Course Content
A. Numbers and Counting
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A.01. Identify and represent integers on a number line.
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A.02. Convert fluently between decimals, fractions, and percentages.
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A.03. Identify and classify numbers as rational or irrational.
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A.04. Compare and order rational numbers using number lines and inequalities.
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A.05. Determine the prime factorization of composite numbers.
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A.06. Calculate and estimate square roots of perfect squares and other numbers.
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A.07. Calculate and estimate cube roots of perfect cubes and other numbers.
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A.08. Explain the difference between rational and irrational numbers with examples.
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A.09. Approximate irrational numbers to a specified decimal place.
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A.10. Investigate and describe the properties of real numbers.
B. Operations with Integers and Rational Numbers
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B.01. Add and subtract integers using number lines and other visual aids.
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B.02. Multiply and divide integers, understanding the rules for signs.
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B.03. Add and subtract rational numbers, including fractions and decimals.
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B.04. Multiply and divide rational numbers, expressing answers in simplest form.
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B.05. Evaluate numerical expressions involving integers using the order of operations (PEMDAS/BODMAS).
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B.06. Evaluate variable expressions involving integers by substituting given values.
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B.07. Evaluate numerical expressions involving rational numbers, applying order of operations.
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B.08. Evaluate variable expressions involving rational numbers, substituting values and simplifying.
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B.09. Solve real-world problems involving operations with rational numbers.
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B.10. Apply the properties of real numbers (commutative, associative, distributive) to simplify expressions.
C. Single-Variable Inequalities
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C.01. Represent inequalities on a number line using appropriate notation (open/closed circles, arrows).
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C.02. Write inequalities from given graphs on a number line.
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C.03. Identify solutions to inequalities from a given set of numbers.
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C.04. Solve one-step linear inequalities using addition and subtraction.
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C.05. Solve one-step linear inequalities using multiplication and division, paying attention to sign changes.
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C.06. Solve general one-step linear inequalities.
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C.07. Graph the solutions to one-step linear inequalities on a number line.
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C.08. Solve two-step linear inequalities.
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C.09. Graph the solutions to two-step linear inequalities on a number line.
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C.10. Solve advanced linear inequalities, including those with distribution or combining like terms.
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C.11. Graph the solutions to advanced linear inequalities on a number line.
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C.12. Formulate and solve linear inequalities to represent and solve real-world constraints.
D. Solve Equations
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D.01. Model and solve simple equations using algebra tiles.
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D.02. Write algebraic equations that represent given diagrams or situations.
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D.03. Solve one-step linear equations using inverse operations.
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D.04. Solve two-step linear equations using inverse operations.
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D.05. Solve advanced linear equations, including those with distribution or combining like terms.
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D.06. Solve linear equations with variables on both sides.
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D.07. Complete the solution of a linear equation given a partially completed solution.
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D.08. Determine the number of solutions (none, one, or infinite) for a given linear equation.
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D.09. Create linear equations with specific solution types (no solution or infinitely many solutions).
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D.10. Translate and solve linear equations from word problems.
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D.11. Solve linear equations in a mixed review format, applying various techniques.
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D.12. Use technology to solve linear equations graphically and numerically.
E. Exponents
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E.01. Evaluate powers with integer bases (positive, negative, and zero exponents).
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E.02. Evaluate powers with decimal and fractional bases.
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E.03. Simplify expressions with negative exponents, rewriting them with positive exponents.
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E.04. Simplify expressions involving multiplication of powers with the same base.
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E.05. Simplify expressions involving division of powers with the same base.
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E.06. Simplify expressions involving both multiplication and division of exponents.
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E.07. Apply the power rule to simplify expressions with powers raised to a power.
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E.08. Evaluate numerical expressions using properties of exponents.
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E.09. Identify equivalent expressions involving exponents, using exponent rules.
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E.10. Use exponents to express repeated multiplication in a concise form.
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E.11. Apply exponent rules to solve real-world problems involving growth and decay.
F. Linear Functions
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F.01. Identify linear functions from equations, graphs, and tables.
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F.02. Determine the slope of a line from its graph.
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F.03. Calculate the slope of a line given two points on the line.
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F.04. Find a missing coordinate of a point on a line, given the slope and another point.
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F.05. Identify the slope and y-intercept of a linear equation in slope-intercept form.
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F.06. Graph a linear equation given in slope-intercept form.
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F.07. Write a linear equation in slope-intercept form from a given graph.
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F.08. Write a linear equation in slope-intercept form given the slope and y-intercept.
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F.09. Write a linear equation in slope-intercept form from a table of values.
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F.10. Write a linear equation in slope-intercept form from a word problem.
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F.11. Write linear functions to model and solve real-world word problems.
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F.12. Complete a table of values and graph a linear function.
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F.13. Compare linear functions presented in different forms (graphs, tables, and equations).
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F.14. Write linear equations in standard form.
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F.15. Determine the x- and y-intercepts of a linear equation in standard form.
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F.16. Graph a linear equation given in standard form.
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F.17. Recognize and write equations of horizontal and vertical lines.
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F.18. Graph horizontal and vertical lines.
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F.19. Graph a linear equation given in point-slope form.
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F.20. Write a linear equation in point-slope form given a point and the slope.
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F.21. Write a linear equation in point-slope form from a graph.
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F.22. Determine the slopes of parallel and perpendicular lines.
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F.23. Write an equation for a line that is parallel or perpendicular to a given line and passes through a given point.
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F.24. Calculate the distance between a point and a line.
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F.25. Calculate the distance between two parallel lines.
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F.26. Describe and perform transformations of linear functions (translations, reflections, stretches/compressions).
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F.27. Apply linear functions to model and solve real-world problems involving constant rates of change.
G. Scientific Notation
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G.01. Convert numbers between standard notation and scientific notation.
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G.02. Compare numbers written in scientific notation.
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G.03. Multiply numbers written in scientific notation, expressing the result in scientific notation.
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G.04. Divide numbers written in scientific notation, expressing the result in scientific notation.
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G.05. Solve real-world problems involving very large or very small numbers using scientific notation.
H. Simultaneous Equations
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H.01. Determine whether a given ordered pair (x, y) is a solution to a system of simultaneous equations.
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H.02. Solve systems of simultaneous equations by graphing.
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H.03. Solve simultaneous equations by graphing to solve word problems.
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H.04. Determine the number of solutions (none, one, or infinite) to a system of simultaneous equations by graphing.
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H.05. Determine the number of solutions (none, one, or infinite) to a system of simultaneous equations by analyzing the equations.
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H.06. Solve systems of simultaneous equations using the substitution method.
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H.07. Solve word problems using systems of simultaneous equations and the substitution method.
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H.08. Solve systems of simultaneous equations using the elimination method (addition/subtraction).
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H.09. Solve word problems using systems of simultaneous equations and the elimination method.
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H.10. Choose the most efficient method (graphing, substitution, or elimination) to solve a given system of equations.
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H.11. Apply systems of equations to solve real-world problems involving multiple variables and constraints.
I. Consumer Maths
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I.05. Solve multi-step problems involving percentages, such as successive discounts or markups.
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I.06. Apply consumer math concepts to solve real-world problems related to budgeting, saving, and spending.
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I.07. Compare and contrast different investment options, considering interest rates and compounding periods.
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I.01. Calculate simple interest earned on an investment or paid on a loan.
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I.02. Calculate compound interest earned on an investment or paid on a loan.
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I.03. Calculate the percent of a number, including applications such as VAT and discounts.
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I.04. Determine the percentage discount or markup on an item.
J. Exponential Functions
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J.01. Evaluate an exponential function for a given input value.
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J.02. Match exponential functions to their corresponding graphs.
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J.03. Determine the domain and range of an exponential function.
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J.04. Solve word problems involving exponential growth and decay.
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J.05. Graph exponential functions and analyze their key features (asymptotes, intercepts).
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J.06. Model real-world phenomena, such as population growth or radioactive decay, using exponential functions.
K. Number Sequences
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K.01. Identify arithmetic and geometric sequences.
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K.02. Determine the common difference in an arithmetic sequence.
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K.03. Determine the common ratio in a geometric sequence.
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K.04. Evaluate variable expressions for terms in a number sequence.
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K.05. Write variable expressions (formulas) for arithmetic sequences.
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K.06. Write variable expressions (formulas) for geometric sequences.
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K.07. Solve mixed review problems involving arithmetic and geometric sequences.
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K.08. Find the next term in a given sequence.
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K.09. Calculate the sum of the first n terms of an arithmetic or geometric sequence.
L. Polynomials
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L.01. Define and identify polynomial vocabulary (terms, coefficients, degree, leading coefficient).
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L.02. Model polynomials using algebra tiles.
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L.03. Add and subtract polynomials using algebra tiles.
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L.04. Add and subtract polynomials algebraically.
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L.05. Apply polynomial addition to find the perimeter of geometric figures.
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L.06. Multiply and divide monomials.
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L.07. Simplify powers of monomials using exponent rules.
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L.08. Multiply a polynomial by a monomial using the distributive property.
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L.09. Multiply two polynomials using algebra tiles.
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L.10. Multiply two binomials using the distributive property or FOIL method.
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L.11. Multiply two binomials that are special cases (difference of squares, perfect square trinomials).
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L.12. Multiply polynomials of any degree.
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L.13. Divide a polynomial by a monomial.
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L.14. Use polynomial operations to solve geometric problems involving area and volume.
M. Factorising
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M.01. Find the highest common factor (HCF) of monomials.
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M.02. Factor out a monomial from a polynomial.
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M.03. Factorise quadratic expressions with a leading coefficient of 1.
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M.04. Factorise quadratic expressions with leading coefficients other than 1.
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M.05. Factorise quadratic expressions that are special cases (difference of squares, perfect square trinomials).
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M.06. Factorise quadratic expressions using algebra tiles.
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M.07. Factorise polynomials by grouping.
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M.08. Factorise polynomials of higher degrees.
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M.09. Apply factoring techniques to simplify rational expressions.
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M.10. Use factorisation to solve real-world problems involving areas and volumes.
N. Quadratic Equations
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N.01. Identify and describe the key characteristics of quadratic functions (vertex, axis of symmetry, intercepts).
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N.02. Complete a function table for a given quadratic function.
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N.03. Solve quadratic equations using square roots.
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N.04. Solve quadratic equations using the zero product property.
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N.05. Solve quadratic equations by factorising.
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N.06. Complete the square to rewrite a quadratic expression in vertex form.
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N.07. Solve quadratic equations by completing the square.
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N.08. Solve quadratic equations using the quadratic formula.
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N.09. Use the discriminant to determine the number and type of solutions to a quadratic equation.
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N.10. Graph quadratic functions and relate the graph to the solutions of the corresponding quadratic equation.
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N.11. Apply quadratic equations to solve real-world problems involving projectile motion, area optimisation, and other applications.
O. Functions: Linear, Quadratic, Exponential
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O.01. Identify linear, quadratic, and exponential functions from their graphs.
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O.02. Identify linear, quadratic, and exponential functions from tables of values.
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O.03. Write equations for linear, quadratic, and exponential functions given various information (points, slope, intercepts).
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O.04. Analyze linear functions over unit intervals to determine the rate of change.
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O.05. Analyze exponential functions over unit intervals to determine the growth or decay factor.
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O.06. Describe and compare linear and exponential growth and decay.
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O.07. Model real-world situations using linear, quadratic, and exponential functions, and interpret the results.
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O.08. Discuss the properties of polynomial, rational, exponential, logarithmic, and trigonometric functions.
P. Radical Expressions
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P.01. Simplify radical expressions by removing perfect square factors.
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P.02. Simplify radical expressions involving fractions by rationalizing the denominator.
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P.03. Multiply radical expressions using the distributive property.
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P.04. Add and subtract radical expressions by combining like terms.
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P.05. Simplify radical expressions using the distributive property.
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P.06. Simplify radical expressions in a mixed review format.
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P.07. Solve equations involving radical expressions.
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P.08. Apply radical expressions to solve geometric problems involving lengths and distances.
Q. Rational Functions and Expressions
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Q.01. Identify asymptotes and excluded values of rational functions.
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Q.02. Simplify complex fractions.
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Q.03. Simplify rational expressions by cancelling common factors.
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Q.04. Multiply and divide rational expressions, expressing the result in simplest form.
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Q.05. Divide polynomials using long division or synthetic division.
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Q.06. Add and subtract rational expressions with like and unlike denominators.
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Q.07. Solve rational equations, checking for extraneous solutions.
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Q.08. Graph simple rational functions and analyze their behavior near asymptotes.
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Q.09. Apply rational functions to model real-world relationships involving inverse variation.
R. Measurement
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R.01. Convert between different units of measurement (e.g., metric to imperial, time units).
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R.02. Convert rates involving different units (e.g., km/h to m/s).
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R.03. Understand the concept of precision in measurement.
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R.04. Determine the greatest possible error in a measurement.
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R.05. Calculate the minimum and maximum possible area and volume given measurement errors.
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R.06. Calculate percent error in a measurement.
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R.07. Calculate percent error in area and volume measurements.
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R.08. Apply measurement concepts to solve real-world problems involving conversions and errors.
S. Points, Lines and Segments
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S.01. Define and identify lines, line segments, and half-lines.
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S.02. Calculate the lengths of segments on a number line.
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S.03. Apply the additive property of length to solve problems involving segment lengths.
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S.04. Find the midpoint of a line segment.
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S.05. Define and identify congruent line segments.
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S.06. Apply the Perpendicular Bisector Theorem.
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S.07. Use the midpoint formula to find the midpoint of a line segment in the coordinate plane.
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S.08. Use the distance formula to find the distance between two points in the coordinate plane.
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S.09. Determine the equation of a perpendicular bisector.
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S.10. Apply geometric concepts of points, lines, and segments to solve real-world problems involving distances and locations.
T. Angles
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T.01. Define and identify angle vocabulary (vertex, sides, interior, exterior).
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T.02. Measure angles using a protractor.
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T.03. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
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T.04. Find measures of complementary, supplementary, vertical, and adjacent angles, given angle relationships.
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T.05. Define and identify angle bisectors.
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T.06. Apply angle relationships to solve geometric problems involving angle measures.
U. Parallel and Perpendicular Lines
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U.01. Identify parallel, perpendicular, and skew lines and planes.
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U.02. Name angle pairs formed by a transversal intersecting two lines.
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U.03. Find angle measures when a transversal intersects parallel lines.
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U.04. Prove lines are parallel based on angle relationships.
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U.05. Solve real-world problems using the geometric properties of parallel and perpendicular lines.
V. Two-Dimensional Figures
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V.01. Define and identify polygon vocabulary (vertices, sides, angles, diagonals).
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V.02. Calculate the perimeter of polygons.
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V.03. Calculate the area of triangles and quadrilaterals.
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V.04. Calculate area and perimeter of polygons in the coordinate plane I.
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V.05. Calculate area and perimeter of polygons in the coordinate plane II.
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V.06. Calculate the area and circumference of circles.
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V.07. Calculate the area of compound figures by decomposing them into simpler shapes.
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V.08. Calculate area and perimeter of similar figures using scale factors.
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V.09. Calculate the area between two shapes.
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V.10. Apply geometric concepts to solve real-world problems involving area, perimeter, and circumference.
W. Introduction to Congruent Figures
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W.05. Apply the concept of congruence to solve real-world problems involving geometric shapes.
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W.01. Write congruence statements for congruent figures and identify corresponding parts.
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W.02. Solve problems involving corresponding parts of congruent figures.
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W.03. Identify congruent figures based on given information.
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W.04. Use transformations to determine if figures are congruent.
X. Congruent Triangles
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X.01. Prove triangle congruence using the SSS and SAS Theorems.
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X.02. Prove triangle congruence using the ASA and AAS Theorems.
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X.03. Apply SSS, SAS, ASA, and AAS Theorems to prove triangle congruence.
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X.04. Apply the SSS Theorem to prove triangle congruence in the coordinate plane.
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X.05. Apply congruency properties in isosceles and equilateral triangles.
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X.06. Prove triangle congruence using the Hypotenuse-Leg (HL) Theorem.
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X.07. Use congruent triangles to prove corresponding parts are congruent (CPCTC).
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X.08. Solve geometric problems using congruent triangle properties.
Y. Transformations
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Y.01. Identify congruence transformations (translations, rotations, reflections).
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Y.02. Graph the image of a figure after a composition of congruence transformations.
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Y.03. Identify transformations that carry a polygon onto itself.
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Y.04. Graph the image of a figure after a dilation.
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Y.05. Find the coordinates of the image of a figure after a dilation.
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Y.06. Determine the scale factor of a dilation and classify it as an enlargement or reduction.
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Y.07. Explore the relationship between dilations and parallel lines.
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Y.08. Describe the effect of transformations on the coordinates of points and the properties of geometric figures.
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Y.09. Use transformations to create tessellations and patterns.
Z. Triangles
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Z.01. Classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).
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Z.02. Apply the Triangle Angle-Sum Theorem to find missing angles in a triangle.
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Z.03. Apply properties of midsegments of triangles.
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Z.04. Explore the relationships between triangles and angle bisectors.
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Z.05. Identify medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle.
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Z.06. Apply angle-side relationships in triangles to determine the order of side lengths and angle measures.
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Z.07. Apply the Triangle Inequality Theorem to determine if three given side lengths can form a triangle.
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Z.08. Apply the properties of triangle to real world problems involving stability and structure.
AA. Similarity
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AA.01. Identify similar figures by comparing corresponding angles and sides.
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AA.02. Determine ratios of corresponding sides in similar figures.
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AA.03. Write similarity statements for similar figures.
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AA.04. Find missing side lengths and angle measures in similar figures.
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AA.05. Use similar triangles and indirect measurement to find unknown lengths.
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AA.06. Compare the perimeters of similar figures.
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AA.07. Apply similarity rules (AA, SSS, SAS) for triangles.
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AA.08. Explore the relationship between similar triangles and similarity transformations.
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AA.09. Compare the areas of similar figures.
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AA.10. Apply the properties of similarity to solve real-world problems involving scale models and maps.
BB. Right Triangles
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BB.01. Apply Pythagoras’ Theorem to find missing side lengths in a right triangle.
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BB.02. Apply the converse of Pythagoras’ Theorem to determine if a triangle is a right triangle.
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BB.03. Apply Pythagoras’ Inequality Theorems to classify triangles as acute or obtuse.
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BB.04. Apply the properties of special right triangles (30-60-90 and 45-45-90) to find missing side lengths.
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BB.05. Use right triangles to solve real-world problems involving distances and heights.
CC. Trigonometry
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CC.01. Define the trigonometric ratios (sin, cos, and tan) for acute angles in a right triangle.
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CC.02. Define the trigonometric ratios (csc, sec, and cot) for acute angles in a right triangle.
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CC.03. Find the trigonometric function values of special angles (30°, 45°, 60°).
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CC.04. Find trigonometric function values using a calculator.
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CC.05. Understand and apply inverses of trigonometric functions (arcsin, arccos, arctan).
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CC.06. Use trigonometric ratios to find a missing side length in a right triangle.
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CC.07. Use trigonometric ratios to find a missing angle measure in a right triangle.
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CC.08. Solve a right triangle (find all missing side lengths and angle measures).
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CC.09. Apply trigonometry to solve real-world problems involving angles of elevation and depression.
DD. Surface Area and Volume
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DD.01. Understand the concepts of surface area and volume.
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DD.02. Calculate the surface area of prisms and cylinders.
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DD.03. Calculate the surface area of pyramids and cones.
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DD.04. Calculate the volume of prisms and cylinders.
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DD.05. Calculate the volume of pyramids and cones.
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DD.06. Calculate the surface area and volume of spheres.
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DD.07. Understand the concept of similar solids.
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DD.08. Calculate the surface area and volume of similar solids using scale factors.
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DD.09. Solve mixed review problems involving surface area and volume.
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DD.10. Apply the concepts of surface area and volume to solve real-world problems involving packaging, construction, and design.
EE. Constructions
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EE.01. Construct the midpoint or perpendicular bisector of a line segment using compass and straightedge.
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EE.02. Construct an angle bisector using compass and straightedge.
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EE.03. Construct a congruent angle using compass and straightedge.
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EE.04. Construct a perpendicular line to a given line through a given point using compass and straightedge.
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EE.05. Construct parallel lines using compass and straightedge.
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EE.06. Construct an equilateral triangle or regular hexagon using compass and straightedge.
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EE.07. Construct a square using compass and straightedge.
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EE.08. Construct a tangent line to a circle from a point outside the circle using compass and straightedge.
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EE.09. Construct the circumcenter or incenter of a triangle using compass and straightedge.
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EE.10. Construct the inscribed or circumscribed circle of a triangle using compass and straightedge.
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EE.11. Construct the centroid or orthocenter of a triangle using compass and straightedge.
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EE.12. Describe the steps involved in each construction and explain why they work.
FF. Problem Solving
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FF.01. Solve problems involving consecutive integers.
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FF.02. Solve rate of travel word problems (distance, rate, time).
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FF.03. Solve weighted averages word problems.
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FF.04. Apply problem-solving strategies (e.g., drawing diagrams, making tables, working backwards).
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FF.05. Formulate and solve mathematical models for real-world scenarios.
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FF.06. Check the reasonableness of solutions and interpret them in the context of the problem.
GG. Probability
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GG.01. Calculate theoretical probability of simple events.
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GG.02. Determine experimental probability based on observed data.
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GG.03. Calculate the number of outcomes for compound events using tree diagrams or the counting principle.
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GG.04. Identify independent and dependent events.
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GG.05. Calculate the probability of independent and dependent events.
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GG.06. Calculate geometric probability.
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GG.07. Understand and apply factorials.
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GG.08. Apply the counting principle to solve combinatorial problems.
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GG.09. Design and conduct simulations to estimate probabilities.
HH. Statistics
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HH.01. Calculate the mean, median, mode, and range of a data set.
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HH.02. Calculate quartiles and interquartile range (IQR) of a data set.
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HH.03. Identify biased samples in statistical studies.
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HH.04. Calculate the mean absolute deviation (MAD) of a data set.
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HH.05. Calculate the variance and standard deviation of a data set.
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HH.06. Apply statistical measures to compare and contrast different data sets.
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HH.07. Discuss the limitations of statistical analysis and the potential for misinterpretation.
II. Data and Graphs
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II.01. Interpret information presented in histograms.
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II.02. Create histograms from given data.
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II.03. Interpret information presented in stem-and-leaf plots.
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II.04. Interpret information presented in box-and-whisker plots.
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II.05. Interpret a scatter plot to identify relationships between two variables.
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II.06. Draw a line of best fit on a scatter plot and determine its equation.
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II.07. Analyze and interpret data presented in various graphical formats to draw conclusions and make predictions.
