8.NS: The Number System

1.1: Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1.ii: Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (such as piĀ²).

Circumference and Area of Circles

8.EE: Expressions and Equations

2.1: Work with radicals and integer exponents.

8.EE.1: Develop, know and apply the properties of integer exponents to generate equivalent numeric and algebraic expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

8.EE.2.ii: Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EE.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EE.4.i: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EE.4.ii: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (such as use millimeters per year for seafloor spreading).

Unit Conversions

8.EE.4.iii: Interpret scientific notation that has been generated by technology.

Unit Conversions

2.2: Understand the connections between proportional relationships, lines, and linear equations.

8.EE.5.i: Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Direct and Inverse Variation

8.EE.6.ii: 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.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

2.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7: Solve linear equations in one variable.

8.EE.7.a.i: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

8.EE.7.a.ii: Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

8.EE.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side

8.EE.8: Analyze and solve pairs of simultaneous linear equations.

8.EE.8.a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

8.EE.8.c: Solve real world and mathematical problems leading to two linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

8.F: Functions

3.1: Define, evaluate, and compare functions.

8.F.1.i: Understand that a function is a rule that assigns to each input exactly one output.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

8.F.1.ii: Understand that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, and/or by verbal descriptions).

Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

8.F.3.i: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8.F.3.ii: Give examples of functions that are not linear.

Absolute Value with Linear Functions
Linear Functions

3.2: Use functions to model relationships between quantities.

8.F.4.i: Construct a function to model a linear relationship between two quantities.

Arithmetic Sequences
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

8.F.4.ii: Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.

Function Machines 1 (Functions and Tables)
Translating and Scaling Functions

8.F.4.iii: Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Point-Slope Form of a Line
Slope-Intercept Form of a Line

8.F.5.i: Describe qualitatively the functional relationship between two quantities by analyzing a graph (may include where the function is increasing or decreasing, linear or nonlinear, etc.).

Graphs of Polynomial Functions
Translating and Scaling Functions

8.F.5.ii: Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Arithmetic Sequences
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

8.G: Geometry

4.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.1: Understand the properties of rotations, reflections, and translations by experimentation:

8.G.1.a: Lines are transformed onto lines, and line segments onto line segments of the same length.

Circles
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.1.b: Angles are transformed onto angles of the same measure.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.1.c: Parallel lines are transformed onto parallel lines.

Reflections
Rotations, Reflections, and Translations
Similar Figures

8.G.2.i: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.

Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

8.G.2.ii: Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

8.G.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

8.G.4.i: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

Dilations
Similar Figures

8.G.4.ii: Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

Dilations
Similar Figures

8.G.5: Use informal arguments to establish facts about:

8.G.5.a: the angle sum and exterior angles of triangles.

Polygon Angle Sum
Triangle Angle Sum

8.G.5.b: the angles created when parallel lines are cut by a transversal.

Triangle Angle Sum

8.G.5.c: the angle-angle criterion for similarity of triangles.

Similar Figures
Similarity in Right Triangles

4.2: Understand and apply the Pythagorean Theorem.

8.G.6: Explain a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Circles
Distance Formula

4.3: Solve real world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9.i: Know the formulas for the volume of cones, cylinders and spheres.

Prisms and Cylinders
Pyramids and Cones

8.G.9.ii: Use the formulas to solve real world and mathematical problems.

Prisms and Cylinders
Pyramids and Cones

8.SP: Statistics and Probability

5.1: Investigate patterns of association in bivariate data.

8.SP.1.i: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

8.SP.1.ii: Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

8.SP.2.i: Know that straight lines are widely used to model relationships between two quantitative variables.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

8.SP.2.ii: For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept(s).

Correlation

8.SP.4.ii: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

Histograms

Correlation last revised: 9/24/2019

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