Chapter 0 Preparing for Algebra

Lesson 0-1: Plan for Problem Solving

CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and to check technological computation.

Lesson 0-2: Real Numbers

CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.

CLE 3102.2.2 Understand properties of and relationships between subsets and elements of the real number system.

CU 3102.2.7 Identify the subsets in the real number system and understand their relationships.

CU 3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line.

SPI 3102.2.3 Describe and/or order a given set of real numbers including both rational and irrational numbers.

Lesson 0-3: Operations with Integers

CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.

CU 3102.2.4 Operate efficiently with both rational and irrational numbers.

Lesson 0-4: Adding and Subtracting Rational Numbers

CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.

CU 3102.2.4 Operate efficiently with both rational and irrational numbers.

Lesson 0-5: Multiplying and Dividing Rational Numbers

CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.

CU 3102.2.4 Operate efficiently with both rational and irrational numbers.

Lesson 0-8: Area

SPI 3102.4.1 Develop and apply strategies to estimate the area of any shape on a plane grid.

Lesson 0-11: Simple Probability and Odds

CU 3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.

Lesson 0-12: Mean, Median, Mode, Range, and Quartiles

CU 3102.5.3 When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range.

CU 3102.5.4 Explore quartiles, deciles, and percentiles of a distribution.

SPI 3102.5.2 Identify the effect on mean, median, mode, and range when values in the data set are changed.

Lesson 0-13: Representing Data

CLE 3102.5.1 Describe and interpret quantitative information.

CU 3102.5.2 Develop a meaning for and identify outliers in a data set and verify.

CU 3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).

CU 3102.5.7 Compare two data sets using graphs and descriptive statistics.

SPI 3102.5.1 Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

Chapter 1 Expressions, Equations, and Functions

Lesson 1-1: Variables and Expressions

CLE 3102.4.1 Use algebraic reasoning in applications involving geometric formulas and contextual problems.

SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation.

Lesson 1-2: Order of Operations

CU 3102.1.15 Apply arithmetic concepts in algebraic contexts.

CU 3102.2.2 Apply the order of operations to simplify and evaluate algebraic expressions.

SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.

Lesson 1-3: Properties of Numbers

CU 3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality).

CU 3102.1.10 Use algebraic properties to develop a valid mathematical argument.

CU 3102.3.3 Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions.

CU 3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume.

SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.

Lesson 1-4: The Distributive Property

CU 3102.1.9 Identify and use properties of the real numbers (including

commutative, associative, distributive, inverse, identity element, closure,

reflexive, symmetric, transitive, operation properties of equality).

CU 3102.1.10 Use algebraic properties to develop a valid mathematical

argument.

CU 3102.1.11 Use manipulatives to model algebraic concepts.

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and

to check technological computation.

CU 3102.2.1 Recognize and use like terms to simplify expressions.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions,

and justify solutions to problems.

Lesson 1-5: Equations

CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem

solving, including testing cases, estimation, and then checking induced errors

and the reasonableness of the solution.

CU 3102.2.2 Apply the order of operations to simplify and evaluate algebraic

expressions.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a

single solution, or all real numbers as solutions.

SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions,

and justify solutions to problems.

Lesson 1-6: Relations

CLE 3102.3.6 Understand and use relations and functions in various

representations to solve contextual problems.

CU 3102.1.12 Create and work flexibly among representations of relations

(including verbal, equations, tables, mappings, graphs).

CU 3102.1.13 Change from one representation of a relation to another

representation, for example, change from a verbal description to a graph.

CU 3102.3.15 Determine domain and range of a relation and articulate

restrictions imposed either by the operations or by the real life situation that

the function represents.

SPI 3102.3.6 Interpret various relations in multiple representations.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a

relation is a function and/or evaluate a function at a specified rational value.

Lesson 1-7: Functions

CLE 3102.3.6 Understand and use relations and functions in various

representations to solve contextual problems.

CU 3102.1.3 Understand and use mathematical symbols, notation, and common

mathematical abbreviations correctly.

CU 3102.1.12 Create and work flexibly among representations of relations

(including verbal, equations, tables, mappings, graphs).

CU 3102.3.16 Determine if a relation is a function from its graph or from a

set of ordered pairs.

CU 3102.3.25 Find function values using f(x) notation or graphs.

CU 3102.5.6 Draw qualitative graphs of functions and describe a general trend

or shape.

SPI 3102.1.1 Interpret patterns found in sequences, tables, and other forms

of quantitative information using variables or function notation.

SPI 3102.1.4 Translate between representations of functions that depict

real-world situations.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a

relation is a function and/or evaluate a function at a specified rational value.

Lesson 1-8: Logical Reasoning and Counterexamples

CLE 3102.1.1 Use mathematical language, symbols, definitions, proofs and

counterexamples correctly and precisely in mathematical reasoning.

CLE 3102.1.3 Develop inductive and deductive reasoning to independently make

and evaluate mathematical arguments and construct appropriate proofs; include

various types of reasoning, logic, and intuition.

CU 3102.1.10 Use algebraic properties to develop a valid mathematical

argument.

Chapter 2 Linear Equations

Lesson 2-1: Writing Equations

CLE 3102.1.5 Recognize and use mathematical ideas and processes that arise in

different settings, with an emphasis on formulating a problem in mathematical

terms, interpreting the solutions, mathematical ideas, and communication of

solution strategies.

CLE 3102.1.6 Employ reading and writing to recognize the major themes of

mathematical processes, the historical development of mathematics, and the

connections between mathematics and the real world.

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CLE 3102.4.1 Use algebraic reasoning in applications involving geometric

formulas and contextual problems.

CU 3102.1.3 Understand and use mathematical symbols, notation, and common

mathematical abbreviations correctly.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson Explore 2-2: Explore: Algebra Lab Solving Equations

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 2-2: Solving One-Step Equations

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.1.9 Identify and use properties of the real numbers (including

commutative, associative, distributive, inverse, identity element, closure,

reflexive, symmetric, transitive, operation properties of equality).

CU 3102.1.15 Apply arithmetic concepts in algebraic contexts.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson Explore 2-3: Explore: Algebra Lab Solving Multi-Step Equations

CU 3102.1.11 Use manipulatives to model algebraic concepts.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 2-3: Solving One-Step Equations

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.3.11 Solve multi-step linear equations with one variable.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 2-4: Solving Equations with the Variable on Each Side

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

CU 3102.3.11 Solve multi-step linear equations with one variable.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a

single solution, or all real numbers as solutions.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 2-5: Solving Equations Involving Absolute Value

CU 3102.3.12 Recognize and articulate when an equation has no solution, a

single solution, or all real numbers as solutions.

CU 3102.3.14 Solve absolute value equations and inequalities (including

compound inequalities) with one variable and graph their solutions on a number

line.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 2-6: Ratios and Proportions

CLE 3102.1.1 Use mathematical language, symbols, definitions, proofs and

counterexamples correctly and precisely in mathematical reasoning.

CLE 3102.1.4 Move flexibly between multiple representations (contextual,

physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic),

to solve problems, to model mathematical ideas, and to communicate solution

strategies.

CU 3102.1.2 Use the terminology of mathematics correctly.

CU 3102.1.5 Use formulas, equations, and inequalities to solve real-world

problems including time/rate/distance, percent increase/decrease,

ratio/proportion, and mixture problems.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

Lesson Extend 2-6: Extend: Spreadsheet Lab Financial Ratios

CLE 3102.1.7 Use technologies appropriately to develop understanding of

abstract mathematical ideas, to facilitate problem solving, and to produce

accurate and reliable models.

CU 3102.1.5 Use formulas, equations, and inequalities to solve real-world

problems including time/rate/distance, percent increase/decrease,

ratio/proportion, and mixture problems.

CU 3102.1.18 Translate syntax of technology to appropriate mathematical

notation.

Lesson 2-7: Percent of Change

CU 3102.1.5 Use formulas, equations, and inequalities to solve real-world

problems including time/rate/distance, percent increase/decrease,

ratio/proportion, and mixture problems.

CU 3102.1.8 Recognize and perform multiple steps in problem solving when

necessary.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

Lesson Extend 2-7: Extend: Algebra Lab Percentiles

CU 3102.5.4 Explore quartiles, deciles, and percentiles of a distribution.

Lesson 2-8: Literal Equations and Dimensional Analysis

CLE 3102.3.5 Manipulate formulas and solve literal equations.

CLE 3102.4.2 Apply appropriate units of measure and convert measures in

problem solving situations.

CU 3102.4.1 Using algebraic expressions solve for measures in geometric

figures as well as for perimeter, area, and volume.

CU 3102.4.5 Use dimensional analysis to convert rates and measurements both

within a system and between systems and check the appropriateness of the

solution.

SPI 3102.4.4 Convert rates and measurements.

Lesson 2-9: Weighted Averages

CLE 3102.1.5 Recognize and use mathematical ideas and processes that arise in

different settings, with an emphasis on formulating a problem in mathematical

terms, interpreting the solutions, mathematical ideas, and communication of

solution strategies.

CU 3102.1.5 Use formulas, equations, and inequalities to solve real-world

problems including time/rate/distance, percent increase/decrease,

ratio/proportion, and mixture problems.

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions,

including real-world problems.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

SPI 3102.4.4 Convert rates and measurements.

Chapter 3 Linear Functions

Lesson Get Started on Chapter 3: Getting Started on Chapter 3

CU 3102.1.1 Develop meaning for mathematical vocabulary.

Lesson 3-1: Graphing Linear Equations

CU 3102.1.16 Understand and express the meaning of the slope and y-intercept

of linear functions in real-world contexts.

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.22 Express the equation of a line in standard form,

slope-intercept, and point-slope form.

CU 3102.3.23 Determine the graph of a linear equation including those that

depict contextual situations.

SPI 3102.1.4 Translate between representations of functions that depict

real-world situations.

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

Lesson 3-2: Solving Linear Equations by Graphing

CLE 3102.3.6 Understand and use relations and functions in various

representations to solve contextual problems.

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions,

including real-world problems.

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and

to check technological computation.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a

single solution, or all real numbers as solutions.

CU 3102.3.15 Determine domain and range of a relation and articulate

restrictions imposed either by the operations or by the real life situation that

the function represents.

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.23 Determine the graph of a linear equation including those that

depict contextual situations.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a

relation is a function and/or evaluate a function at a specified rational

value.

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

Lesson Extend 3-2: Extend: Graphing Technology Lab Graphing Linear Functions

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

Lesson Explore 3-3: Explore: Algebra Lab Rate of Change of a Linear Function

CU 3102.1.16 Understand and express the meaning of the slope and y-intercept

of linear functions in real-world contexts.

CU 3102.3.20 Understand that a linear equation has a constant rate of change

called slope and represent slope in various forms.

Lesson 3-3: Rate of Change and Slope

CU 3102.1.16 Understand and express the meaning of the slope and y-intercept

of linear functions in real-world contexts.

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.20 Understand that a linear equation has a constant rate of change

called slope and represent slope in various forms.

CU 3102.5.9 Determine an equation for a line that fits real-world linear

data; interpret the meaning of the slope and y-intercept in context of the data.

SPI 3102.1.6 Determine and interpret slope in multiple contexts including

rate of change in real-world problems.

Lesson 3-5: Arithmetic Sequences as Linear Functions

CLE 3102.1.3 Develop inductive and deductive reasoning to independently make

and evaluate mathematical arguments and construct appropriate proofs; include

various types of reasoning, logic, and intuition.

CLE 3102.3.1 Use algebraic thinking to analyze and generalize patterns.

CU 3102.1.4 Write a rule with variables that expresses a pattern.

CU 3102.1.17 Connect the study of algebra to the historical development of

algebra.

CU 3102.3.1 Recognize and extend arithmetic and geometric sequences.

CU 3102.3.2 Explore patterns including Pascal's Triangle and the Fibonacci

sequence.

CU 3102.3.15 Determine domain and range of a relation and articulate

restrictions imposed either by the operations or by the real life situation that

the function represents.

SPI 3102.1.1 Interpret patterns found in sequences, tables, and other forms

of quantitative information using variables or function notation.

SPI 3102.1.4 Translate between representations of functions that depict

real-world situations.

SPI 3102.3.1 Express a generalization of a pattern in various representations

including algebraic and function notation.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a

relation is a function and/or evaluate a function at a specified rational value.

Lesson Extend 3-5: Extend: Algebra Lab Inductive and Deductive Reasoning

CLE 3102.1.3 Develop inductive and deductive reasoning to independently make

and evaluate mathematical arguments and construct appropriate proofs; include

various types of reasoning, logic, and intuition.

Lesson 3-6: Proportional and Non-proportional Relationships

CLE 3102.1.3 Develop inductive and deductive reasoning to independently make

and evaluate mathematical arguments and construct appropriate proofs; include

various types of reasoning, logic, and intuition.

CU 3102.1.4 Write a rule with variables that expresses a pattern.

CU 3102.1.5 Use formulas, equations, and inequalities to solve real-world

problems including time/rate/distance, percent increase/decrease,

ratio/proportion, and mixture problems.

CU 3102.3.23 Determine the graph of a linear equation including those that

depict contextual situations.

CU 3102.3.25 Find function values using f(x) notation or graphs.

SPI 3102.1.4 Translate between representations of functions that depict

real-world situations.

SPI 3102.3.1 Express a generalization of a pattern in various representations

including algebraic and function notation.

Chapter 4 Linear Functions and Relations

Lesson Explore 4-1: Explore: Graphing Technology Lab Investigating

Slope-Intercept Form

CU 3102.3.24 Interpret the changes in the slope-intercept form and graph of a

linear equation by looking at different parameters, m and b in the

slope-intercept form.

Lesson 4-1: Graphing Equations in Slope-Intercept Form

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.21 Determine the equation of a line using given information

including a point and slope, two points, a point and a line parallel or

perpendicular, graph, intercepts. .

CU 3102.3.22 Express the equation of a line in standard form,

slope-intercept, and point-slope form.

CU 3102.3.23 Determine the graph of a linear equation including those that

depict contextual situations.

CU 3102.3.24 Interpret the changes in the slope-intercept form and graph of a

linear equation by looking at different parameters, m and b in the

slope-intercept form.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

Lesson Extend 4-1: Extend: Graphing Technology Lab The Family of Linear

Graphs

CLE 3102.1.7 Use technologies appropriately to develop understanding of

abstract mathematical ideas, to facilitate problem solving, and to produce

accurate and reliable models.

CU 3102.1.14 Apply graphical transformations that occur when changes are made

to coefficients and constants in functions.

CU 3102.3.17 Recognize families of functions.

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.24 Interpret the changes in the slope-intercept form and graph of a

linear equation by looking at different parameters, m and b in the

slope-intercept form.

SPI 3102.1.5 Recognize and express the effect of changing constants and/or

coefficients in problem solving.

Lesson 4-2: Writing Equations in Slope-Intercept Form

CLE 3102.1.5 Recognize and use mathematical ideas and processes that arise in

different settings, with an emphasis on formulating a problem in mathematical

terms, interpreting the solutions, mathematical ideas, and communication of

solution strategies.

CU 3102.3.21 Determine the equation of a line using given information

including a point and slope, two points, a point and a line parallel or

perpendicular, graph, intercepts.

CU 3102.3.22 Express the equation of a line in standard form,

slope-intercept, and point-slope form.

CU 3102.3.24 Interpret the changes in the slope-intercept form and graph of a

linear equation by looking at different parameters, m and b in the

slope-intercept form.

SPI 3102.1.2 Write an equation symbolically to express a contextual problem.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

Lesson 4-3: Writing Equations in Point-Slope Form

CU 3102.3.21 Determine the equation of a line using given information

including a point and slope, two points, a point and a line parallel or

perpendicular, graph, intercepts.

CU 3102.3.22 Express the equation of a line in standard form,

slope-intercept, and point-slope form.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 4-4: Parallel and Perpendicular Lines

CU 3102.3.21 Determine the equation of a line using given information

including a point and slope, two points, a point and a line parallel or

perpendicular, graph, intercepts.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

Lesson 4-5: Scatter Plots and Lines of Fit

CLE 3102.5.1 Describe and interpret quantitative information.

CU 3102.1.8 Recognize and perform multiple steps in problem solving when

necessary.

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and

to check technological computation.

CU 3102.5.1 Identify patterns or trends in data.

CU 3102.5.5 Construct and interpret various forms of data representations,

(including line graphs, bar graphs, circle graphs, histograms, scatter-plots,

box-and-whiskers, stem-and-leaf, and frequency tables).

CU 3102.5.8 Examine real-world graphical relationship (including

scatter-plots) to determine type of relationship (linear or nonlinear) and any

association (positive, negative or none) between the variables of the data set.

CU 3102.5.9 Determine an equation for a line that fits real-world linear

data; interpret the meaning of the slope and y-intercept in context of the data.

CU 3102.5.11 Use an equation that fits data to make a prediction.

SPI 3102.5.1 Interpret displays of data to answer questions about the data

set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

SPI 3102.5.3 Using a scatter-plot, determine if a linear relationship exists

and describe the association between variables.

SPI 3102.5.4 Generate the equation of a line that fits linear data and use it

to make a prediction.

Lesson Extend 4-5: Extend: Algebra Lab Correlation and Causation

3102.5.8 Examine real-world graphical relationship (including

scatter-plots) to determine type of relationship (linear or nonlinear) and any

association (positive, negative or none) between the variables of the data set.

Lesson 4-6: Regression and Median-Fit Lines

CLE 3102.5.2 Use statistical thinking to draw conclusions and make

predictions.

CU 3102.5.1 Identify patterns or trends in data.

CU 3102.5.5 Construct and interpret various forms of data representations,

(including line graphs, bar graphs, circle graphs, histograms, scatter-plots,

box-and-whiskers, stem-and-leaf, and frequency tables).

CU 3102.5.8 Examine real-world graphical relationship (including

scatter-plots) to determine type of relationship (linear or nonlinear) and any

association (positive, negative or none) between the variables of the data set.

CU 3102.5.9 Determine an equation for a line that fits real-world linear

data; interpret the meaning of the slope and y-intercept in context of the data.

CU 3102.5.10 Using technology with a set of contextual linear data to examine

the line of best fit; determine and interpret the correlation coefficient.

CU 3102.5.11 Use an equation that fits data to make a prediction.

SPI 3102.5.4 Generate the equation of a line that fits linear data and use it

to make a prediction.

Lesson 4-7: Special Functions

CLE 3102.1.4 Move flexibly between multiple representations (contextual,

physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic),

to solve problems, to model mathematical ideas, and to communicate solution

strategies.

CLE 3102.4.1 Use algebraic reasoning in applications involving geometric

formulas and contextual problems.

CU 3102.3.15 Determine domain and range of a relation and articulate

restrictions imposed either by the operations or by the real life situation that

the function represents.

CU 3102.3.18 Analyze the characteristics of graphs of basic linear relations

and linear functions including constant function, direct variation, identity

function, vertical lines, absolute value of linear functions. Use technology

where appropriate.

CU 3102.3.25 Find function values using f(x) notation or graphs.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a

relation is a function and/or evaluate a function at a specified rational value.

Lesson Extend 4-7: Extend: Graphing Technology Lab Piecewise-Linear Functions

CU 3102.1.19 Recognize and practice appropriate use of technology in

representations and in problem solving.

Chapter 5 Linear Inequalities

Lesson 5-1: Solving Inequalities by Addition and Subtraction

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.1.15 Apply arithmetic concepts in algebraic contexts.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson Explore 5-2: Explore: Algebra Lab Solving Inequalities

CU 3102.1.11 Use manipulatives to model algebraic concepts.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 5-2: Solving Inequalities by Multiplication and Division

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.1.17 Connect the study of algebra to the historical development of

algebra.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

CU 3102.3.13 Solve multi-step linear inequalities with one variable and graph

the solution on a number line.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 5-3: Solving Multi-Step Inequalities

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.1.19 Recognize and practice appropriate use of technology in

representations and in problem solving.

CU 3102.3.3 Justify correct results of algebraic procedures using extension

of properties of real numbers to algebraic expressions.

CU 3102.3.13 Solve multi-step linear inequalities with one variable and graph

the solution on a number line.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson Explore 5-4: Explore: Algebra Lab Reading Compound Statements

CLE 3102.1.6 Employ reading and writing to recognize the major themes of

mathematical processes, the historical development of mathematics, and the

connections between mathematics and the real world.

Lesson 5-4: Solving Compound Inequalities

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 5-5: Inequalities Involving Absolute Value

CU 3102.3.14 Solve absolute value equations and inequalities (including

compound inequalities) with one variable and graph their solutions on a number

line.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson 5-6: Graphing Inequalities in Two Variables

CLE 3102.3.4 Solve problems involving linear equations and linear

inequalities.

CU 3102.1.1 Develop meaning for mathematical vocabulary.

CU 3102.1.2 Use the terminology of mathematics correctly.

CU 3102.3.26 Graph linear inequalities on the coordinate plane and identify

regions of the graph containing ordered pairs in the solution.

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound

inequalities including those containing absolute value.

Lesson Extend 5-6: Extend: Graphing Technology Lab Graphing Inequalities

CU 3102.3.26 Graph linear inequalities on the coordinate plane and identify

regions of the graph containing ordered pairs in the solution.

Chapter 6 Systems of Linear Equations and Inequalities

Lesson 6-1: Graphing Systems of Equations

CLE 3102.1.1 Use mathematical language, symbols, definitions, proofs and

counterexamples correctly and precisely in mathematical reasoning.

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

CU 3102.3.27 Determine the number of solutions for a system of linear

equations (0, 1, or infinitely many solutions).

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two variables.

Lesson Extend 6-1: Extend: Graphing Technology Lab Systems of Equations

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two variables.

Lesson 6-2: Substitution

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

CU 3102.1.8 Recognize and perform multiple steps in problem solving when

necessary.

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two

variables.

Lesson 6-3: Elimination Using Addition and Subtraction

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

CU 3102.1.17 Connect the study of algebra to the historical development of

algebra.

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two variables.

Lesson 6-4: Elimination Using Multiplication

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

Lesson 6-5: Applying Systems of Linear Equations

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and

to check technological computation.

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

CU 3102.3.29 Solve contextual problems involving systems of linear equations

or inequalities and interpret solutions in context.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two variables.

Lesson Extend 6-5: Extend: Spreadsheet Lab Credit Cards and Cash

CU 3102.1.19 Recognize and practice appropriate use of technology in

representations and in problem solving.

Lesson 6-6: Organizing Data Using Matrices

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions,

including real-world problems.

Lesson 6-7: Using Matrices to Solve Systems of Equations

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

CU 3102.3.28 Solve systems of linear equations graphically, algebraically,

and with technology.

SPI 3102.3.9 Solve systems of linear equations/inequalities in two variables.

Lesson 6-8: Systems of Inequalities

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

CU 3102.3.29 Solve contextual problems involving systems of linear equations

or inequalities and interpret solutions in context.

Lesson Extend 6-8: Extend: Graphing Technology Lab Systems of Inequalities

CLE 3102.3.7 Construct and solve systems of linear equations and inequalities

in two variables by various methods.

Chapter 7 Polynomials

Lesson 7-1: Multiplying Monomials

CLE 3102.1.6 Employ reading and writing to recognize the major themes of

mathematical processes, the historical development of mathematics, and the

connections between mathematics and the real world.

CLE 3102.4.1 Use algebraic reasoning in applications involving geometric

formulas and contextual problems.

CU 3102.1.3 Understand and use mathematical symbols, notation, and common

mathematical abbreviations correctly.

CU 3102.3.4 Simplify expressions using exponent rules including negative

exponents and zero exponents.

SPI 3102.3.1 Express a generalization of a pattern in various representations

including algebraic and function notation.

Lesson 7-2 Dividing Monomials

CU 3102.3.4 Simplify expressions using exponent rules including negative

exponents and zero exponents.

Lesson 7-3 Scientific Notation

CU 3102.2.5 Perform operations with numbers in scientific notation (multiply,

divide, powers).

CU 3102.2.6 Use appropriate technologies to apply scientific notation to

real-world problems.

SPI 3102.2.2 Multiply, divide, and square numbers expressed in scientific

notation.

Lesson Explore 7-4 Explore: Algebra Lab Polynomials

CU 3102.1.11 Use manipulatives to model algebraic concepts.

Lesson 7-4 Polynomials

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CU 3102.4.1 Using algebraic expressions solve for measures in geometric

figures as well as for perimeter, area, and volume.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson Explore 7-5 Explore: Algebra Lab Adding and Subtracting Polynomials

CU 3102.3.5 Add, subtract, and multiply polynomials including squaring a

binomial.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson 7-5 Adding and Subtracting Polynomials

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CU 3102.3.5 Add, subtract, and multiply polynomials including squaring a

binomial.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson 7-6 Multiplying a Polynomial by a Monomial

CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem

solving, including testing cases, estimation, and then checking induced errors

and the reasonableness of the solution.

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson Explore 7-7 Explore: Algebra Lab Multiplying Polynomials

CU 3102.3.5 Add, subtract, and multiply polynomials including squaring a

binomial.

CU 3102.3.7 Use various models (including area models) to represent products

of polynomials.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson 7-7 Multiplying Polynomials

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CU 3102.3.5 Add, subtract, and multiply polynomials including squaring a

binomial.

CU 3102.3.7 Use various models (including area models) to represent products

of polynomials.

SPI 3102.3.2 Operate with polynomials and simplify results.

Lesson 7-8 Special Products

CU 3102.3.5 Add, subtract, and multiply polynomials including squaring a

binomial.

CU 3102.3.7 Use various models (including area models) to represent products

of polynomials.

SPI 3102.3.2 Operate with polynomials and simplify results.

Chapter 8 Factoring and Quadratic Equations

Lesson 8-1 Monomials and Factoring

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CU 3102.3.8 Find the GCF of the terms in a polynomial.

SPI 3102.3.3 Factor polynomials.

Lesson Explore 8-2 Explore: Algebra Lab Factoring Using the Distributive

Property

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

SPI 3102.3.3 Factor polynomials.

Lesson 8-2 Using the Distributive Property

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CU 3102.3.8 Find the GCF of the terms in a polynomial.

SPI 3102.3.3 Factor polynomials.

Lesson Explore 8-3 Explore: Algebra Lab Factoring Trinomials

CU 3102.1.11 Use manipulatives to model algebraic concepts.

SPI 3102.3.3 Factor polynomials.

Lesson 8-3 Quadratic Equations: x^2 + bx + c = 0

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real

roots.

CU 3102.1.1 Develop meaning for mathematical vocabulary.

CU 3102.1.2 Use the terminology of mathematics correctly.

CU 3102.3.9 Find two binomial factors of a quadratic expression.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring,

graphing, quadratic formula, or square root principle.

CU 3102.3.32 Recognize the connection among factors, solutions (roots), zeros

of related functions, and x-intercepts in equations that arise from quadratic

functions.

SPI 3102.3.3 Factor polynomials.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a

quadratic function.

Lesson 8-4 Quadratic Equations: ax^2 + bx + c = 0

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real

roots.

CU 3102.3.9 Find two binomial factors of a quadratic expression.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring,

graphing, quadratic formula, or square root principle.

CU 3102.3.32 Recognize the connection among factors, solutions (roots), zeros

of related functions, and x-intercepts in equations that arise from quadratic

functions.

SPI 3102.3.3 Factor polynomials.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a

quadratic function.

Lesson 8-5 Quadratic Equations: Differences of Squares

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real

roots.

CU 3102.3.9 Find two binomial factors of a quadratic expression.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring,

graphing, quadratic formula, or square root principle.

CU 3102.3.32 Recognize the connection among factors, solutions (roots), zeros

of related functions, and x-intercepts in equations that arise from quadratic

functions.

SPI 3102.3.3 Factor polynomials.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a

quadratic function.

Lesson 8-6 Quadratic Equations: Perfect Squares

CLE 3102.3.2 Understand and apply properties in order to perform operations

with, evaluate, simplify, and factor expressions and polynomials.

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real

roots.

CLE 3102.4.1 Use algebraic reasoning in applications involving geometric

formulas and contextual problems.

CU 3102.1.17 Connect the study of algebra to the historical development of

algebra.

CU 3102.3.9 Find two binomial factors of a quadratic expression.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring,

graphing, quadratic formula, or square root principle.

CU 3102.3.32 Recognize the connection among factors, solutions (roots), zeros

of related functions, and x-intercepts in equations that arise from quadratic

functions.

SPI 3102.3.3 Factor polynomials.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a

quadratic function.

Chapter 9 Quadratic and Exponential Functions

Lesson 9-1 Graphing Quadratic Functions

CLE 3102.3.6 Understand and use relations and functions in various representations to solve contextual problems.

CU 3102.1.8 Recognize and perform multiple steps in problem solving when necessary.

CU 3102.1.19 Recognize and practice appropriate use of technology in representations and in problem solving.

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

CU 3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.

CU 3102.3.25 Find function values using f(x) notation or graphs.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

Lesson 9-2 Solving Quadratic Equations by Graphing

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real roots.

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions, including real-world problems.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.

CU 3102.3.32 Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function.

Lesson 9-3 Transformations of Quadratic Functions

CU 3102.1.14 Apply graphical transformations that occur when changes are made to coefficients and constants in functions.

CU 3102.3.17 Recognize families of functions.

CU 3102.3.25 Find function values using f(x) notation or graphs.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.1.5 Recognize and express the effect of changing constants and/or coefficients in problem solving.

SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

Lesson Extend 9-3 Extend: Graphing Technology Lab Systems of Linear and Quadratic Equations

CU 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.

Lesson 9-4 Solving Quadratic Equations by Completing the Square

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real roots.

CU 3102.1.11 Use manipulatives to model algebraic concepts.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function.

Lesson 9-5 Solving Quadratic Equations by Using the Quadratic Formula.

CLE 3102.3.8 Solve and understand solutions of quadratic equations with real roots.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.

CU 3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.

CU 3102.3.31 Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.

SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation.

SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function.

Lesson 9-6 Exponential Functions

CLE 3102.3.6 Understand and use relations and functions in various representations to solve contextual problems.

CLE 3102.3.9 Understand and use exponential functions to solve contextual problems.

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

CU 3102.3.25 Find function values using f(x) notation or graphs.

CU 3102.3.33 Recognize data that can be modeled by an exponential function.

CU 3102.3.34 Graph exponential functions in the form y = a(bx) where b ≠ 0.

CU 3102.3.35 Apply growth/decay and simple/compound interest formulas to solve contextual problems.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

Lesson 9-7 Growth and Decay

CLE 3102.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

CLE 3102.3.9 Understand and use exponential functions to solve contextual problems.

CU 3102.3.33 Recognize data that can be modeled by an exponential function.

CU 3102.3.35 Apply growth/decay and simple/compound interest formulas to solve contextual problems.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

Lesson 9-8 Geometric Sequences as Exponential Functions

CLE 3102.3.1 Use algebraic thinking to analyze and generalize patterns.

CU 3102.1.17 Connect the study of algebra to the historical development of algebra.

CU 3102.3.1 Recognize and extend arithmetic and geometric sequences.

CU 3102.3.2 Explore patterns including Pascal's Triangle and the Fibonacci sequence.

SPI 3102.1.1 Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation.

Lesson 9-9 Analyzing Functions with Successive Differences and Ratios

CLE 3102.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.

CU 3102.1.4 Write a rule with variables that expresses a pattern.

SPI 3102.1.1 Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.

SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation.

Lesson Extend 9-9 Extend: Graphing Technology Lab Curve Fitting

CLE 3102.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

CU 3102.5.1 Identify patterns or trends in data.

CU 3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).

CU 3102.5.8 Examine real-world graphical relationship (including scatter-plots) to determine type of relationship (linear or nonlinear) and any association (positive, negative or none) between the variables of the data set.

CU 3102.5.11 Use an equation that fits data to make a prediction.

Chapter 10 Radical Functions and Geometry

Lesson 10-1 Square Root Functions

CLE 3102.3.6 Understand and use relations and functions in various representations to solve contextual problems.

CU 3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

Lesson Extend 10-1 Extend: Graphing Technology Lab Graphing Square Root Functions

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

CU 3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.

Lesson 10-2 Simplifying Radical Expressions

CU 3102.2.3 Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand.

CU 3102.2.4 Operate efficiently with both rational and irrational numbers.

SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

Lesson Extend 10-2 Extend: Graphing Technology Lab Rational Exponents

CU 3102.1.18 Translate syntax of technology to appropriate mathematical notation.

Lesson 10-3 Operations with Radical Expressions

CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.

CU 3102.2.3 Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand.

SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

Lesson 10-4 Radical Equations

CLE 3102.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

Lesson 10-5 The Pythagorean Theorem

CU 3102.4.2 Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

CU 3102.4.3 Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop the distance formula for a coordinate plane using the Pythagorean Theorem.

3102.4.4 Develop the midpoint formula for segments on a number line or in the coordinate plane.

SPI 3102.4.2 Solve contextual problems using the Pythagorean Theorem.

Lesson 10-6 The Distance and Midpoint Formulas

SPI 3102.4.3 Solve problems involving the distance between points or midpoint of a segment.

Lesson 10-7 Similar Triangles

CU 3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume.

Chapter 11 Rational Functions and Equations

Lesson Explore 11-1 Explore: Graphing Technology Lab Inverse Variation

CLE 3102.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

Lesson 11-1 Inverse Variation

3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.

Lesson Explore 11-2 Explore: Algebra Lab Reading Rational Expressions

CLE 3102.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

Lesson 11-2 Rational Functions

CLE 3102.3.3 Understand and apply operations with rational expressions and equations.

CU 3102.1.14 Apply graphical transformations that occur when changes are made to coefficients and constants in functions.

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

CU 3102.3.17 Recognize families of functions.

CU 3102.3.25 Find function values using f(x) notation or graphs.

SPI 3102.1.4 Translate between representations of functions that depict real-world situations.

SPI 3102.1.5 Recognize and express the effect of changing constants and/or coefficients in problem solving.

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

Lesson 11-3 Simplifying Rational Expressions

CLE 3102.3.3 Understand and apply operations with rational expressions and equations.

CU 3102.3.8 Find the GCF of the terms in a polynomial.

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

Lesson Extend 11-3 Extend: Graphing Technology Lab Simplifying Rational Expressions

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

Lesson 11-4 Multiplying and Dividing Rational Expressions

CLE 3102.3.3 Understand and apply operations with rational expressions and equations.

CLE 3102.4.2 Apply appropriate units of measure and convert measures in problem solving situations.

CU 3102.1.15 Apply arithmetic concepts in algebraic contexts.

CU 3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results.

CU 3102.4.5 Use dimensional analysis to convert rates and measurements both within a system and between systems and check the appropriateness of the solution.

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

SPI 3102.4.4 Convert rates and measurements.

Lesson 11-5 Dividing Polynomials

CLE 3102.3.3 Understand and apply operations with rational expressions and equations.

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions, including real-world problems.

CU 3102.3.6 Find the quotient of a polynomial and a monomial.

CU 3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results.

Lesson 11-6 Adding and Subtracting Rational Expressions

CU 3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results.

Lesson 11-7 Mixed Expressions and Complex Fractions

CLE 3102.3.3 Understand and apply operations with rational expressions and equations.

CU 3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results.

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

Lesson 11-8 Rational Equations

CU 3102.1.1 Develop meaning for mathematical vocabulary.

CU 3102.1.2 Use the terminology of mathematics correctly.

CU 3102.1.8 Recognize and perform multiple steps in problem solving when necessary.

CU 3102.1.19 Recognize and practice appropriate use of technology in representations and in problem solving.

CU 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.

CU 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents.

SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

SPI 3102.4.4 Convert rates and measurements.

Chapter 12 Statistics and Probability

Lesson 12-1 Designing a Survey

CLE 3102.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

Lesson 12-2 Analyzing Survey Results

CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CLE 3102.5.1 Describe and interpret quantitative information.

SPI 3102.5.1 Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

Lesson 12-3 Statistics and Parameters

CLE 3102.5.1 Describe and interpret quantitative information.

CU 3102.5.3 When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range.

SPI 3102.5.2 Identify the effect on mean, median, mode, and range when values in the data set are changed.

Lesson 12-4 Permutations and Combinations

CLE 3102.1.1 Use mathematical language, symbols, definitions, proofs and counter- examples correctly and precisely in mathematical reasoning.

CLE 3102.5.3 Understand basic counting procedures and concepts of probability.

CU 3102.1.3 Understand and use mathematical symbols, notation, and common

mathematical abbreviations correctly.

CU 3102.3.2 Explore patterns including Pascal's Triangle and the Fibonacci sequence.

CU 3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.

Lesson 12-5 Probability of Compound Events

CLE 3102.5.3 Understand basic counting procedures and concepts of probability.

CU 3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.

CU 3102.5.13 Determine the complement of an event and the probability of that complement.

CU 3102.5.14 Determine if two events are independent or dependent.

CU 3102.5.15 Explore joint and conditional probability.

CU 3102.5.18 Make informed decisions about practical situations using probability concepts.

Lesson 12-6 Probability Distributions

CU 3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).

CU 3102.5.18 Make informed decisions about practical situations using probability concepts.

Lesson Extend 12-6 Extend: Graphing Technology Lab The Normal Curve

CLE 3102.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

CU 3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).

Lesson 12-7 Probability Simulations

CLE 3102.5.2 Use statistical thinking to draw conclusions and make predictions.

CU 3102.5.16 Identify situations for which the Law of Large Numbers applies.

CU 3102.5.17 Perform simulations to estimate probabilities.

CU 3102.5.18 Make informed decisions about practical situations using probability concepts.

SPI 3102.5.5 Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.

Lesson Concepts and Skills

Lesson Concepts and Skills 1: Converting Units of Measure

CLE 3102.4.2 Apply appropriate units of measure and convert measures in problem solving situations.

SPI 3102.4.4 Convert rates and measurements.

Lesson Concepts and Skills 5: Venn Diagrams

CU 3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.

Lesson Concepts and Skills 6: Misleading Graphs

SPI 3102.5.1 Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

Lesson Problem-Solving Handbook

Lesson Problem-Solving Handbook: Problem-Solving Handbook

CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

CU 3102.1.4 Write a rule with variables that expresses a pattern.

CU 3102.1.6 Use a variety of strategies to estimate and compute solutions, including real-world problems.

CU 3102.1.7 Identify missing or irrelevant information in problems.

CU 3102.1.20 Estimate solutions to evaluate the reasonableness of results and to check technological computation.

CU 3102.3.2 Explore patterns including Pascal's Triangle and the Fibonacci sequence.

Lesson Study Guide and Review

Lesson Study Guide and Review Chapter 7: Study Guide and Review Chapter 7

CU 3102.1.1 Develop meaning for mathematical vocabulary.

CU 3102.1.2 Use the terminology of mathematics correctly.

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