Ratios, Rates and Proportions

G.01. Explain the concept of a ratio and its representation
G.02. Identify equivalent ratios
G.03. Write an equivalent ratio for a given ratio
G.04. Solve word problems involving equivalent ratios
G.05. Calculate unit rates
G.06. Solve word problems comparing ratios
G.07. Solve word problems comparing rates
G.08. Apply ratios and rates to solve various word problems
G.09. Determine if two ratios form a proportion
G.10. Solve word problems to determine if two ratios form a proportion
G.11. Solve proportions using various methods
G.12. Estimate population size using proportions
G.13. Apply proportions to solve scale drawing word problems
G.14. Use ratio and proportion to convert units of measurement
G.15. Investigate applications of ratios and proportions in real-world scenarios, such as map reading, scale models, and currency exchange

H. Percents

H.01. Convert between percents, fractions and decimals
H.02. Compare percents to fractions and decimals
H.03. Solve percent problems using grid models
H.04. Solve percent problems using strip models
H.05. Find what percent one number is of another
H.06. Find what percent one number is of another: word problems
H.07. Estimate percents of numbers
H.08. Calculate percents of numbers and money amounts
H.09. Solve percents of numbers: word problems
H.10. Compare percents of numbers
H.11. Solve percent equations
H.12. Calculate percent of change
H.13. Solve percent of change: word problems
H.14. Solve percent of change: find the original amount word problems
H.15. Apply percentage concepts to analyze data and make informed decisions
H.16. Investigate the use of percentages in financial calculations, such as interest rates, taxes, and discounts

I. Proportional Relationships

I.07. Graph proportional relationships
I.08. Interpret graphs of proportional relationships
I.09. Write and solve equations for proportional relationships
I.10. Use proportional relationships to solve scaling and similar figure problems
I.11. Analyze and compare different proportional relationships represented in various forms
I.01. Identify the constant of proportionality from a table
I.02. Write equations for proportional relationships from tables
I.03. Identify proportional relationships by graphing
I.04. Find the constant of proportionality from a graph
I.05. Write equations for proportional relationships from graphs
I.06. Identify proportional relationships from tables, graphs and equations

J. Expressions and Properties

J.01. Translate verbal phrases into variable expressions
J.02. Write variable expressions from diagrams
J.03. Create variable expressions from word problems
J.04. Evaluate one-variable expressions by substitution
J.05. Evaluate multi-variable expressions by substitution
J.06. Evaluate rational expressions
J.07. Identify terms and coefficients in algebraic expressions
J.08. Sort factors of expressions
J.09. State and apply properties of addition and multiplication (commutative, associative, distributive, identity, inverse)
J.10. Multiply algebraic expressions using the distributive property
J.11. Simplify variable expressions using algebraic properties
J.12. Add and subtract like terms in algebraic expressions
J.13. Add, subtract and multiply linear expressions
J.14. Factor linear expressions
J.15. Identify equivalent linear expressions using algebra tiles
J.16. Identify equivalent linear expressions
J.17. Solve problems by identifying equivalent linear expressions from word problems
J.18. Apply the distributive property to expand binomial expressions
J.19. Generalize the relationship between algebraic expressions and numerical patterns

K. One-Variable Equations

K.01. Determine which value of x satisfies a given equation
K.02. Write an equation from a verbal statement
K.03. Model and solve equations using algebra tiles
K.04. Write and solve equations that represent diagrams
K.05. Apply properties of equality to solve equations
K.06. Solve one-step equations using inverse operations
K.07. Solve two-step equations using inverse operations
K.08. Solve multi-step equations using inverse operations
K.09. Solve equations involving combining like terms
K.10. Solve equations with variables on both sides
K.11. Solve equations: mixed review
K.12. Solve equations: complete the solution
K.13. Solve equations: word problems
K.14. Formulate and solve linear equations from real-world scenarios
K.15. Analyze and interpret the solutions of linear equations in context

L. One-Variable Inequalities

L.01. Graph inequalities on a number line
L.02. Write inequalities from graphs
L.03. Write and graph inequalities from word problems
L.04. Identify solutions to inequalities
L.05. Solve one-step linear inequalities using addition and subtraction
L.06. Solve one-step linear inequalities using multiplication and division
L.07. Solve one-step linear inequalities
L.08. Graph solutions to one-step linear inequalities
L.09. Solve two-step linear inequalities
L.10. Graph solutions to two-step linear inequalities
L.11. Apply properties of inequalities to justify solution steps
L.12. Write and solve inequalities to represent constraints in real-world situations
L.13. Understand and solve compound inequalities involving “and” and “or”

M. Linear Relations

M.01. Determine if a given ordered pair (x, y) satisfies a linear equation
M.02. Identify independent and dependent variables in a linear relation
M.03. Calculate rate of change from a linear relation
M.04. Recognise constant rate of change
M.05. Find a value using a linear equation
M.06. Complete a table for a linear equation
M.07. Complete a table and graph a linear equation
M.08. Write the equations of horizontal and vertical lines
M.09. Graph a horizontal or vertical line
M.10. Graph a line from a given equation
M.11. Interpret the graph of a linear equation: word problems
M.12. Write a linear equation from a table
M.13. Write linear equations: word problems
M.14. Identify linear and nonlinear relationships: graphs
M.15. Identify linear and nonlinear relationships: tables
M.16. Graph a linear inequality in the coordinate plane
M.17. Interpret the slope and y-intercept of a linear equation in context
M.18. Create and analyze scatter plots to identify trends and relationships in data

N. Consumer Maths

N.01. Interpret and use information from price lists
N.02. Calculate unit prices
N.03. Calculate total prices using unit prices
N.04. Calculate percent of a number in context of GST, discount and more
N.05. Determine the percent of a number in the context of discount and mark-up
N.06. Find the original price given the sale price and discount percentage
N.07. Solve multi-step problems involving percents
N.08. Compare different financial options using consumer math concepts
N.09. Analyse the impact of taxes, tips, and fees on purchases and services

O. Units of Measurement

P. Geometric Measurement

P.01. Calculate the perimeter of various shapes
P.02. Explain the concept of area of a trapezium
P.03. Calculate the area of trapeziums
P.04. Calculate the area of rhombuses
P.05. Mixed review of area calculations
P.06. Calculate the area between two shapes
P.07. Solve word problems involving area and perimeter
P.08. Calculate the circumference of circles
P.09. Calculate the area of circles
P.10. Calculate area, circumference, radius and diameter of circles
P.11. Solve problems involving circles, semicircles and quarter circles
P.12. Solve word problems related to circles
P.13. Calculate the area of compound figures with triangles
P.14. Calculate the area of compound figures with triangles, semicircles and quarter circles
P.15. Calculate the volume of prisms
P.16. Solve word problems involving volume of cubes and rectangular prisms
P.17. Calculate the surface area of prisms
P.18. Solve real-world problems involving geometric measurement and optimization
P.19. Apply geometric measurement principles to design and construction projects

R. Three-Dimensional Figures

Q. Two-Dimensional Figures

Q.19. Calculate lengths and measures of bisected intervals and angles
Q.20. Identify parts of a circle (radius, diameter, circumference, chord, tangent, secant)
Q.21. Explore the relationship between angles, sides, and diagonals in quadrilaterals
Q.22. Investigate tessellations using various two-dimensional shapes
Q.01. Identify and classify polygons based on their properties
Q.02. Classify triangles based on their sides and angles
Q.03. Identify trapeziums
Q.04. Classify quadrilaterals I
Q.05. Classify quadrilaterals II
Q.06. Graph quadrilaterals on the coordinate plane
Q.07. Find missing angles in quadrilaterals I
Q.08. Find missing angles in quadrilaterals II
Q.09. Describe the properties of parallelograms
Q.10. Describe the properties of rhombuses
Q.11. Describe the properties of squares and rectangles
Q.12. Describe the properties of trapeziums
Q.13. Describe the properties of kites
Q.14. Review properties of quadrilaterals
Q.15. Calculate the interior angles of polygons
Q.16. Identify complementary, supplementary, vertical, adjacent and congruent angles
Q.17. Find measures of complementary, supplementary, vertical and adjacent angles
Q.18. Apply the properties of transversals of parallel lines

S. Symmetry and Transformations

S.01. Define and recognize symmetry in two-dimensional figures
S.02. Count the lines of symmetry in various shapes
S.03. Draw lines of symmetry on given shapes
S.04. Identify reflections, rotations and translations
S.05. Graph the image of a figure after a translation
S.06. Find the coordinates of an image after a translation
S.07. Write the rule for a given translation
S.08. Graph the image of a figure after a reflection
S.09. Find the coordinates of an image after a reflection
S.10. Graph the image of a figure after a rotation
S.11. Find the coordinates of an image after a rotation
S.12. Describe transformations of figures on the coordinate plane
S.13. Graph the image of a figure after a sequence of congruence transformations
S.14. Choose the sequence of transformations that maps one figure onto another
S.15. Investigate the properties preserved under different transformations

T. Congruence and Similarity

T.01. Identify congruent figures
T.02. Determine the relationship between side lengths and angle measures of congruent figures
T.03. Write congruence statements and identify corresponding parts of congruent figures
T.04. Determine if two figures are congruent: justify your answer
T.05. Prove triangle congruence using SSS, SAS and ASA postulates
T.06. Prove triangle congruence using RHS postulate
T.07. Identify similar figures
T.08. Apply the angle-angle criterion for similar triangles
T.09. Apply similarity rules for triangles (SAS, SSS)
T.10. Use scale factors to determine side lengths and areas of similar figures
T.11. Apply congruence and similarity concepts to solve real-world problems involving geometric shapes

U. Pythagoras’ Theorem

V. Number Sequences

V.01. Identify arithmetic and geometric sequences
V.02. Determine the next terms in arithmetic sequences
V.03. Determine the next terms in geometric sequences
V.04. Number sequences: mixed review
V.05. Number sequences: word problems
V.06. Evaluate variable expressions for number sequences
V.07. Write variable expressions for arithmetic sequences
V.08. Find a specific term in a sequence using its general rule
V.09. Model real-world situations with arithmetic and geometric sequences
V.10. Explore Fibonacci sequence and its relationship to the Golden Ratio

W. Data and Graphs

W.01. Interpret tables of data
W.02. Interpret bar graphs
W.03. Create bar graphs from data sets
W.04. Interpret line graphs
W.05. Create line graphs from data sets
W.06. Interpret dot plots
W.07. Create dot plots from data sets
W.08. Interpret stem-and-leaf plots
W.09. Create stem-and-leaf plots
W.10. Create frequency charts from data
W.11. Interpret circle graphs
W.12. Understand the relationship between circle graphs and central angles
W.13. Choose the best type of graph to represent a given data set
W.14. Analyze and compare different data representations

X. Statistics

X.01. Calculate mean, median, mode and range of a data set
X.02. Interpret charts to find mean, median, mode and range
X.03. Mean, median, mode and range: find the missing number
X.04. Analyze the changes in mean, median, mode and range when data values are added or removed
X.05. Identify outliers in a data set
X.06. Identify an outlier and describe the effect of removing it on measures of central tendency
X.07. Distinguish between representative, random and biased samples
X.08. Make inferences from multiple samples
X.09. Calculate and interpret measures of dispersion (e.g., variance, standard deviation)
X.10. Compare and contrast different data sets using statistical measures

Y. Probability

Y.01. Determine the probability of simple events
Y.02. Calculate the probability of opposite, mutually exclusive and overlapping events
Y.03. Find probabilities using two-way frequency tables
Y.04. Determine experimental probability from data
Y.05. Make predictions based on probability
Y.06. Determine the number of outcomes in compound events
Y.07. Distinguish between independent and dependent events
Y.08. Calculate the probability of independent and dependent events
Y.09. Apply the counting principle to calculate the total number of outcomes
Y.10. Simulate probability experiments and compare results to theoretical probabilities
Y.11. Develop and apply strategies for calculating probabilities in complex scenarios
Y.12. Calculate conditional probabilities and apply them to real-world problems

Course Content

A. Integers

A.01. Represent integers on horizontal and vertical number lines

A.02. Compare and order integers using number lines and symbols

A.03. Define integers and their relationship to whole numbers

A.04. Graph integers on horizontal and vertical number lines

A.05. Solve real-world problems involving ordering of integers

A.06. Explain the importance of integers in real-world contexts

B. Rational Numbers

B.01. Define rational numbers and differentiate them from irrational numbers

B.02. Write fractions in their lowest terms

B.03. Identify the lowest common denominator of fractions

B.04. Convert between decimals, fractions, and mixed numbers

B.05. Recognise and represent repeating decimals as fractions

B.06. Round decimals and mixed numbers to specified places

B.07. Compare and order rational numbers using various strategies

B.08. Place rational numbers in order from least to greatest and vice versa

B.09. Explore the significance and application of rational numbers in various fields

C. Number Theory

C.01. Identify factors of a given number

C.02. Apply divisibility rules to determine if a number is divisible by another

C.03. Differentiate between prime and composite numbers

C.04. Determine the prime factorisation of a number

C.05. Find the highest common factor (HCF) of two or more numbers

C.06. Determine the lowest common multiple (LCM) of two or more numbers

C.07. Solve word problems involving HCF and LCM

C.08. Classify numbers based on their properties (e.g., square, cube)

C.09. Convert numbers into scientific notation and vice versa

C.10. Apply number theory concepts to solve mathematical puzzles and challenges

C.11. Investigate historical developments and contributions to number theory

D. Operations with Integers

D.01. State and apply the rules for integer addition and subtraction

D.02. Add and subtract integers using visual aids such as counters and number lines

D.03. Calculate sums and differences of integers

D.04. Add and subtract three or more integers in a single expression

D.05. Translate and solve word problems involving integer addition and subtraction

D.06. State and apply the rules for integer multiplication

D.07. Multiply integers, including positive and negative numbers

D.08. State and apply the rules for integer division

D.09. Identify equal quotients of integers

D.10. Divide integers, including positive and negative numbers

D.11. Summarise and apply the rules for integer multiplication and division

D.12. Perform both multiplication and division operations with integers

D.13. Complete multiplication and division equations with integers

D.14. Perform addition, subtraction, multiplication, and division with integers

D.15. Evaluate numerical expressions involving integers using the order of operations

D.16. Develop strategies for checking the reasonableness of calculations with integers

E. Operations with Rational Numbers

E.01. Determine reciprocals and multiplicative inverses of rational numbers

E.02. Add and subtract rational numbers, expressing answers in simplest form

E.03. Solve word problems involving addition and subtraction of rational numbers

E.04. Apply addition and subtraction rules to solve problems with rational numbers

E.05. Multiply and divide rational numbers, expressing answers in simplest form

E.06. Solve word problems involving multiplication and division of rational numbers

E.07. Apply multiplication and division rules to solve problems with rational numbers

E.08. Apply addition, subtraction, multiplication, and division rules to solve multi-step problems with rational numbers

E.09. Evaluate numerical expressions involving rational numbers, using the order of operations

E.10. Create and solve real-world problems involving multiple operations with rational numbers

F. Exponents and Roots

F.01. Understand the definition and notation of exponents

F.02. Evaluate powers of integers, decimals, and fractions

F.03. Solve simple equations with variable exponents

F.04. Evaluate powers with negative bases

F.05. Evaluate powers with decimal and fractional bases

F.06. Simplify expressions involving multiplication with exponents

F.07. Simplify expressions involving division with exponents

F.08. Simplify expressions involving both multiplication and division with exponents

F.09. Apply the power rule to simplify expressions with exponents

F.10. Evaluate expressions using multiple properties of exponents

F.11. Identify equivalent expressions involving exponents (Part I)

F.12. Identify equivalent expressions involving exponents (Part II)

F.13. Determine the square roots of perfect squares

F.14. Estimate square roots of non-perfect squares

F.15. Understand the relationship between squares and square roots

F.16. Solve equations involving squares and square roots

F.17. Determine the cube roots of perfect cubes

F.18. Estimate cube roots of non-perfect cubes

F.19. Solve equations involving cubes and cube roots

F.20. Apply exponential and radical expressions in geometric and scientific contexts

F.21. Explore the connection between exponents, roots, and logarithmic functions