AUSTRALIA MATH YEAR 7 – EDmama Australia

A. Integers

A.01. Represent integers on a number line.
A.02. Understand the concept of integers and their use in real-world contexts.
A.03. Compare integers using inequality symbols.
A.04. Order a set of integers from least to greatest.
A.05. Graph integers on horizontal and vertical number lines.
A.06. Apply the concept of absolute value to real-world situations.

B. Decimals

C. Fractions and Mixed Numbers

D. Ratios, Rates, and Proportions

E. Percents

F. Number Theory

F.01. Define prime and composite numbers.
F.02. Determine if a number is prime or composite.
F.03. Find the prime factorisation of a number.
F.04. Identify multiplicative inverses.
F.05. Apply divisibility rules to determine factors of a number.
F.06. Find the highest common factor (HCF) of two or more numbers.
F.07. Find the lowest common multiple (LCM) of two or more numbers.
F.08. Solve word problems involving HCF and LCM.
F.09. Classify different types of numbers (e.g., rational, irrational).

G. Operations with Integers

G.01. State the rules for adding integers.
G.02. Add integers using counters and number lines.
G.03. Add integers.
G.04. State the rules for subtracting integers.
G.05. Subtract integers using counters and number lines.
G.06. Subtract integers.
G.07. Apply addition and subtraction rules to solve integer problems.
G.08. Add and subtract integers.
G.09. Complete addition and subtraction number sentences with integers.
G.10. Add and subtract integers: word problems.
G.11. State the rules for integer multiplication.
G.12. Multiply integers.
G.13. State the rules for integer division.
G.14. Divide integers.
G.15. Evaluate numerical expressions involving integers using order of operations.

H. Operations with Decimals

H.01. Add and subtract decimals, including word problems.
H.02. Estimate sums and differences of decimals.
H.03. Multiply decimals by whole numbers, including word problems.
H.04. Multiply decimals using grids and standard algorithms.
H.05. Estimate products of decimals.
H.06. Divide decimals by whole numbers, including word problems.
H.07. Divide decimals using long division.
H.08. Estimate quotients of decimals.
H.09. Multiply and divide decimals in word problems.
H.10. Add, subtract, multiply, and divide decimals: word problems.
H.11. Evaluate numerical expressions involving decimals using order of operations.

I. Add and Subtract Fractions

I.01. Add and subtract fractions with like denominators.
I.02. Solve word problems involving addition and subtraction of fractions with like denominators.
I.03. Add fractions with unlike denominators using models.
I.04. Find the lowest common denominator (LCD).
I.05. Add fractions with unlike denominators.
I.06. Subtract fractions with unlike denominators using models.
I.07. Subtract fractions with unlike denominators.
I.08. Add and subtract fractions with unlike denominators: word problems.
I.09. Add and subtract mixed numbers.
I.10. Add and subtract mixed numbers: word problems.
I.11. Estimate sums and differences of mixed numbers.
I.12. Determine and graph solutions for Inequalities with addition and subtraction of fractions and mixed numbers.

J. Multiply and Divide Fractions

J.01. Multiply unit fractions by whole numbers using number lines and models.
J.02. Identify multiples of fractions.
J.03. Multiply fractions by whole numbers using arrays and number lines.
J.04. Multiply fractions and whole numbers.
J.05. Solve word problems involving multiplying fractions and whole numbers.
J.06. Multiply two unit fractions using models.
J.07. Multiply two fractions using models.
J.08. Multiply fractions.
J.09. Multiply fractions: word problems.
J.10. Multiply three or more fractions and whole numbers.
J.11. Divide unit fractions by whole numbers using models.
J.12. Divide whole numbers by unit fractions using models.
J.13. Divide whole numbers and unit fractions using area models.
J.14. Determine reciprocals of numbers.
J.15. Divide whole numbers and unit fractions.
J.16. Divide fractions by whole numbers.
J.17. Divide whole numbers by fractions.
J.18. Divide fractions.
J.19. Divide fractions: word problems.
J.20. Estimate products and quotients of fractions and mixed numbers.
J.21. Evaluate numerical expressions involving fractions.
J.22. Solve word problems involving all operations with fractions and mixed numbers.

K. Rational Numbers

K.01. Represent fractions and decimals on a number line.
K.02. Convert between decimals and fractions or mixed numbers.
K.03. Compare rational numbers using inequality symbols.
K.04. Order a set of rational numbers from least to greatest.
K.05. Add and subtract rational numbers.
K.06. Apply addition and subtraction rules to solve problems.
K.07. Multiply and divide rational numbers.
K.08. Apply multiplication and division rules to solve problems.
K.09. Relate rational numbers to real-world situations.

L. Exponents and Square Roots

M. Consumer Maths

M.01. Compare and contrast different coupons to determine the better deal.
M.02. Add, subtract, multiply, and divide money amounts in word problems.
M.03. Interpret price lists to find costs of items.
M.04. Determine unit prices.
M.05. Use unit prices to calculate the total price of multiple items.
M.06. Calculate the percent of a number for GST, discount and more.
M.07. Determine the percent of discount and mark-up.
M.08. Find the original price given the sale price and discount.
M.09. Solve multi-step problems involving percents.
M.10. Calculate simple interest.

N. Problem Solving and Estimation

N.01. Use estimation to solve word problems.
N.02. Solve multi-step word problems involving various operations.
N.03. Solve problems using the guess-and-check strategy.
N.04. Use Venn diagrams to solve problems involving sets and categories.
N.05. Find the number of each type of coin in a given situation.
N.06. Solve elapsed time word problems.
N.07. Use logical reasoning to solve number puzzles.
N.08. Apply different problem-solving strategies to tackle complex real-world problems.

O. Units of Measurement

P. Expressions and Properties

P.01. Write variable expressions using one operation.
P.02. Write variable expressions using two or three operations.
P.03. Translate word problems into variable expressions.
P.04. Evaluate linear expressions by substituting values for variables.
P.05. Evaluate multi-variable expressions.
P.06. Evaluate nonlinear expressions.
P.07. Identify terms and coefficients in an expression.
P.08. Sort factors of expressions.
P.09. Apply the properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
P.10. Add using properties.
P.11. Multiply using properties.
P.12. Multiply using the distributive property.
P.13. Solve equations using properties.
P.14. Write equivalent expressions using properties.
P.15. Add and subtract like terms.
P.16. Add, subtract and multiply linear expressions.
P.17. Factor linear expressions.
P.18. Identify equivalent linear expressions using algebra tiles.
P.19. Identify equivalent linear expressions using algebraic manipulation.

Q. One-Variable Equations

Q.01. Determine which value of x satisfies a given equation.
Q.02. Translate a word problem into an algebraic equation.
Q.03. Model and solve equations using algebra tiles.
Q.04. Write and solve equations that represent diagrams.
Q.05. Solve one-step equations using inverse operations.
Q.06. Solve two-step equations using inverse operations.
Q.07. Solve equations, completing the solution steps.
Q.08. Solve equations: word problems.
Q.09. Verify the solution to an equation by substitution.

R. Two-Variable Equations

R.01. Determine if an ordered pair (x, y) satisfies a given equation.
R.02. Complete a table of values for a two-variable relationship.
R.03. Write a two-variable equation to represent a relationship.
R.04. Identify the graph of a linear equation.
R.05. Interpret a graph in the context of a word problem.
R.06. Solve word problems involving two-variable equations.
R.07. Identify graphs that represent different scenarios described in word problems.
R.08. Determine the rate of change from a graph or table.
R.09. Identify a constant rate of change in a real-world context.

S. Number Sequences

S.01. Identify arithmetic and geometric sequences.
S.02. Find the next terms in arithmetic sequences.
S.03. Find the next terms in geometric sequences.
S.04. Identify patterns in number sequences.
S.05. Solve number sequences: mixed review.
S.06. Solve number sequences: word problems.
S.07. Evaluate variable expressions for number sequences.
S.08. Write variable expressions for arithmetic sequences.
S.09. Find a specific term in a sequence using a formula.

T. Coordinate Plane

U. Two-Dimensional Figures

U.01. Identify and classify polygons based on their properties.
U.02. Define lines, intervals, and rays.
U.03. Understand the relationships between parallel, perpendicular, and intersecting lines.
U.04. Name, measure, and classify angles.
U.05. Classify triangles based on angle measures (acute, obtuse, right).
U.06. Classify triangles based on side lengths (scalene, isosceles, equilateral).
U.07. Identify parallelograms, trapeziums, rectangles, and rhombuses.
U.08. Identify quadrilaterals by their properties
U.09. Graph triangles and quadrilaterals on the coordinate plane.
U.10. Find missing angles in triangles and quadrilaterals using angle properties.
U.11. Calculate the sums of angles in polygons.
U.12. Identify complementary, supplementary, vertical, adjacent and congruent angles.
U.13. Find measures of complementary, supplementary, vertical and adjacent angles.
U.14. Apply the properties of transversals intersecting parallel lines.
U.15. Find lengths and measures of bisected intervals and angles.
U.16. Identify the parts of a circle (centre, radius, diameter, chord, arc).
U.17. Construct parallel lines using geometric tools.
U.18. Construct the midpoint or perpendicular bisector of an interval.
U.19. Construct a perpendicular line using geometric tools.

V. Symmetry and Transformations

V.01. Identify lines of symmetry in two-dimensional figures.
V.02. Identify reflections, rotations, and translations.
V.03. Perform translations on the coordinate plane and graph the image.
V.04. Determine the coordinates of an image after a translation.
V.05. Perform reflections on the coordinate plane and graph the image.
V.06. Determine the coordinates of an image after a reflection.
V.07. Perform rotations on the coordinate plane and graph the image.
V.08. Determine the coordinates of an image after a rotation.
V.09. Describe sequences of transformations and graph the final image.
V.10. Apply transformations to solve real-world design and pattern problems.

W. Three-Dimensional Figures

X. Geometric Measurement

X.01. Calculate the perimeter of polygons.
X.02. Multiply to find the area of a rectangle made of unit squares.
X.03. Calculate the area of rectangles and squares.
X.04. Explain the relationship between the area of a parallelogram and a rectangle.
X.05. Calculate the area of parallelograms.
X.06. Explain the relationship between the area of a triangle and a parallelogram.
X.07. Calculate the area of triangles.
X.08. Calculate the area between two shapes.
X.09. Solve word problems involving area and perimeter.
X.10. Calculate the surface area of cubes and rectangular prisms.
X.11. Calculate the surface area of triangular prisms.
X.12. Calculate the surface area of pyramids.
X.13. Calculate the volume of cubes and rectangular prisms.
X.14. Solve word problems involving the volume of cubes and rectangular prisms.
X.15. Calculate the volume of triangular prisms.
X.16. Apply geometric measurement formulas to solve practical problems.

Y. Data and Graphs

Y.01. Interpret data presented in tables.
Y.02. Interpret data presented in dot plots.
Y.03. Create dot plots from data sets.
Y.04. Interpret data presented in stem-and-leaf plots.
Y.05. Create stem-and-leaf plots from data sets.
Y.06. Interpret data presented in bar graphs.
Y.07. Create bar graphs from data sets.
Y.08. Create frequency charts to organise data.
Y.09. Interpret data presented in circle graphs (pie charts).
Y.10. Relate circle graphs to central angles and proportions.
Y.11. Interpret data presented in line graphs.
Y.12. Create line graphs from data sets.
Y.13. Choose the best type of graph to represent a given data set.
Y.14. Analyse trends and make predictions based on data in graphs.

Z. Statistics

Z.07. Interpret measures of centre and spread to describe a data set.
Z.08. Identify representative, random, and biased samples.
Z.09. Explain the importance of random sampling in data collection.
Z.01. Calculate the mean, median, mode, and range of a data set.
Z.02. Interpret charts to find the mean, median, mode, and range.
Z.03. Solve problems involving finding a missing number given the mean, median, mode, or range.
Z.04. Describe the effect of changes in a data set on the mean, median, mode, and range.
Z.05. Identify an outlier in a data set.
Z.06. Describe the effect of removing an outlier on the measures of centre and spread.

AA. Probability

AA.01. Determine if an event is more, less, or equally likely to occur.
AA.02. List the sample space of simple events.
AA.03. Calculate the probability of simple events.
AA.04. Calculate the probability of opposite, mutually exclusive, and overlapping events.
AA.05. Determine experimental probability from data.
AA.06. Make predictions based on probability.
AA.07. Identify independent and dependent events.
AA.08. Calculate probabilities of compound events.
AA.09. Use probability to make informed decisions in real-world scenarios.

Course Content

A. Integers

A.01. Represent integers on a number line.

A.02. Understand the concept of integers and their use in real-world contexts.

A.03. Compare integers using inequality symbols.

A.04. Order a set of integers from least to greatest.

A.05. Graph integers on horizontal and vertical number lines.

A.06. Apply the concept of absolute value to real-world situations.

B. Decimals

B.01. Review place value of decimal numbers.

B.02. Represent decimals on a number line.

B.03. Compare and order decimals.

B.04. Round decimals to a specified place value.

B.05. Convert between decimals and fractions.

C. Fractions and Mixed Numbers

C.01. Understand fractions as parts of a whole.

C.02. Write fractions in lowest terms (simplify).

C.03. Identify and generate equivalent fractions using models.

C.04. Compare and order fractions.

C.05. Convert between mixed numbers and improper fractions.

C.06. Solve word problems involving fractions using visual aids.

D. Ratios, Rates, and Proportions

D.03. Identify equivalent ratios.

D.04. Calculate unit rates.

D.05. Determine if two ratios form a proportion.

D.06. Solve proportions using cross-multiplication.

D.07. Apply proportional reasoning to solve real-world problems.

D.01. Define ratios and rates and their use in everyday contexts.

D.02. Write ratios to compare two quantities.

E. Percents

E.01. Define percentage as a ratio out of 100.

E.02. Convert between percents, fractions, and decimals.

E.03. Find the percentage of a number using various methods.

E.04. Solve percent problems involving discounts, tax, and tips.

E.05. Find what percent one number is of another.

E.06. Solve percent equations.

E.07. Apply percentages to consumer math problems.

F. Number Theory

F.01. Define prime and composite numbers.

F.02. Determine if a number is prime or composite.

F.03. Find the prime factorisation of a number.

F.04. Identify multiplicative inverses.

F.05. Apply divisibility rules to determine factors of a number.

F.06. Find the highest common factor (HCF) of two or more numbers.

F.07. Find the lowest common multiple (LCM) of two or more numbers.

F.08. Solve word problems involving HCF and LCM.

F.09. Classify different types of numbers (e.g., rational, irrational).

G. Operations with Integers

G.01. State the rules for adding integers.

G.02. Add integers using counters and number lines.

G.03. Add integers.

G.04. State the rules for subtracting integers.

G.05. Subtract integers using counters and number lines.

G.06. Subtract integers.

G.07. Apply addition and subtraction rules to solve integer problems.

G.08. Add and subtract integers.

G.09. Complete addition and subtraction number sentences with integers.

G.10. Add and subtract integers: word problems.

G.11. State the rules for integer multiplication.

G.12. Multiply integers.

G.13. State the rules for integer division.

G.14. Divide integers.

G.15. Evaluate numerical expressions involving integers using order of operations.

H. Operations with Decimals

H.01. Add and subtract decimals, including word problems.

H.02. Estimate sums and differences of decimals.

H.03. Multiply decimals by whole numbers, including word problems.

H.04. Multiply decimals using grids and standard algorithms.

H.05. Estimate products of decimals.

H.06. Divide decimals by whole numbers, including word problems.

H.07. Divide decimals using long division.

H.08. Estimate quotients of decimals.

H.09. Multiply and divide decimals in word problems.

H.10. Add, subtract, multiply, and divide decimals: word problems.

H.11. Evaluate numerical expressions involving decimals using order of operations.

I. Add and Subtract Fractions

I.01. Add and subtract fractions with like denominators.

I.02. Solve word problems involving addition and subtraction of fractions with like denominators.

I.03. Add fractions with unlike denominators using models.

I.04. Find the lowest common denominator (LCD).