All Lessons

(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.

(G) Apply properties of operations to add and subtract two or three numbers.

(A) Recall basic facts to add and subtract within 20 with automaticity

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

(B) Determine products of a number and 10 or 100 using properties of operations and place value understandings

(Y3) Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

(Y4) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.