# Algebra 2 Khan Academy Video Correlations By SpringBoard Activity

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1 SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in two variables to represent relationships between quantities. Graph two-variable equations 1-3 Learning Targets: Write, solve, and graph absolute value equations. Solve and graph absolute value inequalities. Activity 2 Graphing to Find Solutions 2-1 Learning Targets: Write equations in two variables to represent relationships between quantities. Algebra 2 Khan Academy Video Correlations By SpringBoard Activity Video(s) Unit 1: Equations, Inequalities, Functions One-Variable Equations Representing a relationship with a simple equation Linear equation word problem Word problem: solving equations Solving equations with the distributive property Ex 2: Multi-step equation Variables on both sides Two-Variable Equations Constructing linear equations to solve word problems Exploring linear relationships Graphs of linear equations Application problem with graph Absolute Value Equations and Inequalities Absolute value equations Absolute value equations Absolute value equations 1 Absolute value equation example Absolute value equations example 1 Absolute value equation example 2 Absolute value equation with no solution Absolute Value Inequalities Absolute value inequalities Absolute value inequalities example 1 Absolute inequalities 2 Absolute value inequalities example 3 Writing Linear Equations Constructing linear equations to solve word problems Graphing and Interpreting Two-Variable Equations Graphing a line in slope intercept form Interpreting intercepts of linear functions

2 Graph equations on coordinate axes with labels and scales. 2-2 Learning Targets: Represent constraints by equations or inequalities. Use a graph to determine solutions of a system of inequalities. Activity 3 Systems of Linear Equations 3-1 Learning Targets: Use graphing, substitution, and elimination to solve systems of linear equations in two variables. Formulate systems of linear equations in two variables to model real-world situations. 3-2 Learning Targets: Solve systems of three linear equations in three variables using substitution and Gaussian elimination. Formulate systems of three linear equations in three variables to model a real-world situation. 3-3 Learning Targets: Add, subtract, and multiply matrices. Use a graphing calculator to perform operations on matrices. 3-4 Learning Targets: Solve systems of two linear equations in two variables by using graphing calculators with matrices. Solve systems of three linear equations in three variables by using graphing calculators with matrices. Graphing Systems of Inequalities Graphing systems of inequalities Graphing systems of inequalities 2 Visualizing the solution set for a system of inequalities Solving Systems of Two Equations in Two Variables: Graphing Solving linear systems by graphing Solving systems graphically Graphing systems of equations Graphical systems application problem Example 2: Graphically solving systems Example 3: Graphically solving systems Solving Systems of Two Equations in Two Variables: Substitution Example 1: Solving systems by substitution Example 2: Solving systems by substitution Example 3: Solving systems by substitution The substitution method Substitution method 2 Substitution method 3 Practice using substitution for systems Solving Systems of Two Equations in Two Variables: Elimination Example 1: Solving systems by elimination Example 2: Solving systems by elimination Example 3: Solving systems by elimination Addition elimination method 1 Addition elimination method 2 Addition elimination method 3 Addition elimination method 4 Simple elimination practice Systems with elimination practice Consistent, Inconsistent, Dependent, and Independent Systems Consistent and inconsistent systems Independent and dependent systems

3 Activity 4 Piecewise-Defined Functions 4-1 Learning Targets: Graph piecewise-defined Write the domain and range of functions using interval notation, inequalities, and set notation. 4-2 Learning Targets: Graph step functions and absolute value Describe the attributes of these 4-3 Learning Targets: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k). Find the value of k, given these graphs. Activity 5 Function Composition and Operations 5-1 Learning Targets: Combine functions using arithmetic operations. Build functions that model real-world scenarios. 5-2 Learning Targets: Write functions that describe the relationship between two quantities. Explore the composition of two functions through a real-world scenario. Solving Systems of Three Equations in Three Variables Systems of three variables Systems of three variables 2 Solutions to three variable system Solutions to three variable system 2 Three equation application problem Matrix Operations Introduction to the matrix Representing data with matrices Matrix addition and subtraction Matrix multiplication introduction Multiplying a matrix by a matrix Defined and undefined matrix operations Solving Matrix Equations Matrix equations and systems Piecewise Defined Functions What is a function? Finding a piecewise function definition from graph Absolute Value Functions Graphs of absolute value functions Absolute value graphing exercise example Operations with Functions Sum of functions Difference of functions Product of functions Quotient of functions Composition of Functions Introduction to function composition Creating new function from composition Evaluating composite functions example

7 Activity 13 Systems of Linear and Nonlinear Equations 13-1 Learning Targets: Use graphing to solve a system consisting of a linear and a nonlinear equation. Interpret the solutions of a system of equations Learning Targets: Use substitution to solve a system consisting of a linear and nonlinear equation. Determine when a system consisting of a linear and nonlinear equation has no solution. Non-linear systems of equations 1 Non-linear systems of equations 2 Non-linear systems of equations 3 Systems of nonlinear equations 1 Systems of nonlinear equations 2 Systems of nonlinear equations 3 Unit 3: Polynomials Activity 14 Polynomial Basics Introduction to Polynomials Terms coefficients and exponents in a polynomial 14-1 Learning Targets: Write a third-degree equation that represents a real-world situation. End Behavior Of Polynomial Functions Graph a portion of this equation and Polynomial end behavior evaluate the meaning of a relative Polynomial end behavior example maximum. Another polynomial end behavior example 14-2 Learning Targets: Sketch the graphs of cubic Polynomial end behavior exercise example Identify the end behavior of polynomial Even and Odd Functions Recognizing odd and even functions 14-3 Learning Targets: Connection between even and odd numbers and Recognize even and odd functions given an functions equation or graph. Distinguish between even and odd functions and even-degree and odd-degree Activity 15 Polynomial Operations 15-1 Learning Targets: Use a real-world scenario to introduce polynomial addition and subtraction. Add and subtract polynomials Learning Targets: Add, subtract, and multiply polynomials. Understand that polynomials are closed under the operations of addition, subtraction, and multiplication Learning Targets: Adding and Subtraction Polynomials Addition and subtraction of polynomials Multiplying Polynomials Multiplying polynomials example Multiplying polynomials example 2 Dividing Polynomials Polynomial division Polynomial divided by monomial Dividing polynomials 1 Dividing polynomials with remainders

8 Determine the quotient of two polynomials. Prove a polynomial identity and use it to describe numerical relationships. Activity 16 Binomial Theorem 16-1 Learning Targets: Find the number of combinations of an event. Create Pascal s triangle Learning Targets: Know the Binomial Theorem. Apply the Binomial Theorem to identify the coefficients or terms of any binomial expansion. Activity 17 Factors of Polynomials 17-1 Learning Targets: Determine the linear factors of polynomial functions using algebraic methods. Determine the linear or quadratic factors of polynomials by factoring the sum or difference of two cubes and factoring by grouping Learning Targets: Know and apply the Fundamental Theorem of Algebra. Write polynomial functions, given their degree and roots. Activity 18 Graphs of Polynomials 18-1 Learning Targets: Graph polynomial functions by hand or using technology, identifying zeros when suitable factorizations are available, and showing end behavior. Recognize even and odd functions from their algebraic expressions Learning Targets: Dividing polynomials with remainders example Pascal s Triangle Pascal s triangle for binomial expansion Binomial Theorem Binomial theorem Determining coefficient in binomial expansion Connecting Pascal s triangle to binomial combinatorics Algorithm for mentally computing binomial expansion coefficients Binomial theorem combinatorics connection Factoring Polynomials: Algebraic Methods Factor by grouping and factoring completely Example: basic grouping Example 1: Factoring by grouping Example 2: Factoring by grouping Example 3: Factoring by grouping Example 4: Factoring by grouping Example 5: Factoring by b y grouping Example 6: Factoring by grouping Difference of cubes factoring Factoring sum of cubes The Fundamental Theorem of Algebra Fundamental theorem of algebra Fundamental theorem of algebra for quadratic Possible number of real roots Graphing Polynomial Functions Polynomial end behavior Polynomial end behavior example Another polynomial end behavior example Polynomial end behavior exercise example Recognizing odd and even functions Connection between even and odd numbers and functions

9 Know and apply the Rational Root Theorem and Descartes Rule of Signs. Know and apply the Remainder Theorem and the Factor Theorem Learning Targets: Compare properties of two functions each represented in a different way. Solve polynomial inequalities by graphing. Finding the Roots of a Polynomial Function Synthetic division Synthetic division example 2 Why synthetic division works Polynomial remainder theorem Polynomial remainder theorem example Polynomial remainder theorem to test factor Polynomial remainder theorem proof Comparing Polynomial Functions Recognizing features of functions (example 1) Recognizing features of functions (example 2) Recognizing features of functions (example 3) Unit 4: Series, Exponential and Logarithmic Functions Activity 19 Arithmetic Sequences Arithmetic Sequences and Series Explicit and recursive definitions of sequences 19-1 Learning Targets: Arithmetic sequences Determine whether a given sequence is Finding the 100th term in a sequence arithmetic. Find the common difference of an Equations of sequence patterns arithmetic sequence. Arithmetic Series Write an expression for an arithmetic Explicitly defining a series sequence, and calculate the nth term. Sigma Notation 19-2 Learning Targets: Sigma notation for sums Write a formula for the nth partial sum of an arithmetic series. Writing a series in sigma notation Calculate partial sums of an arithmetic series Learning Targets: Identify the index, lower and upper limits, and general term in sigma notation. Express the sum of a series using sigma notation. Find the sum of a series written in sigma notation. Activity 20 Geometric Sequences and Series 20-1 Learning Targets: Identify the index, lower and upper limits, and general term in sigma notation. Geometric Sequences Geometric sequences introduction Geometric sequences Geometric Series Series as sum of sequence

10 Express the sum of a series using sigma notation. Find the sum of a series written in sigma notation Learning Targets: Derive the formula for the sum of a finite geometric series. Calculate the partial sums of a geometric series Learning Targets: Determine if an infinite geometric sum converges. Find the sum of a convergent geometric series. Activity 21 Exponential Functions and Graphs 21-1 Learning Targets: Identify data that grow exponentially. Compare the rates of change of linear and exponential data Learning Targets: Identify and write exponential Determine the decay factor or growth factor of an exponential function Learning Targets: Determine when an exponential function is increasing or decreasing. Describe the end behavior of exponential Identify asymptotes of exponential 21-4 Learning Targets: Explore how changing parameters affects the graph of an exponential function. Graph transformations of exponential 21-5 Learning Targets: Graph the function f(x) = e x. Graph transformations of f(x) = e x. Activity 22 Logarithms and Their Properties 22-1 Learning Targets: Complete tables and plot points for exponential data. Geometric series Formula for a finite geometric series Sum of an infinite geometric series Another derivation of the sum of an infinite geometric series Convergence and Divergence Geometric series convergence and divergence examples Exponential Functions Understanding linear and exponential models Exponential growth and decay word problems Decay of cesium 137 example Modeling ticket fines with exponential function Graphs of Exponential Functions Graphing exponential functions Constructing linear and exponential functions from graphs Exponential Functions Graphing exponential functions Constructing linear and exponential functions from data Matching functions to their graphs Logarithms

11 Write and graph an exponential function for a given context. Find the domain and range of an exponential function Learning Targets: Use technology to graph y = log x. Evaluate a logarithm using technology. Rewrite exponential equations as their corresponding logarithmic equations. Rewrite logarithmic equations as their corresponding exponential equations Learning Targets: Make conjectures about properties of logarithms. Write and apply the Product Property and Quotient Property of Logarithms. Rewrite logarithmic expressions by using properties Learning Targets: Make conjectures about properties of logarithms. Write and apply the Power Property of Logarithms. Rewrite logarithmic expressions by using their properties. Activity 23 Inverse Functions: Exponential and Logarithmic Functions 23-1 Learning Targets: Use composition to verify two functions as inverse. Define the logarithm of y with base b. Write the Inverse Properties for logarithms Learning Targets: Apply the properties of logarithms in any base. Compare and expand logarithmic expressions. Use the Change of Base Formula Learning Targets: Find intercepts and asymptotes of logarithmic Determine the domain and range of a logarithmic function. Logarithms Writing in logarithmic l and exponential form Introduction to logarithm properties Introduction to logarithm properties (part 2) Logarithms in Other Bases Change of base formula Change of base formula proof Graphing Logarithmic Functions Graphing logarithmic functions Graphs of logarithmic functions

13 Check the reasonableness of solutions. Activity 26 Inverses: Roots, Squares, and Cubes 26-1 Learning Targets: Graph and write the inverse of square root Find a square root model for a given table of data Learning Targets: Graph and write the inverse of square root Find the inverse relations of quadratic 26-3 Learning Targets: Graph and write the inverse of cube root Find the inverse relations of cubic Activity 27 Introduction to Rational Functions 27-1 Learning Targets: Formulate rational equations that model real-world situations. Graph equations on coordinate axes Learning Targets: Formulate rational equations that model real-world situations. Graph equations on coordinate axes Learning Targets: Determine the horizontal and vertical asymptotes of a rational function. Graph a rational function on the coordinate plane. Activity 28 Inverse Variation and Rational Functions 28-1 Learning Targets: Create, solve, and graph an equation involving inverse variation. Solve an equation involving combined variation Learning Targets: Describe transformations of the parent function f(x)=1/x and sketch the graphs. Inverse Functions Introduction to function inverses Function inverses example 2 Function inverses example 3 Graphs of Rational Functions Matching rational functions to their graphs Another rational function graph example A third example of graphing a rational function Asymptotes of Rational Functions Asymptotes of rational functions Horizontal and vertical asymptotes of function Direct and Inverse Variation Direct and inverse variation Recognizing direct and inverse variation

14 Identify the x-intercepts, y-intercepts, and asymptotes of transformations of the parent function f(x)=1/x. Activity 29 Simplifying Rational Expressions 29-1 Learning Targets: Simplify rational expressions. Multiply and divide rational expressions Learning Targets: Add and subtract rational expressions. Simplify complex fractions Learning Targets: Identify the vertical asymptotes of rational functions by finding the domain values that make the functions undefined. Use the degrees of the numerator and denominator of rational functions to identify the horizontal asymptotes Learning Targets: Analyze and graph rational functions, identifying any asymptotes, intercepts, and holes. Analyze and graph rational functions representing real-world scenarios. Activity 30 Rational Equations and Inequalities 30-1 Learning Targets: Solve rational equations, identifying any extraneous solutions. Create and solve rational equations that represent work problems Learning Targets: Solve rational inequalities by graphing. Solve rational inequalities by finding the sign of the inequality on either side of the numerator and denominator zeros. Multiplying and Dividing Rational Expressions Simplifying rational expressions introduction Simplifying rational expressions 1 Simplifying rational expressions 2 Simplifying rational expressions 2 Simplifying rational expressions 3 Multiplying and simplifying rational expressions Multiplying and dividing rational expressions 1 Multiplying and dividing rational expressions 2 Multiplying and dividing rational expressions 3 Adding and Subtracting Rational Expressions Adding and subtracting rational expressions Adding and subtracting rational expressions 2 Subtracting ting rational expressions Simplifying first for subtracting rational expressions Rationalizing denominators of expressions Finding Horizontal and Vertical Asymptotes Asymptotes of rational functions Horizontal and vertical asymptotes of function Graphing Rational Functions Matching rational functions to their graphs Another rational function graph example A third example of graphing a rational function Solving Rational Equations Ex 1: Multi step equation Rational equations Solving rational equations 1 Solving rational equations 2 Solving rational equations 3 Applying rational equations 1 Applying rational equations 2 Applying rational equations 3 Extraneous solutions to rational equations Solving Rational Inequalities

16 Identify periodic Find the period, midline, and amplitude of periodic 34-2 Learning Targets: Graph the sine function, y = a sin b x. Find the period, midline, and amplitude of sine 34-3 Learning Targets: Graph the cosine function, y = a cos bx. Find the period, midline, and amplitude of cosine 34-4 Learning Targets: Graph the tangent function, y = a tan b x. Find the period, and midline of tangent 34-5 Learning Targets: Describe and graph functions of the form y = a sin b(x h) + k, y = a cos b(x h) + k, and y = a tan b(x h) + k. Find the period, amplitude, and midline of these trigonometric Activity 35 Choosing Functions to Model Periodic Phenomena 35-1 Learning Targets: Use trigonometric functions to model realworld periodic phenomena. Identify key features of these Plotting maxima, minima and midline intersections of trig function Sine Function Example: Graph, domain, and range of sine function Cosine Function Example: Graph of cosine Example: Intersection of sine and cosine Transformations Example: Amplitude and period transformations Example: Amplitude and period cosine transformations Tangent graph Tangent Function Modeling Periodic Phenomena Modeling annual temperature variation with trigonometry Applying inverse trig function with model Modeling temperature through the day Day length in Alaska Example: Figure out the trig function Determining the equation of a trig function Unit 7: Probability and Statistics Activity 36 Distribution Normal Distribution Comparing means of distributions 36-1 Learning Targets: Means and medians of different distributions Represent distribution with appropriate Normal Distribution data plots. Interpret shape of a distribution and relate shape to measures of center and spread. Introduction to the normal distribution 36-2 Learning Targets: normal distribution problems: Qualitative sense of Recognize characteristics of a normal normal distributions distribution. Use mean and standard deviation to completely describe a normal distribution Learning Targets: Estimate probabilities associated with z- scores using normal curve sketches.

17 Determine probabilities for z-scores using a standard normal table Learning Targets: Determine probabilities for z-scores using technology. Use a normal distribution, when appropriate, as a model for a population from which a sample of numeric data has been drawn. Activity 37 Random Sampling 37-1 Learning Targets: Explain why random sampling is advantageous when conducting a survey 37-2 Learning Targets: Explain why random allocation of treatments is critical to a good experiment Learning Targets:.Identify a confounding variable in an observational study. Activity 38 Simulations Activity 39 Margin of Error 39-1 Learning Targets: Use margin of error in an estimate of a population proportion. Use simulation models for random samples Learning Targets: Use margin of error in an estimate of a population proportion. Relate margin of error to the population proportion and to the sample size. Activity 40 Designing and Conducting Simulations Sampling Introduction to random sampling Random sampling intuition Reasonable samples Inferring population mean from sample s mean N/A Error Standard error of the mean Population standard deviation Sample standard deviation and bias Sampling distribution of the sample mean Sampling distribution of the sample mean 2 Sampling distribution example problem N/A

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