Heart of Algebra  eTAP Lesson 

Linear Equations in One Variable  
Create and use linear equations in one variable to solve problems in a variety of contexts.
SAT.MATH.1.1.1 
Equations as Relations Basic Operations Adding the Same Number Subtracting the Same Number Dividing the Same Number to Each Side of an Equation, Solving for an Unknown When to do What Setting Up and Solving Equations Completing the Square Simultaneous Equations With Strange Solutions 
Create a linear equation in one variable, and when in context interpret solutions in terms of the context.
SAT.MATH.1.1.2 
Equations as Relations Basic Operations Adding the Same Number Subtracting the Same Number Dividing the Same Number to Each Side of an Equation, Solving for an Unknown When to do What Setting Up and Solving Equations 
Solve a linear equation in one variable, making strategic use of algebraic structure.
SAT.MATH.1.1.3 
Equations as Relations Basic Operations Adding the Same Number Dividing the Same Number to Each Side of an Equation, Solving for an Unknown When to do What Setting Up and Solving Equations 
For a linear equation in one variable,
SAT.MATH.1.1.4 
Equations as Relations Basic Operations When to do What Setting Up and Solving Equations 
Fluently solve a linear equation in one variable.
SAT.MATH.1.1.5 
Equations as Relations Basic Operations Dividing the Same Number to Each Side of an Equation, Solving for an Unknown When to do What Setting Up and Solving Equations 
Linear Functions  
In the first case, the variable is the input and the value of the expression is the output. In the second case, one of the variables is designated as the input and determines a unique value of the other variable, which is the output. Create and use linear functions to solve problems in a variety of contexts. SAT.MATH.1.2.1 
Functions 
Create a linear function to model a relationship between two quantities.
SAT.MATH.1.2.2 
Functions 
For a linear function that represents a context,
SAT.MATH.1.2.3 
Functions Determine the Equation from a Relation Solving Equations Using Several Operations 
Make connections between verbal, tabular, algebraic, and graphical representations of a linear function by
SAT.MATH.1.2.4 
Functions Determine the Equation from a Relation Slope of a Line 
Write the rule for a linear function given two input/output pairs or one input/output pair and the rate of change.
SAT.MATH.1.2.5 
Functions Determine the Equation from a Relation Direct and Inverse Variation Slope of a Line 
Linear Equations in Two Variables  
A linear equation in two variables can be used to represent a constraint or condition on twovariable quantities in situations where neither of the variables is regarded as an input or an output. A linear equation can also be used to represent a straight line in the coordinate plane. Create and use a linear equation in two variables to solve problems in a variety of contexts. SAT.MATH.1.3.1 
Graphing Systems of Inequalities Solving Equations When Several Terms and Procedures are Involved Variables and Expressions 
Create a linear equation in two variables to model a constraint or condition on two quantities.
SAT.MATH.1.3.2 
Solving Equations When Several Terms and Procedures are Involved Variables and Expressions 
For a linear equation in two variables that represents a context,
SAT.MATH.1.3.3 
Solving Equations When Several Terms and Procedures are Involved Slope of a Line 
Make connections between tabular, algebraic, and graphical representations of a linear equation in two variables by
SAT.MATH.1.3.4 
Functions as Graphs in the Coordinate System How to Use Graphs 
Write an equation for a line given two points on the line, one point and the slope of the line, or one point and a parallel or perpendicular line.
SAT.MATH.1.3.5 
Slope of a Line Slope Intercept Form of Equations 
Systems of Two Linear Equations in Two Variables  
Create and use a system of two linear equations in two variables to solve problems in a variety of contexts.
SAT.MATH.1.4.1 
Simultaneous Equations 
Create a system of linear equations in two variables, and when in context interpret solutions in terms of the context.
SAT.MATH.1.4.2 
Simultaneous Equations 
Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other.
SAT.MATH.1.4.3 
Graphing Systems of Equations 
Solve a system of two linear equations in two variables, making strategic use of algebraic structure.
SAT.MATH.1.4.4 
The Substitution Method The Addition  Subtraction Method 
For a system of linear equations in two variables,
SAT.MATH.1.4.5 
Simultaneous Equations With Strange Solutions 
Fluently solve a system of linear equations in two variables
SAT.MATH.1.4.6 
Substitution Elimination 
Linear Inequalities in One or Two Variables  
Create and use linear inequalities in one or two variables to solve problems in a variety of contexts.
SAT.MATH.1.5.1 
Inequalities with Several Operations 
Create linear inequalities in one or two variables, and when in context interpret the solutions in terms of the context.
SAT.MATH.1.5.2 
Inequalities with Several Operations 
For linear inequalities in one or two variables, interpret a constant, variable, factor, or term, including situations where seeing structure provides an advantage.
SAT.MATH.1.5.3 
Inequalities with Several Operations 
Make connections between tabular, algebraic, and graphical representations of linear inequalities in one or two variables by deriving one from the other.
SAT.MATH.1.5.4 
Graphing Systems of Inequalities 
Given a linear inequality or system of linear inequalities, interpret a point in the solution set.
SAT.MATH.1.5.5 
Graphing Systems of Inequalities 
Problem Solving and Data Analysis  eTAP Lesson 
Ratios, Rates, Proportional Relationships, and Units  
Items will require students to solve problems by using a proportional relationship between quantities, calculating or using a ratio or rate, and/or using units, derived units, and unit conversion. Apply proportional relationships, ratios, rates, and units in a wide variety of contexts. Examples include but are not limited to scale drawings and problems in the natural and social sciences. SAT.MATH.2.1.1 
Ratios & Rates Direct and Inverse Variation 
Solve problems involving
SAT.MATH.2.1.2 
Word Problems of Ratios & Rates Direct and Inverse Variation 
Understand and use the fact that when two quantities are in a proportional relationship, if one changes by a scale factor, then the other also changes by the same scale factor.
SAT.MATH.2.1.3 
Direct and Inverse Variation 
Percentages  
Use percentages to solve problems in a variety of contexts. Examples include, but are not limited to, discounts, interest, taxes, tips, and percent increases and decreases for many different quantities.
SAT.MATH.2.2.1 
Percent, Decimals & Fractions 
Understand and use the relationship between percent change and growth factor (5% and 1.05, for example); include percentages greater than or equal to 100%.
SAT.MATH.2.2.2 
Exponential Functions and Data 
OneVariable Data: Distributions and Measures of Center and Spread  
Choose an appropriate graphical representation for a given data set.
SAT.MATH.2.3.1 
Basic Methods of Describing Data 
Interpret information from a given representation of data in context.
SAT.MATH.2.3.2 
Visually Representing Numerical Data 
Analyze and interpret numerical data distributions represented with frequency tables, histograms, dot plots, and boxplots.
SAT.MATH.2.3.3 
Showing Orderly Data with Histograms Seeking Trends with Line Graphs Boxplot, Interquartile Range, and Midhinge Methods of Collecting, Representing, and Displaying Data 
For quantitative variables, calculate, compare, and interpret mean, median, and range. Interpret (but don’t calculate) standard deviation.
SAT.MATH.2.3.4 
Boxplot, Interquartile Range, and Midhinge Frequency Distribution Table, Summation Notation, and Mean Formula Standard Deviation of Random Variable 
Compare distributions using measures of center and spread, including distributions with different means and the same standard deviations and ones with the same mean and different standard deviations.
SAT.MATH.2.3.5 
Standard Deviation of Random Variable 
Understand and describe the effect of outliers on mean
SAT.MATH.2.3.6 
Paired Data Sets and Scatterplots Regression Models and Least Square Methods 
Given an appropriate data set, calculate the mean.
SAT.MATH.2.3.7 
Geometric Mean, Harmonic Mean, and Weighted Arithmetic Mean 
TwoVariable Data: Models and Scatterplots  
Using a model that fits the data in a scatterplot, compare values predicted by the model to values given in the data set.
SAT.MATH.2.4.1 
Paired Data Sets and Scatterplots 
Interpret the slope and intercepts of the line of best fit in context.
SAT.MATH.2.4.2 
How to Use Graphs 
Given a relationship between two quantities, read and interpret graphs and tables modeling the relationship.
SAT.MATH.2.4.3 
How to Use Graphs 
Analyze and interpret data represented in a scatterplot or line graph; fit linear, quadratic, and exponential models.
SAT.MATH.2.4.4 
Correlations Paired Data Sets and Scatterplots 
Select a graph that represents a context, identify a value on a graph, or interpret information on the graph.
SAT.MATH.2.4.5 
How to Use Graphs 
For a given function type (linear, quadratic, exponential), choose the function of that type that best fits given data.
SAT.MATH.2.4.6 
Paired Data Sets and Scatterplots 
Compare linear and exponential growth.
SAT.MATH.2.4.7 
The number e Using Logarithms to Model Data 
Estimate the line of best fit for a given scatterplot; use the line to make predictions.
SAT.MATH.2.4.8 
Correlations 
Probability and Conditional Probability  
Use one and twoway tables, tree diagrams, area models, and other representations to find relative frequency, probabilities, and conditional probabilities. Compute and interpret probability and conditional probability in simple contexts. SAT.MATH.2.5.1 
Conditional Probability What is Probability? Conditional Probability 
Understand formulas for probability and conditional probability in terms of frequency.
SAT.MATH.2.5.2 
Conditional Probability Discrete Probability Distribution 
Inference From Sample Statistics and Margin of Error  
Use sample mean and sample proportion to estimate population mean and population proportion. Utilize, but do not calculate, margin of error.
SAT.MATH.2.6.1 

Interpret margin of error; understand that a larger sample size generally leads to a smaller margin of error.
SAT.MATH.2.6.2 

Evaluating Statistical Claims: Observational Studies and Experiments  
With random samples, describe which population the results can be extended to.
SAT.MATH.2.7.1 
Multiple Events Methods of Collecting, Representing, & Displaying Data 
Given a description of a study with or without random assignment, determine whether there is evidence for a causal relationship.
SAT.MATH.2.7.2 
Planning and Conducting an Experiment 
Understand why random assignment provides evidence for a causal relationship.
SAT.MATH.2.7.3 
Independent and Dependent Events 
Understand why a result can be extended only to the population from which the sample was selected.
SAT.MATH.2.7.4 
Independent and Dependent Events 
Analyzing Advanced Expressions  eTAP Lesson 
Equivalent Expressions  
Make strategic use of algebraic structure and the properties of operations to identify and create equivalent expressions, including
SAT.MATH.3.1.1 
Rational Expressions with Like and Unlike Denominators Quadratic Formula Exponential Functions and Data 
Fluently add, subtract, and multiply polynomials.
SAT.MATH.3.1.2 
Adding and Subtracting Polynomials Multiplying and Dividing Polynomials 
Nonlinear Equations in One Variable and Systems of Equations in Two Variables  
Make strategic use of algebraic structure, the properties of operations, and reasoning about equality to
SAT.MATH.3.2.1 
Correlations Solve Single Variable Equations Radical Equations Exponential and Logarithmic Equations Solving Quadratic Equations Joe's Method Completing the Square Adding and Subtracting Integers Absolute Value Inequalities Simultaneous Equations With Strange Solutions 
Given a nonlinear equation in one variable that represents a context, interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage.
SAT.MATH.3.2.2 
Exponential and Logarithmic Equations 
Given an equation or formula in two or more variables that represents a context, view it as an equation in a single variable of interest where the other variables are parameters and solve for the variable of interest.
SAT.MATH.3.2.3 
Ratios and Proportions Direct and Inverse Variation 
Fluently solve quadratic equations in one variable, written as a quadratic expression in standard form equal to zero, where using the quadratic formula or completing the square is the most efficient method for solving the equation.
SAT.MATH.3.2.4 
Solving Quadratic Equations Joe's Method Completing the Square Quadratic Formula 
Nonlinear Functions  
Create and use quadratic or exponential functions to solve problems in a variety of contexts
SAT.MATH.3.3.1 
Graphing Data 
For a quadratic or exponential function,
SAT.MATH.3.3.2 
Function Notation Exponential Functions and Data Graphs of Exponential Functions Using Logarithms to Model Data Simple Quadratic Functions Parabolas Quadratic Functions in Intercept Form Graphing Quadratic Functions 
For a factorable or factored polynomial or simple rational function,
SAT.MATH.3.3.3 
Factoring Quadratics How to Use Graphs Function Notation 
Additional Topics in Math  eTAP Lesson 
Area and Volume  
Solve realworld and mathematical problems about a geometric figure or an object that can be modeled by a geometric figure using given information such as length, area, surface area, or volume.
SAT.MATH.4.1 
Triangle Areas Surface Area Rectangular Prism Volume Areas of Rectangles and Parallelograms 
Lines, Angles, and Triangles  
Use concepts and theorems relating to congruence and similarity of triangles to solve problems.
SAT.MATH.4.2.1 
Triangles SSS and SAS Congruencies 
Determine which statements may be required to prove certain relationships or to satisfy a given theorem.
SAT.MATH.4.2.2 
Geometric Proofs Postulates of Geometry Direct Proofs Symbols of Logic 
Apply knowledge that changing by a scale factor of k changes all lengths by a factor of k, but angle measures remain unchanged
SAT.MATH.4.2.3 
Similar Triangles Properties of Isometrics 
Know and directly apply relevant theorems such as
SAT.MATH.4.2.4 
Parallelograms and Parallel Lines Related Proofs Proving Angle Conjectures Triangles Sum Conjecture ASA Congruencies AAS and HL Congruencies Similar Triangles 
Right Triangles and Trigonometry  
Solve problems in a variety of contexts using
SAT.MATH.4.3.1 
Special Right Triangles The Theorem of Pythagoras Trigonometric Calculations 
Use similarity to calculate values of sine, cosine, and tangent.
SAT.MATH.4.3.2 
Ratios and Proportions 
Understand that when given one side length and one acute angle measure in a right triangle, the remaining values can be determined.
SAT.MATH.4.3.3 
The Theorem of Pythagoras 
Solve problems using the relationship between sine and cosine of complementary angles.
SAT.MATH.4.3.4 
SineCosine Relationships 
Fluently apply properties of special right triangles to determine side lengths and calculate trigonometric ratios of 30, 45, and 60 degrees.
SAT.MATH.4.3.5 
Special Right Triangles 
Circles  
Use definitions, properties, and theorems relating to circles and parts of circles, such as radii, diameters, tangents, angles, arcs, arc lengths, and sector areas, to solve problems.
SAT.MATH.4.4.1 
Arc Length Definition  Circles 
Solve problems using
SAT.MATH.4.4.2 
Tangent Properties Circumference/Diameter Ratio Radians 
Create an equation to represent a circle in the xyplane.
SAT.MATH.4.4.3 
Corresponding Parts 
Describe how
SAT.MATH.4.4.4 

Understand that the ordered pairs that satisfy an equation of the form (x – h)^{2} + (y – k)^{2} = r^{2} form a circle when plotted in the xyplane.
SAT.MATH.4.4.5 

Convert between angle measures in degrees and radians.
SAT.MATH.4.4.6 
Radians 
Complete the square in an equation representing a circle to determine properties of the circle when it is graphed in the xyplane, and use the distance formula in problems related to circles.
SAT.MATH.4.4.7 

Complex Numbers  
Apply knowledge and understanding of the complex number system to add, subtract, multiply, and divide with complex numbers and solve problems.
SAT.MATH.4.5 
Complex Numbers 