All Lessons

L.9-10.5.A Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.

L.11-12.4.A Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word's position or function in a sentence) as a clue to the meaning of a word or phrase.

L.11-12.4.B Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable).

(A) Simplify numerical radical expressions involving square roots

(G) Rewrite radical expressions that contain variables to equivalent forms

(Y10A) Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)

HSN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = (5^(1/3))^3 to hold, so (5^(1/3))^3 must equal 5.

HSN.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

(Y7) Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

HSN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = (5^(1/3))^3 to hold, so (5^(1/3))^3 must equal 5.

(D) Graph the solution set of linear inequalities in two variables on the coordinate plane

(Y10) Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology (ACMNA237)

HSA.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

(C) Model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

(Y8) Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

HSA.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.