1: Number Sense, Properties, and Operations

1.1: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

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.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

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.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.

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.

1.1.h.i: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Unit Conversions

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

Unit Conversions

2: Patterns, Functions, and Algebraic Structures

2.1: Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

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.

Direct and Inverse Variation

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: Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

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 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 II
Solving Equations by Graphing Each Side

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: Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions

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 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).

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.

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

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.

Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

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.

Cat and Mouse (Modeling with Linear Systems)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
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)
Points, Lines, and Equations

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

Function Machines 3 (Functions and Problem Solving)

2.3.b.v: Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Function Machines 3 (Functions and Problem Solving)

3: Data Analysis, Statistics, and Probability

3.1: Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

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

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

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.

Histograms

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

Histograms

4: Shape, Dimension, and Geometric Relationships

4.1: Apply transformation to numbers, shapes, functional representations, and data

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.

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.

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.

Dilations
Similar Figures

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

Dilations
Similar Figures

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.

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

4.2: Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions

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

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: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.