All Lessons

(C) Represent integer operations with concrete models and connect the actions with the models to standardized algorithms

(D) Add, subtract, multiply, and divide integers fluently

(Y7) Compare, order, add and subtract integers (ACMNA280)

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.1.D Apply properties of operations as strategies to add and subtract rational numbers.

(D) Add, subtract, multiply, and divide integers fluently

(Y8) Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.2.A Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.2.B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2.C Apply properties of operations as strategies to multiply and divide rational numbers.

(D) Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods

HSN.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

(B) Add, subtract, and multiply polynomials

(Y9) Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

L.2.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies.

L.2.4.A Use sentence-level context as a clue to the meaning of a word or phrase.

HSA.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

(B) Multiply polynomials of degree one and degree two

(Y9) Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

HSA.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

(F) Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

(E) Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

(Y9) Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

HSA.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 - y^2)(x^2 + y^2).

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

(Y10) Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

L.1.2.C Use commas in dates and to separate single words in a series.

HSA.SSE.3.B Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

(B) Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points

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

(Y10) Solve linear inequalities and graph their solutions on a number line (ACMNA236)

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

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.

HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

(E) Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

(Y10) Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

HSA.SSE.3.A Factor a quadratic expression to reveal the zeros of the function it defines.

(D) Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

(B) Add, subtract, and multiply polynomials

(Y9) Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

HSA.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

(F) Solve quadratic and square root equations

(Y10) Solve simple quadratic equations using a range of strategies (ACMNA241)

(Y10A) Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

HSA.REI.4 Solve quadratic equations in one variable.

(H) Graph the solution set of systems of two 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.