Heart of Algebra | eTAP Lesson |
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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 two-variable 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 |
One-Variable 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 |
Two-Variable 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 two-way 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 |
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Interpret margin of error; understand that a larger sample size generally leads to a smaller margin of error.
SAT.MATH.2.6.2 |
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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 real-world 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 |
Sine-Cosine 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 xy-plane.
SAT.MATH.4.4.3 |
Corresponding Parts |
Describe how
SAT.MATH.4.4.4 |
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Understand that the ordered pairs that satisfy an equation of the form (x – h)2 + (y – k)2 = r2 form a circle when plotted in the xy-plane.
SAT.MATH.4.4.5 |
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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 xy-plane, and use the distance formula in problems related to circles.
SAT.MATH.4.4.7 |
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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 |