8.NS: The Number System

8.NS.1: Explore the real number system and its appropriate usage in real-world situations.

8.NS.1.a: Recognize the differences between rational and irrational numbers.

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

8.NS.1.b: Understand that all real numbers have a decimal expansion.

Comparing and Ordering Decimals
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Sums and Differences with Decimals

8.NS.2: Estimate and compare the value of irrational numbers by plotting them on a number line.

Circumference and Area of Circles
Square Roots

8.NS.3: Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.

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

8.F: Functions

8.F.1: Explore the concept of functions.

8.F.1.a: Understand that a function 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.c: Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.

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

8.F.1.d: Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.

Introduction to Functions
Linear Functions
Points, Lines, and Equations

8.F.1.e: Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

Absolute Value with Linear Functions
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
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Radical Functions

8.F.2: Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.

Function Machines 2 (Functions, Tables, and Graphs)
Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

8.F.3: Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8.F.3.a: Define an equation in slope-intercept form (y = mx + b) as being a linear function.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8.F.3.b: Recognize that the graph of a linear function has a constant rate of change.

Absolute Value with Linear Functions
Compound Interest
Direct and Inverse Variation
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8.F.3.c: Provide examples of nonlinear functions.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

8.F.4: Apply the concepts of linear functions to real-world and mathematical situations.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Translating and Scaling Functions

8.F.4.a: Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions

8.F.4.b: Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.

Absolute Value with Linear Functions
Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions

8.F.4.c: Construct a function in slope-intercept form that models a linear relationship between two quantities.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Translating and Scaling Functions

8.F.4.d: Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Translating and Scaling Functions

8.F.4.e: Explore the relationship between linear functions and arithmetic sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences

8.F.5: Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.

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

8.F.5.a: Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).

Absolute Value with Linear Functions
Arithmetic Sequences
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

8.F.5.b: Sketch the graph of a function from a verbal description.

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

8.F.5.c: Write a verbal description from the graph of a function with and without scales.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Improper Fractions and Mixed Numbers
Introduction to Exponential Functions
Multiplying with Decimals
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations
Using Algebraic Expressions

8.EEI: Expressions, Equations, and Inequalities

8.EEI.1: Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.

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

8.EEI.2: Investigate concepts of square and cube roots.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EEI.2.a: Find the exact and approximate solutions to equations of the form x² = p and x³ = p where p is a positive rational number.

Operations with Radical Expressions
Roots of a Quadratic
Simplifying Radical Expressions
Square Roots

8.EEI.2.b: Evaluate square roots of perfect squares.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EEI.2.d: Recognize that square roots of non-perfect squares are irrational.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EEI.3: Explore the relationship between quantities in decimal and scientific notation.

Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.3.a: Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ≤ a < 10 and b is an integer.

Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.3.b: Translate between decimal notation and scientific notation.

Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.3.c: Estimate and compare the relative size of two quantities in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.4: Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.4.a: Multiply and divide numbers expressed in both decimal and scientific notation.

Multiplying with Decimals
Square Roots
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.4.b: Select appropriate units of measure when representing answers in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.4.c: Translate how different technological devices display numbers in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EEI.5: Apply concepts of proportional relationships to real-world and mathematical situations.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

8.EEI.5.a: Graph proportional relationships.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

8.EEI.5.b: Interpret unit rate as the slope of the graph.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

8.EEI.5.c: Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

8.EEI.6: Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships.

8.EEI.6.a: Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
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

8.EEI.6.b: Derive the slope-intercept form (y = mx + b) for a non-vertical line.

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

8.EEI.6.c: Relate equations for proportional relationships (y = kx) with the slope-intercept form (y = mx + b) where b = 0.

Direct and Inverse Variation

8.EEI.7: Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.

8.EEI.7.a: Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

8.EEI.7.b: Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b).

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

8.EEI.7.c: Generate linear equations with the three types of solutions.

Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

8.EEI.7.d: Justify why linear equations have a specific type of solution.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

8.EEI.8: Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.

8.EEI.8.a: Graph systems of linear equations and estimate their point of intersection.

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.EEI.8.b: Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.

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.EEI.8.c: Solve systems of linear equations algebraically, including methods of substitution and elimination, or through 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.EEI.8.d: Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

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.GM: Geometry and Measurement

8.GM.1: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).

8.GM.1.a: Verify that lines are mapped to lines, including parallel lines.

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

8.GM.1.b: Verify that corresponding angles are congruent.

Congruence in Right Triangles
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.GM.1.c: Verify that corresponding line segments are congruent.

Rotations, Reflections, and Translations
Translations

8.GM.2: Apply the properties of rigid transformations (rotations, reflections, translations).

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

8.GM.2.a: Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

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

8.GM.2.b: Reflect geometric figures with respect to the x - axis and/or y - axis.

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

8.GM.2.c: Translate geometric figures vertically and/or horizontally.

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

8.GM.2.d: Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.

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

8.GM.2.e: Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

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

8.GM.3: Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).

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

8.GM.3.a: Use coordinate geometry to describe the effect of transformations on two-dimensional figures.

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

8.GM.3.b: Relate scale drawings to dilations of geometric figures.

Dilations

8.GM.4: Apply the properties of transformations (rotations, reflections, translations, dilations).

Dilations
Similar Figures

8.GM.4.a: Dilate geometric figures using scale factors that are positive rational numbers.

Dilations
Similar Figures

8.GM.4.b: Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.

Circles
Dilations
Rock Art (Transformations)
Similar Figures

8.GM.4.c: Given two similar figures, describe the series of transformations that justifies this similarity.

Circles
Dilations
Rock Art (Transformations)
Similar Figures

8.GM.4.d: Use proportional reasoning to find the missing side lengths of two similar figures.

Beam to Moon (Ratios and Proportions)

8.GM.5: Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

8.GM.5.a: Discover that the sum of the three angles in a triangle is 180 degrees.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

8.GM.5.b: Discover and use the relationship between interior and exterior angles of a triangle.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

8.GM.5.c: Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

8.GM.5.d: Recognize that two similar figures have congruent corresponding angles.

Congruence in Right Triangles
Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

8.GM.6: Use models to demonstrate a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

8.GM.7: Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.

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

8.GM.8: Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.

Circles
Distance Formula
Pythagorean Theorem

8.GM.9: Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders

8.DSP: Data Analysis, Statistics, and Probability

8.DSP.1: Investigate bivariate data.

8.DSP.1.a: Collect bivariate data.

Describing Data Using Statistics

8.DSP.1.b: Graph the bivariate data on a scatter plot.

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

8.DSP.1.c: Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).

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

8.DSP.2: Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.

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

8.DSP.3: Apply concepts of an approximate line of best fit in real-world situations.

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

8.DSP.3.a: Find an approximate equation for the line of best fit using two appropriate data points.

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

8.DSP.3.b: Interpret the slope and intercept.

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

8.DSP.3.c: Solve problems using the equation.

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

8.DSP.4: Investigate bivariate categorical data in two-way tables.

Histograms

8.DSP.4.a: Organize bivariate categorical data in a two-way table.

Histograms

8.DSP.4.b: Interpret data in two-way tables using relative frequencies.

Histograms

8.DSP.4.c: Explore patterns of possible association between the two categorical variables.

Correlation
Histograms

8.DSP.5: Organize data in matrices with rational numbers and apply to real-world and mathematical situations.

8.DSP.5.c: Add and subtract matrices of the same size.

Translations