NS: Number Sense and Operations

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

NS.A.1: Explore the real number system.

NS.A.1.a: Know the differences between rational and irrational numbers.

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

NS.A.1.b: Understand that all rational numbers have a decimal expansion that terminates or repeats.

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

NS.A.1.c: Convert decimals which repeat into fractions and fractions into repeating decimals.

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

NS.A.1.d: Generate equivalent representations of rational numbers.

Dividing Mixed Numbers
Improper Fractions and Mixed Numbers
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values

NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.

Circumference and Area of Circles
Square Roots

EEI: Expressions, Equations and Inequalities

EEI.A: Work with radicals and integer exponents.

EEI.A.1: Know and apply the properties of integer exponents to generate equivalent expressions.

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

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

EEI.A.2.a: Solve equations of the form x² = p and x³ = p, where p is a positive rational number.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

EEI.A.2.b: Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 1000.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

EEI.A.2.c: Recognize that square roots of non-perfect squares are irrational.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

EEI.A.3: Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.

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

EEI.A.4: Use scientific notation to solve problems.

EEI.A.4.a: 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

EEI.A.4.b: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

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

EEI.B.1: Graph proportional relationships.

EEI.B.1.a: Interpret the unit rate as the slope of the graph.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Distance-Time and Velocity-Time Graphs

EEI.B.1.b: Compare two different proportional relationships.

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

EEI.B.2: Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.

EEI.B.2.a: Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.

Cat and Mouse (Modeling with Linear Systems)
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

EEI.B.2.b: 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

EEI.C: Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations.

EEI.C.1: Solve linear equations and inequalities in one variable.

EEI.C.1.a: Create and identify linear equations with one solution, infinitely many solutions or no solutions.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Solving Two-Step Equations

EEI.C.1.b: Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

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

EEI.C.2: Analyze and solve systems of linear equations.

EEI.C.2.a: Graph systems of linear equations and recognize the intersection as the solution to the system.

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)

EEI.C.2.b: Explain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs.

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)

EEI.C.2.c: Explain why systems of linear equations can have one solution, no solution or infinitely many solutions.

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)

EEI.C.2.d: Solve systems of two linear equations.

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)

GM: Geometry and Measurement

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

GM.A.1: Verify experimentally the congruence properties of rigid transformations.

GM.A.1.a: Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations.

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

GM.A.1.b: Investigate if orientation is preserved under rigid transformations.

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

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

GM.A.2.a: Describe a possible sequence of rigid transformations between two congruent figures.

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

GM.A.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

GM.A.4: Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.

GM.A.4.a: Describe a possible sequence of transformations between two similar figures.

Dilations
Similar Figures

GM.A.5: Explore angle relationships and establish informal arguments.

GM.A.5.a: Derive the sum of the interior angles of a triangle.

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

GM.A.5.b: Explore the relationship between the 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

GM.A.5.c: Construct and explore the angles created when 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

GM.A.5.d: Use the properties of similar figures to solve problems.

Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

GM.B: Understand and apply the Pythagorean Theorem.

GM.B.1: Use models to demonstrate a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

GM.B.2: Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts.

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

GM.B.3: Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system.

Circles
Distance Formula
Pythagorean Theorem

GM.C: Solve problems involving volume of cones, pyramids and spheres.

GM.C.1: Solve problems involving surface area and volume.

GM.C.1.a: Understand the concept of surface area and find surface area of pyramids.

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

GM.C.1.b: Understand the concepts of volume and find the volume of pyramids, cones and spheres.

Prisms and Cylinders
Pyramids and Cones

DSP: Data Analysis, Statistics and Probability

DSP.A: Investigate patterns of association in bivariate data.

DSP.A.1: Construct and interpret scatter plots of 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

DSP.A.2: Generate and use a trend line for bivariate data, and informally assess the fit of the line.

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

DSP.A.3: Interpret the parameters of a linear model of bivariate measurement data to solve problems.

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

DSP.A.4: Understand the patterns of association in bivariate categorical data displayed in a two-way table.

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

Histograms

DSP.A.4.b: Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Histograms

F: Functions

F.A: Define, evaluate and compare functions.

F.A.1: Explore the concept of functions. (The use of function notation is not required.)

F.A.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

F.A.1.b: Determine if a relation is a function.

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

F.A.1.c: Graph a 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
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Standard Form of a Line

F.A.2: Compare characteristics of two functions each represented in a different way.

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

F.A.3: Investigate the differences between linear and nonlinear functions.

F.A.3.a: Interpret the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the y-intercept (b).

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

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

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

F.A.3.c: Give 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

F.B: Use functions to model relationships between quantities.

F.B.1: Use functions to model linear relationships between quantities.

F.B.1.a: Explain the parameters of a linear function based on the context of a problem.

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

F.B.1.b: Determine the parameters of a linear function.

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

F.B.1.c: Determine the x-intercept of a linear function.

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

F.B.2: Describe the functional relationship between two quantities from a graph or a verbal description.

Absolute Value with Linear Functions
Arithmetic Sequences
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions