Grade Level and High School Content Expectations

N.ME.08.01: Understand the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to the volume of a cube.

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

N.ME.08.02: Understand meanings for zero and negative integer exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

N.ME.08.03: Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g., 0.1 repeating = 1/9; 0.3 repeating = 1/3.

Adding on the Number Line

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

N.ME.08.04: Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, e.g., square root of 2, square root of 3, pi, on the number line.

Circumference and Area of Circles

N.FL.08.05: Estimate and solve problems with square roots and cube roots using calculators.

N.FL.08.06: Find square roots of perfect squares and approximate the square roots of non-perfect squares by locating between consecutive integers, e.g., square root of 130 is between 11 and 12.

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

N.MR.08.08: Solve problems involving percent increases and decreases.

N.FL.08.09: Solve problems involving compounded interest or multiple discounts.

Compound Interest

Percent of Change

N.MR.08.10: Calculate weighted averages such as course grades, consumer price indices, and sports ratings.

Mean, Median, and Mode

Populations and Samples

N.FL.08.11: Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

A.RP.08.01: Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax³); roots (y = the square root of x); and exponentials (y = a to the x power, a > 0); using tables, graphs, and equations.

Absolute Value with Linear Functions

Addition and Subtraction of Functions

Arithmetic Sequences

Compound Interest

Direct and Inverse Variation

Exponential Functions

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Exponential Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

Roots of a Quadratic

Slope-Intercept Form of a Line

Translating and Scaling Functions

A.PA.08.02: For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.

Compound Interest

Direct and Inverse Variation

Translating and Scaling Functions

A.PA.08.03: Recognize basic functions in problem context, e.g., area of a circle is pi r², volume of a sphere is 4/3pi r³, and represent them using tables, graphs, and formulas.

Exponential Functions

Introduction to Exponential Functions

A.RP.08.04: Use the vertical line test to determine if a graph represents a function in one variable.

A.RP.08.05: Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function.

Quadratics in Factored Form

Quadratics in Polynomial Form

A.RP.08.06: Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x² – 36, y = (x – 2)² – 9; y = – x²; y = – (x – 3)².

Quadratics in Factored Form

Quadratics in Polynomial Form

A.FO.08.08: Factor simple quadratic expressions with integer coefficients, e.g., x² + 6x + 9, x² + 2x – 3, and x² – 4; solve simple quadratic equations, e.g., x² = 16 or x² = 5 (by taking square roots); x² – x – 6 = 0, x² – 2x = 15 (by factoring); verify solutions by evaluation.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

A.FO.08.11: Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.

Solving Equations by Graphing Each Side

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

A.FO.08.12: Solve linear inequalities in one and two variables, and graph the solution sets.

Compound Inequalities

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

A.FO.08.13: Set up and solve applied problems involving simultaneous linear equations and linear inequalities.

Estimating Population Size

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

G.GS.08.01: Understand at least one proof of the Pythagorean Theorem; use the Pythagorean Theorem and its converse to solve applied problems including perimeter, area, and volume problems.

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Surface and Lateral Areas of Pyramids and Cones

G.LO.08.02: Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem.

G.SR.08.03: Understand the definition of a circle; know and use the formulas for circumference and area of a circle to solve problems.

G.SR.08.04: Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals, triangles, circles).

G.SR.08.05: Solve applied problems involving areas of triangles, quadrilaterals, and circles.

Area of Parallelograms

Perimeter and Area of Rectangles

G.SR.08.06: Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and pyramids (1/3 (area of base) x height), and spheres (4/3 pi (radius)³) and apply them to solve problems. G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and cylinders.

Prisms and Cylinders

Pyramids and Cones

G.SR.08.07: Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and cylinders.

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.SR.08.08: Sketch a variety of two-dimensional representations of three-dimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets; use such two-dimensional representations to help solve problems.

3D and Orthographic Views

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

G.TR.08.09: Understand the definition of a dilation from a point in the plane, and relate it to the definition of similar polygons.

G.TR.08.10: Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems.

D.AN.08.01: Determine which measure of central tendency (mean, median, mode) best represents a data set, e.g., salaries, home prices, for answering certain questions; justify the choice made.

Movie Reviewer (Mean and Median)

D.PR.08.04: Apply the Basic Counting Principle to find total number of outcomes possible for independent and dependent events, and calculate the probabilities using organized lists or tree diagrams.

D.PR.08.05: Find and/or compare the theoretical probability, the experimental probability, and/or the relative frequency of a given event.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

D.PR.08.06: Understand the difference between independent and dependent events, and recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll.

Independent and Dependent Events

Theoretical and Experimental Probability

Correlation last revised: 5/17/2018