NS: The Number System

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

NS.A.B.1: Basic students identify numbers as being rational or irrational;

Rational Numbers, Opposites, and Absolute Values

EE: Expressions and Equations

EE.B: Work with radicals and integer exponents.

EE.B.A.1: Advanced students apply the properties of integer exponents with integers involving multiple negative exponents;

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

EE.B.P.3: Proficient students evaluate square roots of perfect squares up to 144 and cube roots of perfect cubes up to 1,000;

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

EE.B.B.3: Basic students express numbers in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

EE.B.P.4: Proficient students compare or multiply/divide two numbers in scientific notation;

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

EE.B.A.3: Advanced students compare or apply the four operations (+, -, x, and ÷) between two or more numbers in scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

EE.B.P.5: Proficient students choose units of appropriate size for measurements of very large or very small quantities in scientific notation.

Unit Conversions

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

EE.C.B.1: Basic students graph proportional relationships from a table of values;

Direct and Inverse Variation
Proportions and Common Multipliers

EE.C.P.1: Proficient students graph proportional relationships from the equation y = mx;

Points, Lines, and Equations

EE.C.A.2: Advanced students explain why the slope (m) is equivalent between any two different points located on any non-vertical line in the coordinate plane;

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

EE.C.P.3: Proficient students derive the equation y = mx with slope (m) from a table or graph and derive the equation y = mx + b with slope (m) and y-intercept (b) from a table or graph.

Point-Slope Form of a Line
Slope-Intercept Form of a Line

EE.C.A.3: Advanced students derive the equation y = mx + b with slope (m) and y-intercept (b) from a verbal description.

Slope-Intercept Form of a Line

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

EE.D.A.1: Advanced students solve linear equations in one variable with rational number coefficients and constants that require multi-steps and identify the solution of a linear equation in one variable as infinitely many solutions or no solutions;

Solving Algebraic Equations II

EE.D.B.2: Basic students identify the solution to a system of two linear equations from 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)

EE.D.P.2: Proficient students solve systems of two linear equations in two variables algebraically or graphically.

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

EE.D.B.3: Advanced students construct and solve systems of two linear equations which represent real-world or mathematical problems.

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

F: Functions

F.E: Define, evaluate, and compare functions.

F.E.P.2: Proficient students identify if a table of values or a graph in the coordinate plane represent a function;

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
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

F.E.P.3: Proficient students compare the properties of two linear functions represented in different ways;

Function Machines 1 (Functions and Tables)

F.E.B.3: Basic students identify linear and non-linear functions represented by graphs.

Compound Interest
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

F.E.P.4: Proficient students identify linear and non-linear functions represented by equations and tables.

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

F.E.A.3: Advanced students identify linear and non-linear functions represented by verbal descriptions.

Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

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

F.F.B.1: Basic students construct a graph to model a real-world linear relationship between two quantities;

Arithmetic Sequences
Compound Interest
Linear Functions
Slope-Intercept Form of a Line

F.F.P.1: Proficient students create an equation to represent a function which models a real-world linear relationship between two quantities;

Compound Interest
Linear Functions
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side

F.F.A.1: Advanced students use the graph and equation representing a function to analyze the relationship between two quantities;

Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

F.F.B.2: Basic students determine the rate of change and initial value of a function from a graph;

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Slope

F.F.P.2: Proficient students determine the rate of change and initial value of a function from a table;

Cat and Mouse (Modeling with Linear Systems)
Function Machines 3 (Functions and Problem Solving)
Slope

F.F.A.2: Advanced students determine the rate of change and initial value of a function from a verbal description;

Cat and Mouse (Modeling with Linear Systems)

F.F.B.3: Basic students interpret the rate of change and initial value of a real-world linear function in terms of its graph;

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

F.F.P.3: Proficient students interpret the rate of change and initial value of a real-world linear function in terms of its graph or table of values;

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

F.F.A.3: Advanced students interpret the rate of change and initial value of a real-world linear function in terms of a verbal description;

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

F.F.B.4: Basic students identify graphs of functional relationships as being linear or non-linear.

Absolute Value with Linear Functions
Exponential Functions
Linear Functions

F.F.P.4: Proficient students identify and describe the qualitative features from analyzing a linear function.

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

F.F.A.4: Advanced students identify and describe the qualitative features from analyzing a non-linear function.

Absolute Value with Linear Functions
Linear Functions

G: Geometry

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

G.G.B.1: Basic students identify the transformations (rotation, reflection, and translation) of figures;

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

G.G.P.1: Proficient students describe the effects on lines, line segments, and angles of figures when rotations, reflections, and translations are performed;

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

G.G.P.2: Proficient students describe the properties of congruency between two figures when at most two transformations are performed;

Rock Art (Transformations)

G.G.A.1: Advanced students describe the properties of congruency between two figures when three or more transformations are performed;

Rock Art (Transformations)

G.G.B.2: Basic students translation is performed on the coordinate plane;

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

G.G.P.3: Proficient students identify coordinates when a sequence of rotations, reflections, translations, or dilations are performed in the coordinate plane;

Rock Art (Transformations)

G.G.A.2: Advanced students explain the sequence of rotations, reflections, translations, and dilations performed on the pre-image to determine the image;

Rock Art (Transformations)

G.G.B.3: Basic students identify similarity from a sequence of transformations;

Rock Art (Transformations)

G.G.P.4: Proficient students describe the properties of similarity between two figures when transformations are performed;

Circles
Dilations
Rock Art (Transformations)

G.G.A.3: Advanced students describe the property of similarity with triangles when identifying and establishing the Angle-Angle (AA) criterion for the triangles.

Similar Figures

G.G.B.4: Basic students determine the interior angle measure(s) of a triangle;

Polygon Angle Sum
Triangle Angle Sum

G.G.P.5: Proficient students determine the interior and exterior angle measures of a triangle;

Polygon Angle Sum
Triangle Angle Sum

G.G.B.5: Basic students identify the types of angles created when parallel lines are cut by a transversal.

Triangle Angle Sum

G.H: Understand and apply the Pythagorean theorem.

G.H.B.1: Basic students apply the Pythagorean Theorem in mathematical problems by setting up the equation a² + b² = c².

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

G.H.P.1: Proficient students calculate the unknown side lengths in right triangles in real-world and mathematical problems;

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

G.H.A.1: Advanced students explain and identify the proofs of the Pythagorean Theorem and the converse of the Pythagorean Theorem;

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

G.H.P.2: Proficient students calculate the distance between two points on a grid by applying the Pythagorean Theorem.

Distance Formula

G.H.A.2: Advanced students calculate the distance between two points by applying the distance formula.

Distance Formula

G.I: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

G.I.B.1: Basic students identify the formulas for the volumes of cones, cylinders, and spheres.

Prisms and Cylinders
Pyramids and Cones

G.I.P.1: Proficient students calculate the volumes of a cone, cylinder, or sphere as a decimal value or in terms of pi.

Prisms and Cylinders
Pyramids and Cones

G.I.A.1: Advanced students solve for a component part (radius or height) given the volume of a cone, cylinder, or sphere and determine the volume of a composite figure containing two to more cones, cylinders, or spheres.

Prisms and Cylinders
Pyramids and Cones

SP: Statistics and Probability

SP.J: Investigate patterns of association in bivariate data.

SP.J.B.1: Basic students identify the pattern of association in scatter plots as a positive association, negative association, or no association;

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

SP.J.P.1: Proficient students identify the pattern of association as a positive association, negative association, or no association given data in a table and describe characteristics of scatter plots such as clustering, outliers, and linear versus non-linear association;

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

SP.J.A.1: Advanced students identify the pattern of association given a verbal description as a positive association, negative association, or no association;

Correlation

SP.J.P.2: Proficient students identify a line of best fit for scatter plots;

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

SP.J.A.2: Advanced students graph a curve of best fit for scatter plots;

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

SP.J.B.2: Basic students use the equation of a linear model in the context of data to identify slope and intercepts;

Cat and Mouse (Modeling with Linear Systems)
Correlation
Linear Functions
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Solving Using Trend Lines
Trends in Scatter Plots

SP.J.P.3: Proficient students use the equation of a linear model in the context of data to interpret the meaning of the slope and intercepts;

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

SP.J.A.3: Advanced students use the data in a scatter plot to create an equation of a line of best fit;

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