Academic Standards

1.1: In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line

1.1.a: Students can: Define irrational numbers.

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

1.1.b: Students can: Demonstrate informally that every number has a decimal expansion.

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

1.1.b.i: For rational numbers show that the decimal expansion repeats eventually.

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

1.1.b.ii: Convert a decimal expansion which repeats eventually into a rational number.

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

1.1.c: Students can: 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.

Circumference and Area of Circles

Square Roots

1.1.d: Students can: Apply the properties of integer exponents to generate equivalent numerical expressions.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

1.1.e: Students can: Use square root and cube root symbols to represent solutions to 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

1.1.f: Students can: Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

1.1.g: Students can: Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Number Systems

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

1.1.h: Students can: 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

1.1.h.i: 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

1.1.h.ii: Interpret scientific notation that has been generated by technology.

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

2.1: Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically

2.1.b: Students can: Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

2.1.c: Students can: Compare two different proportional relationships represented in different ways.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

2.1.d: Students can: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Standard Form of a Line

2.1.e: Students can: 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

2.2: Properties of algebra and equality are used to solve linear equations and systems of equations

2.2.a: Students can: Solve linear equations in one variable.

2.2.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 by Graphing Each Side

Solving Equations on the Number Line

Solving Two-Step Equations

2.2.a.ii: 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 I

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Two-Step Equations

2.2.b: Students can: Analyze and solve pairs of simultaneous linear equations.

2.2.b.i: Explain 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)

2.2.b.ii: 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)

2.2.b.iii: 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)

2.3: Graphs, tables and equations can be used to distinguish between linear and nonlinear functions

2.3.a: Students can: Define, evaluate, and compare functions.

2.3.a.i: Define a function as 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

2.3.a.ii: Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding 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

2.3.a.iii: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Function Machines 2 (Functions, Tables, and Graphs)

Graphs of Polynomial Functions

Linear Functions

Quadratics in Polynomial Form

2.3.a.iv: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.

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

2.3.a.v: Give examples of functions that are not linear.

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

2.3.b: Students can: Use functions to model relationships between quantities.

2.3.b.i: Construct a function to model 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

2.3.b.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.

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)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Polynomial Form

Slope-Intercept Form of a Line

Translating and Scaling Functions

2.3.b.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.

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

2.3.b.iv: Describe qualitatively the functional relationship between two quantities by analyzing a graph.

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

2.3.b.v: 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)

Graphs of Polynomial Functions

Linear Functions

Slope-Intercept Form of a Line

Translating and Scaling Functions

3.1: Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge

3.1.a: Students can: 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

3.1.b: Students can: 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

Trends in Scatter Plots

3.1.c: Students can: 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

3.1.d: Students can: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

3.1.e: Students can: Explain patterns of association seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

3.1.e.i: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

3.1.e.ii: Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

4.1: Transformations of objects can be used to define the concepts of congruence and similarity

4.1.a: Students can: Verify experimentally the properties of rotations, reflections, and translations:

Holiday Snowflake Designer

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Similar Figures

Translations

4.1.b: Students can: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Dilations

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

4.1.c: Students can: Demonstrate 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.

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

4.1.d: Students can: Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

4.1.e: Students can: Demonstrate 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.

4.1.f: Students can: Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

4.1.g: Students can: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

4.2: Direct and indirect measurement can be used to describe and make comparisons

4.2.a: Students can: Explain a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

4.2.b: Students can: 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

4.2.c: Students can: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Circles

Distance Formula

Pythagorean Theorem

4.2.d: Students can: State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Prisms and Cylinders

Pyramids and Cones

Correlation last revised: 9/22/2020