1: The Number System

1.1: Explore the real number system and its appropriate usage in real-world situations.

1.1.2: Understand that all real numbers have a decimal expansion.

Comparing and Ordering Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals

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

Circumference and Area of Circles

1.3: 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

2: Functions

2.1: Explore the concept of functions.

2.1.1: 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

2.1.3: 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

2.1.4: 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

2.1.5: 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 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Radical Functions

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

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

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

2.3.2: Recognize that the graph of a linear function has a constant rate of change.

Compound Interest
Direct and Inverse Variation
Slope-Intercept Form of a Line

2.3.3: Provide examples of nonlinear functions.

Absolute Value with Linear Functions
Linear Functions

2.4: Apply the concepts of linear functions to real-world and mathematical situations.

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

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Points, Lines, and Equations
Roots of a Quadratic
Slope-Intercept Form of a Line

2.4.2: 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
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Exponential Functions
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

2.4.3: Construct a function in slope-intercept form that models a linear relationship between two quantities.

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

2.4.4: Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
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

2.4.5: Explore the relationship between linear functions and arithmetic sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences

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

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

Absolute Value with Linear Functions
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

2.5.2: Sketch the graph of a function from a verbal description.

Function Machines 3 (Functions and Problem Solving)

2.5.3: 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

3: Expressions, Equations, and Inequalities

3.1: 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

3.2: Investigate concepts of square and cube roots.

3.2.2: Evaluate square roots of perfect squares.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

3.2.4: Recognize that square roots of non-perfect squares are irrational.

Simplifying Radical Expressions

3.3: Explore the relationship between quantities in decimal and scientific notation.

3.3.1: 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.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

3.3.2: Translate between decimal notation and scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

3.3.3: Estimate and compare the relative size of two quantities in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

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

3.4.1: 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

3.4.2: Select appropriate units of measure when representing answers in scientific notation.

Unit Conversions

3.4.3: Translate how different technological devices display numbers in scientific notation.

Unit Conversions

3.5: Apply concepts of proportional relationships to real-world and mathematical situations.

3.5.1: Graph proportional relationships.

Direct and Inverse Variation

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

3.6.1: 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
Slope-Intercept Form of a Line

3.6.2: 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

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

3.7.1: 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.

Solving Algebraic Equations II

3.7.2: 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

3.7.3: Generate linear equations with the three types of solutions.

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

3.7.4: Justify why linear equations have a specific type of solution.

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

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

3.8.1: 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)

3.8.2: 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)

3.8.3: Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.

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

3.8.4: 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)

4: Geometry and Measurement

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

4.1.1: Verify that lines are mapped to lines, including parallel lines.

Circles
Rock Art (Transformations)

4.1.2: Verify that corresponding angles are congruent.

Similar Figures

4.1.3: Verify that corresponding line segments are congruent.

Rotations, Reflections, and Translations
Translations

4.2: Apply the properties of rigid transformations (rotations, reflections, translations).

4.2.1: Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

Dilations
Rotations, Reflections, and Translations

4.2.2: Reflect geometric figures with respect to the x - axis and/or y - axis.

Rotations, Reflections, and Translations

4.2.3: Translate geometric figures vertically and/or horizontally.

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

4.2.4: 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.

Rock Art (Transformations)

4.2.5: Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

Rock Art (Transformations)

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

4.3.1: Use coordinate geometry to describe the effect of transformations on two-dimensional figures.

Dilations
Rotations, Reflections, and Translations
Translations

4.3.2: Relate scale drawings to dilations of geometric figures.

Dilations

4.4: Apply the properties of transformations (rotations, reflections, translations, dilations).

4.4.2: 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

4.4.3: Given two similar figures, describe the series of transformations that justifies this similarity.

Circles
Dilations
Rock Art (Transformations)
Similar Figures

4.4.4: Use proportional reasoning to find the missing side lengths of two similar figures.

Beam to Moon (Ratios and Proportions)

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

4.5.1: Discover that the sum of the three angles in a triangle is 180 degrees.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

4.5.2: Discover and use the relationship between interior and exterior angles of a triangle.

Triangle Angle Sum

4.5.3: Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

Constructing Congruent Segments and Angles
Triangle Angle Sum

4.5.4: Recognize that two similar figures have congruent corresponding angles.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

4.6: Use models to demonstrate a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

4.7: 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

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

Circles
Distance Formula
Parabolas

4.9: 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

5: Data Analysis, Statistics, and Probability

5.1: Investigate bivariate data.

5.1.1: Collect bivariate data.

Describing Data Using Statistics

5.1.2: Graph the bivariate data on a scatter plot.

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

5.1.3: 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

5.2: 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

5.3: Apply concepts of an approximate line of best fit in real-world situations.

5.3.1: 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

5.3.2: Interpret the slope and intercept.

Solving Using Trend Lines
Trends in Scatter Plots

5.3.3: Solve problems using the equation.

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

5.4: Investigate bivariate categorical data in two-way tables.

5.4.1: Organize bivariate categorical data in a two-way table.

Histograms

5.4.2: Interpret data in two-way tables using relative frequencies.

Histograms

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

5.5.3: Add and subtract matrices of the same size.

Translations