AUSTRALIA MATH YEAR 9 – EDmama Australia

A. Numbers and Counting

A.01. Classify different types of numbers (e.g., natural, integer, rational, irrational)
A.02. Represent numbers on a number line
A.03. Convert fluently between decimals, fractions, and percentages
A.04. Compare and order rational numbers
A.05. Identify and approximate square roots of perfect squares
A.06. Identify and approximate cube roots of perfect cubes
A.07. Locate irrational numbers approximately on a number line
A.08. Determine if the sum or product of two irrational numbers is rational or irrational
A.09. Understand the relationship between sets and subsets of real numbers

B. Operations with Integers and Rational Numbers

B.01. Add, subtract, multiply, and divide integers
B.02. Add and subtract rational numbers
B.03. Multiply and divide rational numbers
B.04. Apply the order of operations to evaluate numerical expressions involving integers
B.05. Apply the order of operations to evaluate numerical expressions involving rational numbers
B.06. Evaluate variable expressions involving integers
B.07. Evaluate variable expressions involving rational numbers
B.08. Solve real-world problems involving operations with rational numbers
B.09. Use estimation to check the reasonableness of calculations with integers and rational numbers

C. Properties of Operations and Expressions

D. Ratios, Rates, and Proportions

D.09. Apply proportional reasoning to real-world scenarios such as currency conversion
D.10. Use proportions to model indirect measurements
D.01. Identify equivalent ratios
D.02. Write an equivalent ratio
D.03. Determine unit rates from given information
D.04. Calculate unit prices for comparison
D.05. Determine if two ratios form a proportion
D.06. Solve proportions using cross-multiplication
D.07. Solve proportion word problems, including scale drawings and population estimation
D.08. Use proportions to solve problems involving similar figures

E. Percentages

E.01. Convert between percents, fractions, and decimals
E.02. Solve basic percent equations (e.g., finding the percentage of a number)
E.03. Solve percent word problems, including those involving discounts, markups, and taxes (GST)
E.04. Calculate percent of change (increase or decrease)
E.05. Solve percent of change word problems
E.06. Calculate simple interest earned on an investment or paid on a loan
E.07. Solve multi-step problems involving percentages
E.08. Calculate commission, profit, and loss in financial scenarios
E.09. Analyze the impact of different percentage changes in real-world contexts

F. Measurement and Error

F.01. Convert rates and measurements between different units
F.02. Determine the precision of a measurement
F.03. Calculate the greatest possible error in a measurement
F.04. Calculate the minimum and maximum area and volume based on measurement precision
F.05. Calculate percent error in measurements
F.06. Calculate percent error in area and volume measurements
F.07. Apply significant figures to measurements and calculations
F.08. Use dimensional analysis to solve multi-step conversion problems
F.09. Compare and contrast different units of measurement across various systems (metric, imperial)

G. Geometric Measurement

G.01. Calculate the perimeter of various shapes
G.02. Calculate the area of various shapes, including circles, semicircles, and quarter circles
G.03. Determine the area of compound figures involving triangles, semicircles, and quarter circles
G.04. Calculate the area between two shapes
G.05. Determine the sum of interior angles of polygons
G.06. Apply properties of transversals intersecting parallel lines to find angle measures
G.07. Calculate the volume of cylinders and prisms
G.08. Solve word problems involving the volume of cubes and rectangular prisms
G.09. Calculate the surface area of cylinders and prisms
G.10. Calculate the volume and surface area of composite 3D shapes
G.11. Solve real-world problems involving perimeter, area, volume, and surface area
G.12. Apply the concepts of density and mass to solve related problems

H. Coordinate Plane

I. Relations and Functions

I.01. Represent relations using tables, graphs, mappings, and lists of points
I.02. Identify independent and dependent variables in a relationship
I.03. Determine if a relation is a function
I.04. Use the vertical line test to identify functions from graphs
I.05. Find values using function graphs
I.06. Evaluate a function given an input value
I.07. Evaluate a function by plugging in an expression
I.08. Complete a function table from a graph
I.09. Complete a function table from an equation
I.10. Interpret the graph of a function in a word problem
I.11. Determine the domain and range of a function
I.12. Use function notation to represent and evaluate functions

J. Proportional Relationships

J.01. Find the constant of proportionality from a table
J.02. Write equations for proportional relationships based on tables
J.03. Identify proportional relationships by graphing
J.04. Find the constant of proportionality from a graph
J.05. Write equations for proportional relationships based on graphs
J.06. Identify proportional relationships from various representations (tables, graphs, equations, descriptions)
J.07. Graph proportional relationships
J.08. Interpret graphs of proportional relationships in real-world contexts
J.09. Write and solve equations for proportional relationships
J.10. Compare and contrast proportional and non-proportional relationships
J.11. Apply proportional reasoning to solve scale problems and map-related tasks

K. Linear Equations

K.01. Identify linear and nonlinear relationships from graphs, tables, and equations
K.02. Find the gradient (slope) of a line from a graph
K.03. Find the gradient of a line given two points on the line
K.04. Find a missing coordinate given the gradient and another point on the line
K.05. Find the gradient and y-intercept of a linear equation
K.06. Graph a linear equation in slope-intercept form (y = mx + c)
K.07. Write the equation of a line in slope-intercept form from a graph
K.08. Write the equation of a line in slope-intercept form given the gradient and y-intercept
K.09. Write the equation of a line in slope-intercept form from a table
K.10. Write the equation of a line in slope-intercept form from a word problem
K.11. Solve linear equations for y
K.12. Write linear equations to solve word problems
K.13. Complete a table and graph a linear equation
K.14. Write linear equations in standard form (Ax + By = C)
K.15. Find the x- and y-intercepts of a linear equation in standard form
K.16. Graph a linear equation in standard form
K.17. Write equations of horizontal and vertical lines
K.18. Graph horizontal and vertical lines
K.19. Graph a line given its equation in point-slope form
K.20. Write the equation of a line in point-slope form given a point and the gradient
K.21. Write the equation of a line in point-slope form from a graph
K.22. Determine the gradients of parallel and perpendicular lines
K.23. Write the equation of a line parallel or perpendicular to a given line
K.24. Describe transformations of linear functions (translations, reflections, stretches)
K.25. Model real-world scenarios using linear equations and inequalities

L. Solve Equations

L.01. Solve one-step linear equations
L.02. Solve two-step linear equations
L.03. Solve advanced linear equations, including those with parentheses and fractions
L.04. Solve equations with variables on both sides
L.05. Solve equations and complete the solution process by providing justifications for each step
L.06. Determine the number of solutions to a linear equation (none, one, or infinitely many)
L.07. Create equations with no solutions or infinitely many solutions
L.08. Solve linear equations in word problems
L.09. Solve linear equations in a mixed review context
L.10. Solve multi-step word problems involving consecutive integers
L.11. Solve multi-variable equations by rearranging them to isolate a specific variable

M. Percents

M.01. Convert between percents, fractions and decimals
M.02. Solve percent equations
M.03. Percent word problems
M.04. Percent of change
M.05. Percent of change: word problems
M.06. Simple interest
M.07. Percent of a number: GST, discount and more
M.08. Find the percent: discount and mark-up
M.09. Multi-step problems with percents

N. Exponents

N.01. Evaluate powers with integer bases
N.02. Evaluate powers with decimal and fractional bases
N.03. Simplify expressions involving multiplication with positive exponents
N.04. Simplify expressions involving division with positive exponents
N.05. Simplify expressions involving multiplication and division with positive exponents
N.06. Apply the power rule with positive exponents
N.07. Understand and apply negative exponents
N.08. Simplify expressions involving multiplication with integer exponents
N.09. Simplify expressions involving division with integer exponents
N.10. Simplify expressions involving multiplication and division with integer exponents
N.11. Apply the power rule with integer exponents
N.12. Evaluate expressions using properties of exponents
N.13. Identify equivalent expressions involving exponents
N.14. Simplify complex expressions involving multiple exponents and operations
N.15. Explore applications of exponents, such as exponential growth and decay

O. Monomials

P. Scientific Notation

Q. Polynomials and Factorising

Q.01. Define polynomial vocabulary (terms, coefficients, degree, constant)
Q.02. Model polynomials with algebra tiles
Q.03. Add and subtract polynomials using algebra tiles
Q.04. Add and subtract polynomials symbolically
Q.05. Add polynomials to find the perimeter of a shape
Q.06. Multiply a polynomial by a monomial
Q.07. Multiply two polynomials using algebra tiles
Q.08. Multiply two binomials using the FOIL method
Q.09. Multiply two binomials that are special cases (difference of squares, perfect square trinomials)
Q.10. Multiply polynomials of higher degree
Q.11. Find the highest common factor (HCF) of monomials
Q.12. Factorise out a monomial from a polynomial
Q.13. Factorise quadratic expressions with a leading coefficient of 1
Q.14. Factorise quadratic expressions with a leading coefficient greater than 1
Q.15. Apply factoring techniques to solve real-world problems

R. Pythagoras’ Theorem

R.01. Apply Pythagoras’ theorem to find the length of the hypotenuse of a right triangle
R.02. Apply Pythagoras’ theorem to find the missing leg length of a right triangle
R.03. Apply Pythagoras’ theorem to find the missing leg or hypotenuse length
R.04. Apply Pythagoras’ theorem to find the perimeter of a shape
R.05. Solve word problems involving Pythagoras’ theorem
R.06. Use the converse of Pythagoras’ theorem to determine if a triangle is a right triangle
R.07. Apply the properties of special right triangles (30-60-90 and 45-45-90)
R.08. Extend Pythagoras’ theorem to solve 3D problems
R.09. Prove Pythagoras’ theorem using geometric arguments

S. Congruence and Similarity

S.01. Identify corresponding sides and angles in congruent figures
S.02. Determine if triangles are congruent using SSS, SAS, and ASA congruence postulates
S.03. Perform dilations on figures in the coordinate plane and graph the image
S.04. Find the coordinates of an image after a dilation
S.05. Determine the scale factor of a dilation and classify it as an enlargement or reduction
S.06. Identify similar figures
S.07. Determine ratios of corresponding sides in similar figures
S.08. Write similarity statements for similar figures
S.09. Find missing side lengths and angle measures in similar figures
S.10. Solve problems involving similar triangles and indirect measurement
S.11. Relate the perimeters of similar figures
S.12. Apply similarity rules for triangles (AA, SSS, SAS)
S.13. Relate the areas of similar figures
S.14. Define similar solids
S.15. Relate the volume and surface area of similar solids
S.16. Determine the effect of changes in scale on perimeter, area, and volume
S.17. Prove triangle similarity using geometric theorems

T. Trigonometry

T.01. Define the trigonometric ratios (sin, cos, tan)
T.02. Define the reciprocal trigonometric ratios (csc, sec, cot)
T.03. Find trigonometric functions of special angles (30°, 45°, 60°) without a calculator
T.04. Find trigonometric functions using a calculator
T.05. Understand and apply the inverses of trigonometric functions (arcsin, arccos, arctan)
T.06. Use trigonometric ratios to find a side length in a right triangle
T.07. Use trigonometric ratios to find an angle measure in a right triangle
T.08. Solve a right triangle completely (find all side lengths and angle measures)
T.09. Explain why trigonometric ratios are constant in similar right triangles
T.10. Apply the law of sines and cosines to solve non-right triangles
T.11. Use trigonometric functions to model periodic phenomena

U. Quadratic Equations

U.01. Identify linear and quadratic functions from graphs
U.02. Identify linear and quadratic functions from tables
U.03. Identify the characteristics of quadratic graphs (vertex, axis of symmetry, intercepts)
U.04. Identify the characteristics of quadratic equations (coefficients, degree)
U.05. Complete a table of values for a quadratic equation
U.06. Graph quadratic equations
U.07. Solve a quadratic equation using square roots
U.08. Solve a quadratic equation using the zero product property
U.09. Solve a quadratic equation with leading coefficient 1 by factorising
U.10. Describe transformations of quadratic functions
U.11. Solve quadratic equations using the quadratic formula
U.12. Determine the discriminant of a quadratic equation and relate it to the nature of the roots

V. Circles in the Coordinate Plane

W. Data and Graphs

W.01. Interpret bar graphs and line graphs
W.02. Create bar graphs and line graphs
W.03. Interpret histograms
W.04. Create histograms
W.05. Interpret circle graphs (pie charts)
W.06. Interpret stem-and-leaf plots
W.07. Create stem-and-leaf plots
W.08. Create box-and-whisker plots
W.09. Analyze data using measures of central tendency (mean, median, mode) and spread (range, interquartile range)

X. Statistics

X.01. Calculate mean, median, mode, and range for a data set
X.02. Interpret charts to find mean, median, mode, and range
X.03. Solve for a missing number given the mean, median, mode, or range
X.04. Calculate quartiles and the interquartile range
X.05. Identify biased samples
X.06. Calculate standard deviation
X.07. Compare and contrast different types of data displays and their appropriateness for different data sets
X.08. Analyze the effect of outliers on measures of central tendency and spread

Y. Probability

Y.01. Calculate theoretical probability
Y.02. Calculate experimental probability
Y.03. Find probabilities using two-way frequency tables
Y.04. Calculate the number of outcomes in compound events
Y.05. Identify independent and dependent events
Y.06. Calculate the probability of independent and dependent events
Y.07. Calculate conditional probabilities
Y.08. Use probability to make predictions and informed decisions
Y.09. Design and conduct probability experiments

Course Content

A. Numbers and Counting

A.01. Classify different types of numbers (e.g., natural, integer, rational, irrational)

A.02. Represent numbers on a number line

A.03. Convert fluently between decimals, fractions, and percentages

A.04. Compare and order rational numbers

A.05. Identify and approximate square roots of perfect squares

A.06. Identify and approximate cube roots of perfect cubes

A.07. Locate irrational numbers approximately on a number line

A.08. Determine if the sum or product of two irrational numbers is rational or irrational

A.09. Understand the relationship between sets and subsets of real numbers

B. Operations with Integers and Rational Numbers

B.01. Add, subtract, multiply, and divide integers

B.02. Add and subtract rational numbers

B.03. Multiply and divide rational numbers

B.04. Apply the order of operations to evaluate numerical expressions involving integers

B.05. Apply the order of operations to evaluate numerical expressions involving rational numbers

B.06. Evaluate variable expressions involving integers

B.07. Evaluate variable expressions involving rational numbers

B.08. Solve real-world problems involving operations with rational numbers

B.09. Use estimation to check the reasonableness of calculations with integers and rational numbers

C. Properties of Operations and Expressions

C.01. Identify and apply properties of addition and multiplication (commutative, associative, distributive, identity, inverse)

C.02. Apply the distributive property to simplify expressions

C.03. Simplify variable expressions using properties of operations

C.04. Identify and apply properties of equality (addition, subtraction, multiplication, division)

C.05. Simplify complex variable expressions by combining like terms and using the distributive property

C.06. Justify steps in simplifying an expression or solving an equation using properties

C.07. Model and solve equations using algebra tiles and diagrams

D. Ratios, Rates, and Proportions

D.09. Apply proportional reasoning to real-world scenarios such as currency conversion

D.10. Use proportions to model indirect measurements

D.01. Identify equivalent ratios

D.02. Write an equivalent ratio

D.03. Determine unit rates from given information

D.04. Calculate unit prices for comparison

D.05. Determine if two ratios form a proportion

D.06. Solve proportions using cross-multiplication

D.07. Solve proportion word problems, including scale drawings and population estimation

D.08. Use proportions to solve problems involving similar figures

E. Percentages

E.01. Convert between percents, fractions, and decimals

E.02. Solve basic percent equations (e.g., finding the percentage of a number)

E.03. Solve percent word problems, including those involving discounts, markups, and taxes (GST)

E.04. Calculate percent of change (increase or decrease)

E.05. Solve percent of change word problems

E.06. Calculate simple interest earned on an investment or paid on a loan

E.07. Solve multi-step problems involving percentages

E.08. Calculate commission, profit, and loss in financial scenarios

E.09. Analyze the impact of different percentage changes in real-world contexts

F. Measurement and Error

F.01. Convert rates and measurements between different units

F.02. Determine the precision of a measurement

F.03. Calculate the greatest possible error in a measurement

F.04. Calculate the minimum and maximum area and volume based on measurement precision

F.05. Calculate percent error in measurements

F.06. Calculate percent error in area and volume measurements

F.07. Apply significant figures to measurements and calculations

F.08. Use dimensional analysis to solve multi-step conversion problems

F.09. Compare and contrast different units of measurement across various systems (metric, imperial)

G. Geometric Measurement

G.01. Calculate the perimeter of various shapes

G.02. Calculate the area of various shapes, including circles, semicircles, and quarter circles

G.03. Determine the area of compound figures involving triangles, semicircles, and quarter circles

G.04. Calculate the area between two shapes

G.05. Determine the sum of interior angles of polygons

G.06. Apply properties of transversals intersecting parallel lines to find angle measures

G.07. Calculate the volume of cylinders and prisms

G.08. Solve word problems involving the volume of cubes and rectangular prisms

G.09. Calculate the surface area of cylinders and prisms

G.10. Calculate the volume and surface area of composite 3D shapes

G.11. Solve real-world problems involving perimeter, area, volume, and surface area

G.12. Apply the concepts of density and mass to solve related problems

H. Coordinate Plane

H.01. Review basic concepts of the coordinate plane (quadrants, axes, ordered pairs)

H.02. Apply the midpoint formula to find the midpoint of a line segment

H.03. Apply the midpoint formula to find an endpoint of a line segment, given the other endpoint and midpoint

H.04. Calculate the distance between two points using the distance formula

H.05. Determine the equation of a line given two points on the line

H.06. Find the area of polygons graphed on the coordinate plane