All Lessons

8(9)(D) Describe how the author's use of figurative language such as extended metaphor achieves specific purposes.

L.8.4.A Use context (e.g., the overall meaning of a sentence or paragraph; a word's position or function in a sentence) as a clue to the meaning of a word or phrase.

8(2)(B) Use context within or beyond a paragraph to clarify the meaning of unfamiliar or ambiguous words.

8(10)(B)(i) Develop drafts into a focused, structured, and coherent piece of writing by organizing with purposeful structure, including an introduction, transitions, coherence within and across paragraphs, and a conclusion.

8(10)(D)(ii) Edit drafts using standard English conventions, including consistent, appropriate use of verb tenses and active and passive voice.

(C) Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

(A) Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

(Y8) Investigate the concept of irrational numbers, including π (ACMNA186)

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

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

(F) Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

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

8.EE.8.B Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

HSA.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

(A) Generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

(Y7) Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

(A) Simplify numerical radical expressions involving square roots

(Y7) Investigate and use square roots of perfect square numbers (ACMNA150)

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

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) Approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

(Y7) Investigate and use square roots of perfect square numbers (ACMNA150)

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

(A) Represent linear proportional situations with tables, graphs, and equations in the form of y = kx

(B) Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

(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

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.