Unit Overview. Content Area: Algebra 2 Unit Title: Preparing for Advanced Algebra Target Course/Grade Level Duration: 10 days

 Oswald Freeman
 3 months ago
 Views:
Transcription
1 Content Area: Algebra 2 Unit Title: Preparing for Advanced Algebra Target Course/Grade Level Duration: 10 days 11 th or 12 th graders Description This chapter 0 contains lessons on topics from previous courses. We use this chapter as a review of topics that students previously completed in other courses. We will review several concepts, skills, and vocabulary terms. Students are evaluated by a unit test along with other alternate assessments throughout the unit. Representing functions FOIL Factoring polynomials Counting techniques Adding probabilities Multiplying probabilities Congruent and similar figures The Pythagorean theorem Measures of center, spread and position CPI Codes FIF.HS.04 FIF.HS.05 GCO.HS.01 GCO.HS.07 GMG.HS.03 GSRT.HS.02 GSRT.HS.05 GSRT.HS.08 SMD.HS.06 SMD.HS st Century Themes and Skills See addendum What is the domain of a function? What is the range of a function? What does FOIL method mean? How to factor polynomials? How to find the total number of outcomes? How to find the probabilities of compound, independent, and dependent events? What are congruent figures? What are similar figures? What is the Pythagorean Theorem? How to find the measures of center, spread, and position? Identify the domain and range of functions. Use the FOIL method to multiply binomials. Use various techniques to factor polynomials. Find the total number of outcomes using of outcomes using a variety of methods. Compute theoretical and experimental probabilities. Compute probabilities of compound events. Find probabilities of independent and dependent events. Identify and use congruent and similar figures. Use the Pythagorean Theorem and its converse. Find measures of center, spread, and position.
2 Students will... Identify the domain and range of functions. Use the FOIL method to multiply binomials. Use various techniques to factor polynomials. Find the total number of outcomes using of a variety of methods. Compute theoretical and experimental probabilities. Compute probabilities of compound events. Find probabilities of independent and dependent events. Identify and use congruent and similar figures. Use the Pythagorean Theorem and its converse. Find measures of center, spread, and position. Locate coordinates Use a mapping illustration Use the Distributive Property Use factors and sums Use special products Fundamental counting principle Permutations of n objects taken r at a time Combinations of n objects taken r at a time Theoretical and experimental probability Probability of independent events Probability of dependent events Conditional probability Twoway frequency table Determine congruency Determine similarity Solve a problem involving similarity Find hypotenuse measures Find leg measures Identify a right triangle Measures of center Measures of spread Fivenumber summary Effect of an outlier Content Area: Mathematics Unit Title: Algebra 2 Equations and Inequalities. Target Course/Grade Level 11 th and/or 12 th graders Duration: 23 Days Description : Students begin this unit by using a number line to graph and order real numbers and by identifying the properties of real numbers in operations. After evaluating and simplifying algebraic expressions, students solve linear equations. They also rewrite equations with more than one variable, including formulas. To set up and solve reallife applications, students use a general fivestep problem solving plan, and implement various strategies such as drawing a model or looking for a pattern. Finally students use these skills to solve simple and compound inequalities as well as absolute value equations and inequalities. Students are evaluated by a unit test along with other alternate assessments throughout the unit.
3 Expressions and formulas Properties of real numbers Solving equations Solving absolute value equations Solving inequalities Solving compound and absolute value inequalities CPI Codes Use the order of operations to evaluate expressions. Use formulas. Classify real numbers. Use the properties of real numbers to evaluate expressions. Translate verbal expressions into algebraic expressions and equations and vice versa. Solve equations using the properties of equality. Evaluate expressions involving absolute values. Solve absolute value equations. Solve onestep inequalities. Solve multistep inequalities. Solve compound inequalities. Solve absolute value inequalities. MA.CC APR.HS.01 CED.HS.04 REI.HS.01 REI.HS st Century Themes and Skills See addendum What is the order of operations? How do we classify real numbers? What are the common properties to evaluate expressions? How do you evaluate expressions? How do we solve absolute value equations? How do we solve onestep inequalities? How do we solve compound inequalities? How do we solve absolute value inequalities? Students will... Use the order of operations to evaluate expressions. Use formulas. Classify real numbers. Use the properties of real numbers to evaluate expressions. Translate verbal expressions into algebraic expressions and equations and vice versa. Solve equations using the properties of equality. Evaluate expressions involving absolute values. Solve absolute value equations. Solve onestep inequalities. Solve multistep inequalities.
4 Solve compound inequalities. Solve absolute value inequalities. Review the graphing of equations on a plane. (y=mx + b) Apply method to reallife situations: wreaths for the holiday s problem. Discuss solutions as they relate to graphs and the kinds of solutions possible. (One, none, many). Use the linear combination method to solve a system when terms are lined up, when they are not lined up, when neither, one or both need to be multiplied in order to be solved. Determine the number of solutions to a given system and why. Use the substitution method to solve a system when it is in the y=mx+b form and when it has to be rewritten. Determine the number of solutions to a given system and why. Determine the bounds formed by constraints in order to find optimized values. Use optimization method on reallife situations. Evaluate functions of two variables. Plot points in three dimensions. Graph linear equations in three variables. Content Area: Algebra 2 Unit Title: Polynomials and Polynomial Functions Target Course/Grade Level 11 th and/or 12th Duration: 18 Days Description Students use properties of exponents and scientific notation to simplify algebraic expressions and to model reallife problems. They use synthetic substitution to evaluate polynomial expressions. They also graph polynomials and investigate their end behavior. They will add, subtract, multiply and divide polynomial functions and will use factoring, synthetic division, and rational zero theorem to find the zeros of polynomial functions. Students will see how the fundamental theorem of algebra can be used to determine the number of solutions of a polynomial equation and will use graphing calculators to approximate the real zeros of a polynomial function. They will use zeros to write polynomial functions and they will use xintercepts and turning points to graph polynomial functions. Students are evaluated by a unit test along with other alternative assessments throughout the unit. Operations with polynomials Dividing polynomials Polynomial functions Analyzing graphs of polynomial functions Solving polynomial equations The remainder and factor theorems Roots and zeros Rational zero theorem Multiply, divide and simplify monomials and expressions involving powers. Add, subtract, and multiply polynomials. Divide polynomials using long division. Divide polynomials using synthetic division. Evaluate polynomial functions. Identify general shapes of graphs of polynomial functions. Graph polynomial functions and locate their zeros. Find the relative maxima and minima of polynomial functions. Factor polynomials. Solve polynomial equations by factoring. Evaluate functions by using synthetic substitution. Determine whether a binomial is a factor of a polynomial by using synthetic substitution. Determine the number and type of roots for a polynomial equation. Find the zeros of a polynomial function. Identify possible rational zeros of a polynomial function.
5 CPI Codes APR.HS.01 APR.HS.02 APR.HS.03. APR.HS.04 APR.HS.05 REI.HS.11 NQ.HS.03 Find all of the rational zeros of a polynomial function. 21 st Century Themes and Skills See addendum What is a power? What is a base? What is the product of powers property? What is the power of a power property? What is the negative exponent property? What is the zero exponent property? What is the quotient of powers property? What is the power of a quotient property? How do you simplify expressions using the properties of exponents? What is a polynomial function? What is the leading coefficient? What is the degree of a polynomial function? What is the standard form of a polynomial function? How do you identify a polynomial function? How do you evaluate a polynomial function? What is direct substitution? What is synthetic substitution? How do you graph a polynomial function? How do you add polynomials? How do you subtract polynomials? How do you multiply polynomials? How do you factor a quadratic expression? How do you factor a polynomial expression? How do you factor the sum or difference of cubes? How do you factor by grouping? How do you factor polynomials in quadratic form? How do you solve polynomials equations using factoring? What is the remainder theorem? What is the factor theorem? How does the remainder theorem relate to the factor theorem? How do you divide a polynomial using polynomial long division? How do you divide a polynomial using synthetic division? What is the rational zero theorem? How do you find the rational zeros of a polynomial function using the rational zero theorem? How are zeros, factors, solutions, and xintercepts closely related? How do you use xintercepts to graph a polynomial function? What are turning points of a polynomial function?
6 How do you find turning points? What is the local maximum and minimum of a polynomial function? What is a cubic function? What is a finite difference? How do you find finite differences? What are the properties of finite differences? How do you model with finite differences? How do you model with cubic regression? Students will... Multiply, divide and simplify monomials and expressions involving powers. Add, subtract, and multiply polynomials. Divide polynomials using long division. Divide polynomials using synthetic division. Evaluate polynomial functions. Identify general shapes of graphs of polynomial functions. Graph polynomial functions and locate their zeros. Find the relative maxima and minima of polynomial functions. Factor polynomials. Solve polynomial equations by factoring. Evaluate functions by using synthetic substitution. Determine whether a binomial is a factor of a polynomial by using synthetic substitution. Determine the number and type of roots for a polynomial equation. Find the zeros of a polynomial function. Identify possible rational zeros of a polynomial function. Find all of the rational zeros of a polynomial function. Evaluate a polynomial function using direct substitution and synthetic substitution. Graph polynomials Use the properties of exponents and scientific notation in a reallife problem. Model polynomial subtraction and multiplication. Solve a polynomial equation by factoring. Divide a polynomial using polynomial long division and by using synthetic division. Find the rational zeros of a polynomial function using the rational zero theorem. Test the zeros using synthetic division. Use the fundamental theorem of Algebra to determine the number of zeros a polynomial function has. Determine the zeros of a polynomial function. Use zeros to write a polynomial function. Graph a polynomial function using xintercepts. Find the turning points of a polynomial function. Content Area: Algebra 2 Unit Title: Inverses and Radical Functions and Relations Target Course/Grade Level Duration: 15 Days 11 th and/or 12th Description Students learn how to evaluate nth roots of real numbers using both radical and exponential notation. They use properties of rational exponents to evaluate and simplify expressions, and they evaluate power functions and perform arithmetic operations with functions as well as composition of functions. They will find inverses of functions, and they observe the graphing of square root and cube root functions. Students will solve equations that have radicals or rational exponents. They use roots, rational exponents, power functions, function operations, and radical equations to solve reallife problems. Students are evaluated by a unit test along with other alternate assessments throughout the unit.
7 CPI Codes Operations on functions Inverse functions and relations Square root functions and inequalities Nth roots Operations with radical expressions Rational exponents Solving radical equations and inequalities REI.HS.02 FBF.HS.04 FIF.HS.01 FIF.HS.02 FIF.HS.07 FIF.HS.08 N RN.HS.01 N RN.HS.02 N RN.HS.03 Find the sum, difference, product, and quotient of functions. Find the composition of functions. Find the inverse of a function or relation. Determine whether two functions or relations are inverses. Graph and analyze square root functions. Graph square root inequalities. Simplify radicals. Use a calculator to approximate radicals. Simplify radical expressions. Add, subtract, multiply, and divide radical expressions. Write expressions with rational exponents in radical form and vice versa. Simplify expressions in exponential or radical form. Solve equations containing radicals. Solve inequalities containing radicals. 21 st Century Themes and Skills See addendum How to evaluating Nth Roots? How to using Nth Roots in Real Life? How do you find the nth root of a number? How do you evaluate expressions with rational exponents? How do you solve equations using nth roots?
8 How do you use properties of rational exponents to simplify expressions How do you use write radicals in simplest form? How do you add and subtract roots and radicals? How to use properties of rational exponents in real life? How do you add and subtract functions? How do you multiply and divide functions? How do you find the composition of functions? Students will... Find the sum, difference, product, and quotient of functions. Find the composition of functions. Find the inverse of a function or relation. Determine whether two functions or relations are inverses. Graph and analyze square root functions. Graph square root inequalities. Simplify radicals. Use a calculator to approximate radicals. Simplify radical expressions. Add, subtract, multiply, and divide radical expressions. Write expressions with rational exponents in radical form and vice versa. Simplify expressions in exponential or radical form. Solve equations containing radicals. Solve inequalities containing radicals. Evaluating nth roots of real numbers using both radical notation and rational exponent notation. Using properties of rational exponents to evaluate and simplify expression Perform operations with functions including power functions. Find inverses of linear functions and find inverses of nonlinear functions. Graph square root and cube root functions. Solve equations that contain radicals or rational exponents. Use measures of central tendency and measures of dispersion to describe data sets and use boxandwhisker plots and histograms to represent data graphically. Content Area: Algebra 2 Unit Title: Exponential and Logarithmic Functions and Relations Target Course/Grade Level 11 th and/or 12th Duration: days Description The chapter begins by defining b to the x power, when x is an integer and extending the existing properties to include rational exponents. The meaning of b to the x power is extended to include irrational values of x. Students relate to the exponential functions. Students define composites and inverse functions, leading to the definition of the logarithmic function as the exponential inverse. The culmination of the topic ends in students solving equations of the type 2 to the x = 5. Students extend and apply these skills to reallife situations. Evaluation of student learning occurs via homework, quizzes and test upon completion of the chapter.
9 Graphing exponential functions Solving exponential equations and inequalities Logarithms and logarithmic functions Solving logarithmic equations and inequalities Properties of logarithms Common logarithms Base e and natural logarithms Using exponential and logarithmic functions CPI Codes FLE.HS.02 FLE.HS.03 FLE.HS.04 Graph exponential growth functions. Graph exponential decay functions. Solve exponential equations. Solve exponential inequalities. Evaluate logarithmic expressions. Graph logarithmic functions. Solve logarithmic equations. Solve logarithmic inequalities. Simplify and evaluate expressions using the properties of logarithms. Solve logarithmic equations using the properties of logarithms. Solve exponential equations and inequalities using common logarithms. Evaluate logarithmic expressions using the change of base formula. Evaluate expressions involving the natural base and natural logarithm. Solve exponential equations and inequalities using natural logarithms. Use logarithms to solve problems involving exponential growth and decay. Use logarithms to solve problems involving logistic growth. 21 st Century Themes and Skills See addendum What is the exponential form? What is the radical form? What is an exponent equation? What does the graph of an exponential function look like? What is the composite of the functions? What are the inverse functions? What is log? How do you write an equation in logarithmic form? How do you solve a logarithmic equation? What are the laws of logarithms? How can one use a calculator to find logarithms? How can solve an exponential equation using logarithms? What is exponential growth? What is exponential decay? What is the natural logarithm?
10 Students will... Graph exponential growth functions. Graph exponential decay functions. Solve exponential equations. Solve exponential inequalities. Evaluate logarithmic expressions. Graph logarithmic functions. Solve logarithmic equations. Solve logarithmic inequalities. Simplify and evaluate expressions using the properties of logarithms. Solve logarithmic equations using the properties of logarithms. Solve exponential equations and inequalities using common logarithms. Evaluate logarithmic expressions using the change of base formula. Evaluate expressions involving the natural base and natural logarithm. Solve exponential equations and inequalities using natural logarithms. Use logarithms to solve problems involving exponential growth and decay. Use logarithms to solve problems involving logistic growth. Write an expression in exponential form Write an expression in simplest radical form Show the graph of exponential function. Solve an exponential equation. Find the composition of functions. Show the inverse of a function. Evaluate functions. Write an equation in exponential form. Write an equation in logarithmic form. Simplify logarithms. Content Area: Algebra 2 Unit Title: Linear Equations and Functions Target Course/Grade Level 11 th and/or 12th Duration: 27Days Description Students begin this unit by identifying and representing relations and functions, and by graphing and evaluating linear functions. They find the slope of a line, and identify parallel and perpendicular lines from their slopes. Students generalize slope as a rate of change. They graph linear equations using both slopeintercept and standard forms and identify and graph horizontal and vertical lines. They write equations of lines using the slope and intercept, a point and the slope, or two points. Students write direct variation equations. They explore positive and negative correlation using scatter plots, and approximate bestfitting lines. Students then complete the unit by graphing linear inequalities in two variables, piece wise functions, and absolute value functions, while using all of these to model reallife applications. Students are evaluated by a unit test along with other alternate assessments throughout the unit. Relations and functions Linear relations and functions Rate of change and slope Analyze relations and functions. Use equations of relations and functions. Identify linear relations and functions.
11 CPI Codes Garfield High School Writing linear equations Scatter plots and lines of regression Special functions Parent functions and transformations Graphing linear and absolute value inequalities CED.HS.02 REI.HS.10 REI.HS.11 FIF.HS.01 FIF.HS.02 FIF.HS.07 SID.HS.07 SID.HS st Century Themes and Skills See addendum What is a function? What forms of equations do you know? What is the slopeintercept form of a line? What forms of equations do you know? What is a scatter plot? What is the first step in graphing an inequality on a plane? What does piecewise mean? What is meant by absolute value? Students will... Analyze relations and functions. Use equations of relations and functions. Identify linear relations and functions. Write linear equations in standard form. Write an equation of a line given the slope and a point on the line. Write an equation of a line parallel or perpendicular to a given line. Write linear equations in standard form. Write an equation of a line given the slope and a point on the line. Write an equation of a line parallel or perpendicular to a given line. Use scatter plots and prediction equations. Model data using lines of regression. Write and graph piecewisedefined functions. Write and graph step and absolute value functions. Identify and use parent functions. Describe transformations of functions. Graph linear inequalities. Graph absolute value inequalities.
12 Use scatter plots and prediction equations. Model data using lines of regression. Write and graph piecewisedefined functions. Write and graph step and absolute value functions. Identify and use parent functions. Describe transformations of functions. Graph linear inequalities. Graph absolute value inequalities. Represent relations and functions as well as to graph and evaluate linear functions. Find slopes of lines and classify parallel and perpendicular lines as well as solving reallife problems. Use the slopeintercept form of a line to graph linear equations. Write linear equations in different forms given various types of data: slopes, points, intercepts, or graphs. Graph linear inequalities in two variables on a plane. Represent piecewise functions on a graph and to use piecewise functions to represent reallife situations. Represent and write absolute value functions. Content Area: Algebra 2 Unit Title: Quadratic Functions and Relations Target Course/Grade Level 11 th and/or 12th Duration: 23 Days Description Students are led through all major topics involving quadratic functions. First quadratic equations are graphed and then the standard, vertex and intercept forms are introduced. These forms are used throughout the unit and students learn to convert between them. Quadratic expressions are factored then quadratic equations are solved by factoring, finding square roots, completing the square or using the Quadratic Formula. Factoring is also used to find the zeroes of quadratic function. Students solve quadratic equations with complex solutions and perform operations with complex numbers. The discriminate is used to determine the number and nature of the solutions to a quadratic equation. Students are evaluated by a unit test along with other alternate assessments throughout the unit. Graphing quadratic functions Solving quadratic equations by graphing Solving quadratic equations by factoring Complex numbers Completing the square The quadratic formula and the discriminate Transformations of quadratic graphs Quadratic inequalities Graph quadratic functions. Find and interpret the maximum and minimum values of a quadratic function. Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing. Write quadratic equations in standard form. Solve quadratic equations by factoring. Perform operations with pure imaginary numbers. Perform operations with complex numbers. Solve quadratic equations by using the Square Root Property. Solve quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula.
13 CPI Codes Garfield High School Use the discriminate to determine the number and type of roots of a quadratic equation. Write a quadratic function in the form Transform graphs of quadratic functions of the form Graph quadratic inequalities in two variables. Solve quadratic inequalities in one variable. REI.HS.10 N CN.HS.01 N CN.HS.02 N CN.HS.03 N CN.HS.04 N CN.HS.05 N CN.HS.07 N CN.HS st Century Themes and Skills See addendum How do we graph a quadratic function? What are the maximum and the minimum values of a quadratic function? How do we estimate the solutions of a quadratic equation? How do we factor quadratic equations? What is an imaginary number? What is a complex number? How do we perform operations with imaginary and complex numbers? What is the Square Root Property? What is the quadratic formula? How can we use the discriminate to predict the type and number of solutions in a quadratic equation? What is the vertex formula of a quadratic equation? How do we solve quadratic inequalities with one or two variables? Students will... Graph quadratic functions. Find and interpret the maximum and minimum values of a quadratic function.
14 Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing. Write quadratic equations in standard form. Solve quadratic equations by factoring. Perform operations with pure imaginary numbers. Perform operations with complex numbers. Solve quadratic equations by using the Square Root Property. Solve quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula. Use the discriminate to determine the number and type of roots of a quadratic equation. Write a quadratic function in the form Transform graphs of quadratic functions of the form Graph quadratic inequalities in two variables. Solve quadratic inequalities in one variable. Graphing quadratic function and writing it in standard form Using the quadratic model Factoring a trinomial and monomial. Solving a quadratic equation by finding the zeros Using a quadratic equation as a model. Modeling a falling object s height with a quadratic faction. Adding, subtracting, multiplying, dividing and finding the absolute value of complex numbers. Solving a quadratic equation with two real numbers and two imaginary numbers. Solving vertical motion problems. Using a quadratic inequality as a model Writing a quadratic function in a vertex form. Finding a quadratic model for data set. Using a quadratic recession to find model. Content Area: Algebra 2 Unit Title: Rational Functions and Relations Target Course/Grade Level 11 th and/or 12th Duration: 15 days Description Students study rational algebraic expressions studied. The laws of exponents are reviewed and extended to include zero and negative exponents. Students use scientific notation by applying the law of exponents in practical applications. They will simplify, add, subtract, multiply, and divide rational expressions in word problems. Students then extend the skills to solve equations with fractional coefficients and fractional equations. They also extend and apply these skills to reallife situations. Variation is presented by way of problems in physics and other areas. Students apply direct variation and proportion with real life application. Inverse and joint variation follows. Long division for polynomials is presented and is related synthetic division introduced. Students extend and apply these skills to reallife situations. Evaluation of student learning occurs via homework, quizzes and test upon completion of the chapter. Multiplying and dividing rational expressions Adding and subtracting rational expressions. Graphing reciprocal functions Simplify rational expressions. Simplify complex fractions. Determine the LCM of polynomials.
15 CPI Codes Graphing rational functions Variation functions Solving rational equations and inequalities APR.HS.01 APR.HS.02 APR.HS.03 APR.HS.04 APR.HS.06 APR.HS.07 CED.HS.01 SSE.HS.02 APR.HS.01 APR.HS.07 SSE.HS.03 SSE.HS.04 FBF.HS.01 FBF.HS.03 Add and subtract rational expressions. Determine properties of reciprocal functions. Graph transformations of reciprocal functions. Recognize and solve direct and joint variation problems. Recognize and solve inverse and combined variation problems. Solve rational equations. Solve rational inequalities.
16 FIF.HS.08 FIF.HS.09 FLE.HS st Century Themes and Skills See addendum How do you simplify fractions with exponents? How do you simplify expressions with zero and negative exponents? How do you write a number in scientific notation? How do you simplify rational expression? What are the domain and the zeros of a given function? How do you find a significant digit? How do you simplify rational expression using addition and subtraction? How do you simplify complex fractions? How do you solve an equation with fractional coefficients? How do you solve an inequality with fractional coefficients? How do you solve a fractional equation? What is direct variation? How to find the constant in direct variation? What is Inverse Variation? What is Joint Variation? Students will... Simplify rational expressions. Simplify complex fractions. Determine the LCM of polynomials. Add and subtract rational expressions. Determine properties of reciprocal functions. Graph transformations of reciprocal functions. Recognize and solve direct and joint variation problems. Recognize and solve inverse and combined variation problems. Solve rational equations. Solve rational inequalities. Simplify fractions with exponents. Write expressions in simplest form without negative or zero exponents. Find a onesignificantdigit estimate of each given quotient. Find the domain of each given function and its zeros, if any. Simplify given rational expressions. Solve inequality and equations. Solve problems involving direct variation and find the constant of direct variation. Use synthetic division to divide a polynomial by a binomial. Divide one polynomial by another polynomial. Content Area: Algebra 2 Unit Title: Systems of Linear Equations and Inequalities Target Course/Grade Level 11 th and/or 12th
17 Duration: 25 Days Description In this unit students learn to solve systems of two linear equations in two variables algebraically and by graphing. Included are these systems with one solution, no solution, and many solutions. They also learn to graph the solutions of systems of linear inequalities. Systems of linear equations and inequalities are used to model and solve reallife problems. The work with linear equations is extended to linear programming problems, which are used to solve reallife optimization problems. Students learn to add, subtract and multiply matrices by a scalar and by another matrix. They then use these operations to solve realworld problems. Students find determinants of a 2 x 2 and a 3 x 3 matrix. Then, using Cramer's Rule, the determinants are used to solve systems of equations. Students are evaluated by a unit test along with other alternative assessments throughout the unit. The graphing calculator becomes an invaluable at this point, as the value of the determinant is calculated using this technology. Students are evaluated by a unit test along with other alternate assessments throughout the unit. Solving systems of equations Solving systems of inequalities by graphing Optimization with linear programming Systems of equations in three variables Operations with matrices Multiplying matrices Solving systems of equations using Cramer s Rule Solving systems of equations using inverse matrices CPI Codes REI.HS.01 REI.HS.05 REI.HS.06 REI.HS.10 Solve systems of linear equations graphically. Solve systems of linear equations algebraically. Solve systems of inequalities by graphing. Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. Find the maximum and minimum values of a function over a region. Solve realworld optimization problems using linear programming. Solve systems of linear equations in three variables. Solve realworld problems using systems of linear equations in three variables. Analyze data in matrices. Perform algebraic operations with matrices. Multiply matrices. Use the properties of matrix multiplication. Evaluate determinants. Solve systems of linear equations by using Cramer s Rule. Find the inverse of a 2 Write and solve matrix equations for a system of equations.
18 REI.HS.12 N VM.HS.06 N VM.HS.07 N VM.HS.08 N VM.HS.09 N VM.HS.10 N VM.HS.11 N VM.HS st Century Themes and Skills See addendum What is the order of a matrix? How do you know if you can perform operations on two matrices? What are equal matrices? What are corresponding entries? How do you add or subtract two matrices? What is a scalar? How do you multiply a matrix by a scalar? How do you determine if you two matrices can be multiplied together? How do you determine the order of the product of two matrices? How do you calculate the product of two matrices? What is a square matrix? What is a determinant? How do you find the determinant of a 2x2 matrix? How do you find the determinant of a 3x3 matrix? What is Cramer's Rule? How do you solve a linear system of equations using Cramer's rule? What is and identity matrix? What does a 2x2 identity matrix look like? What does a 3x3 identity matrix look like? What are the relationship between and identity and inverse matrix? How do you determine the inverse of a 2x2 matrix? How do you determine the inverse of a 2x2 matrix? How do you solve linear systems of equations using inverse matrices?
19 Students will... Solve systems of linear equations graphically. Solve systems of linear equations algebraically. Solve systems of inequalities by graphing. Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. Find the maximum and minimum values of a function over a region. Solve realworld optimization problems using linear programming. Solve systems of linear equations in three variables. Solve realworld problems using systems of linear equations in three variables. Analyze data in matrices. Perform algebraic operations with matrices. Multiply matrices. Use the properties of matrix multiplication. Evaluate determinants. Solve systems of linear equations by using Cramer s Rule. Find the inverse of a 2 Write and solve matrix equations for a system of equations. Review the graphing of equations on a plane. Apply method to reallife situations. Discuss solutions as they relate to graphs and the kinds of solutions possible. Use the linear combination method to solve a system when terms are lined up, when they are not lined up, when neither, one or both need to be multiplied in order to be solved. Determine the number of solutions to a given system and why. Graph systems of inequalities on a plane Determine the bounds formed by constraints in order to find optimized values Determine the optimized value for an unbounded region. Use o Identify and compare the orders of two matrices. Add and subtract two matrices. Multiply a matrix by a scalar. Determine if two matrices can be multiplied. Describe the order of matrix products Calculate the products of two matrices. Find the determinant of a 2x2 matrix Find the determinant of a3x3 matrix. Solve a linear system of equations using Cramer's Rule. Recognize 2x2 and 3x3 identity matrices Determine the inverse of a 2x2 matrix. Optimization method on reallife situations. Plot points in three dimensions.
20 Content Area: Algebra 2 and Trigonometry Unit Title: Products and Factors of Polynomials Target Course/Grade Level: Duration: 3 weeks Description : This chapter consists of working with polynomials, factors of polynomials and applications of factoring. The terminology of polynomials is reviewed and the laws of exponents are used to develop the concepts used to find the products of polynomials. Greatest common factors and least common multiples are used to develop methods of factoring polynomials. Students develop methods to illustrate how to solve polynomial equations, inequalities and word problems. These skills are applied to reallife situations. Student learning is evaluated via homework, quizzes and test upon completion of the chapter. Laws of Exponents Factoring Polynomials Applications of Factoring to Problem Solving RealLife Extension of Factoring to Problem Extending Problem Solving Methods to Inequalities CPI Codes APR.HS. 01 APR.HS. 02 APR.HS. 03 APR.HS. 04 APR.HS. The laws of exponents can be applied to simplify complex polynomial expressions. Rewriting sum and differences into products is essential in algebra. Operations with polynomials must utilize laws of exponents. Factoring quadratic polynomials using GCF, difference of two squares, perfect trinomial squares, general method, sum/difference of two cubes and grouping is essential to problem solving. Applying factoring methods to general quadratic equations is a basic concept. RealLife problem solving by applying methods of factoring gives validity to studying factoring. The extension of solving equations can be extended and broadened to inequalities.
21 05 APR.HS. 06 APR.HS st Century Themes and Skills See Addendum What is the degree of a polynomial? How do you add polynomials? How do you subtract polynomials? What does simplify a polynomial mean? How do you simplify a product of powers? When do you use a power of a product? How do you simplify a power of a power? How do you multiply two binomials? How do you multiply a binomial with a polynomial? What is the prime factorization? How do you find the GCF of integers and monomials? How do you find the LCM of integers and monomials? What is a perfect square trinomial? What does a difference of squares mean? How do you factor the sum and the difference of cubes? Why does regrouping a polynomial is important? How to factor a trinomial? How to factor a trinomial with a coefficient that is negative or positive? How to determine whether a polynomial is prime? How to set an equation to zero? How to factor a polynomial equation? How to find the zeros of an equation or function? How do you know how to set up a polynomial equation for a certain word problem? How do you find and graph the solution set of a polynomial inequality? Students will... Simplify, add, and subtract polynomials. Use the laws of exponents to multiply a polynomial by a monomial. Multiply polynomials. Find the Greatest Common Factor and the Least Common Multiple of integers and monomials. Factor polynomials by using the GCF, by recognizing special products, and by grouping terms. To factor quadratic polynomials. Solve polynomial equations. Solve problems in reallife situations using polynomial equations. Solve polynomial inequalities. Write the degree of a polynomial. Add, subtract and simplify polynomials. Simplify the product of a power and the power of a product. Multiply two binomials. Multiply and simplify a binomial and a polynomial.
22 Prime factorization of an integer. GCF and LCM of 2 integers. Find the GCF and LCM of monomials. Factor a trinomial that is the sum or difference of squares. Factor a sum or a difference of 2 cubes. Polynomial by regrouping. trinomial where the coefficient of x^2 is 1 trinomial where the coefficient of x^2 is Determine that a polynomial is prime. Set an equation to zero. Factor a polynomial equation. Find the zeros of an equation or a function. Solve reallife situations using polynomial equations. Content Area: Algebra 2 and Trigonometry Unit Title: Inequalities Target Course/Grade Level: Duration: 2 weeks Description : Students are presented with the basic techniques of solving equations and this procedure is extended to inequalities. Methods for solving inequalities involving conjunction and disjunction and methods for solving inequalities involving absolute value are also introduced. Students solve absolute value problems h algebraically and graphically. These skills are extended to reallife situations. Student learning is evaluated via homework, quizzes and test upon completion of the chapter. Inequalities in One Variable. Combined Inequalities. Problem Solving with Inequalities. Absolute Value in Open Sentences CPI Codes REI.HS.03 REI.HS.04 REI.HS.10 REI.HS.11 Use of the number line to see that there are an infinite number of solutions to inequalities. Disjunction and conjunction illustrate union and intersection of sets to solve combined inequalities. Applications of algebraic solutions to inequalities are studied. Absolute value problems are solved both graphically and algebraically.
23 REI.HS st Century Themes and Skills See Addendum How do you solve and graph a linear inequality? How do you solve and graph an inequality with the variable on both sides? How do you graph the solution set of a conjunction? How do you graph the solution set of a compound inequality? How do you graph the solution set of a disjunction? What does the expression "at least" mean? How can I find consecutive integers whose sum is a certain number? How do you solve an absolute value equation? How do you solve an absolute value inequality using <? How do you solve an absolute value inequality using >? What is the distance between the graphs of each pair of numbers? How do you solve graphically an absolute value equation? How do you solve graphically an absolute value inequality using < or >? Students will... Solve simple inequalities in one variable. Solve conjunctions and disjunctions. Solve word problems by using inequalities in one variable. Solve open sentences involving absolute value. Use number lines to obtain quick solutions to certain equations and inequalities involving absolute value. Solve & graph a various linear inequality and inequalities with the variable on both sides. Graph the solution set of a conjunction, disjunction and compound inequality. Solve a word problem with consecutive integers in an inequality. To solve an absolute value inequality using <,> and an absolute value equation. To solve using a graph an absolute value equation. To solve using a graph an absolute value inequality with > and <. Content Area: Algebra 2 and Trigonometry Unit Title: Target Course/Grade Level: Duration: 3 Weeks The Language of Algebra Description : Students review the basic concepts and skills of algebra studied in previous courses. This includes real numbers and expressions, operations with real numbers and problem solving in realworld situations so that students can see practical applications of algebra being taught. Emphasis is placed on dealing with real numbers symbolically and in context of word problems. Student learning is evaluated with quizzes and a chapter test upon completion of the chapter. Real Numbers All real numbers can be represented on a number
24 Order of Operations Simplifying Expressions. Field Properties of Real Numbers. Solving Equations. line which will reinforce the relationships between rational and irrational numbers and help in understanding the order. The need to use the order of operations is required to simplify mathematical expression. Algebraic expressions are converted to numerical expressions and the order of operations is used to simply. Applications of the field properties of equality, closure, associative, commutative, inverse, identity and distributive laws are required to solve equations. The plan for problem solving is necessary so that word problems can be set up and solved. CPI Codes CED.HS.01 CED.HS.03 REI.HS.03 REI.HS.04 SSE.HS.01 SSE.HS.03 N RN.HS.01 N RN.HS st Century Themes and Skills See Addendum 1. How to find coordinates of a point 2. How to write the inequality statement 3. How to find the absolute value of an expression 4. how to use equation and inequality 5. how to simplify expressions 6. how to evaluate algebraic expressions 7. How to choose the right property/ 8. How to simplify an algebraic expression using steps? 9. How to choose the right property?
25 10. How to simplify an algebraic expression using steps? 11. How to simplify and name the property in each step of an expression? 12. How to solve an equation for a given variable? 13. How to translate a phrase into an algebraic expression? 14. How to pick a variable to represent an unknown? Students will... Graph real numbers on a number line, to compare numbers, and to find their absolute values. Review the methods used to simplify numerical expressions and to evaluate algebraic expressions. Review properties of equality of real numbers and properties for adding and multiplying real numbers. Review the rules for adding and subtracting real numbers. Review rules for multiplying and dividing real numbers. Solve certain equations in one variable. Translate word phrases into algebraic expressions and word sentences into equations. Graph the given two numbers, and then write an inequality statement comparing them. Find the coordinate of the point one third of the way from C to D Find the value of each absolute value expression. Use the inequality and equality symbols to make a true statement. Simplify the given expressions using the order of operations and grouping symbols. Evaluate the algebraic expressions when the values of the variables are given. Name the properties of equality illustrated in each given statement. Choose a variable to represent an unknown number, and then write and solve an equation to describe the given situation. Content Area: Algebra 2 and Trigonometry Unit Title: Rational Expressions Target Course/Grade Level: Duration: 3 Weeks Description : Students study rational algebraic expressions studied. The laws of exponents are reviewed and extended to include zero and negative exponents. Students use scientific notation by applying the law of exponents in practical applications. They will be able to simplify, add, subtract, multiply, and divide rational expressions in word problems. Students then extend the skills to solve equations with fractional coefficients and fractional equations. They also extend and apply these skills to reallife situations. Evaluation of student learning occurs via homework, quizzes and test upon completion of the chapter. Quotients of Monomials Fractional Coefficients Fractional Equations Zero and Negative Exponents Rational Algebraic Expressions Products, Quotients, Sums and Differences of Rational Expressions. Complex Fractions The basic arithmetic operations of fractions are extended to algebraic expressions. The use of laws of exponents is combined with scientific notation to solve reallife problems. Factoring of polynomials is utilized to operate with rational expressions. The use of greatest common factor and least common multiple is applied to add and subtract
26 CPI Codes Garfield High School APR.HS.01 APR.HS.02 APR.HS.03 APR.HS.04 APR.HS.06 APR.HS.07 CED.HS.01 SSE.HS st Century Themes and Skills See Addendum How do you simplify fractions with exponents? How do you simplify expressions with zero and negative exponents? How do you write a number in scientific notation? How do you simplify rational expression? What are the domain and the zeros of a given function? How do you find a significant digit? How do you simplify rational expression using addition and subtraction? How do you simplify complex fractions? How do you solve an equation with fractional coefficients? How do you solve an inequality with fractional coefficients? How do you solve a fractional equation? rational algebraic problems. The use of greatest common factor is extended to provide tools to solve rational equations. Students will... Simplify fractions with and without variables. Review the first three laws of exponents and learn laws 4 and 5. Simplify expressions involving zero and negative exponents. Write very small or very large numbers in scientific notation. Analyze the problems to see how many digits the least accurate approximation has. Apply these skills in physics and chemistryrelated problems. Simplify rational algebraic expressions and how to find the domain and zeros of a rational function.
27 multiply and divide rational expressions using the multiplication and division rules for fraction Explain, in words, the procedures for multiplying and dividing rational expressions. Use the rules for adding and subtracting fractions to add and subtract rational expressions. Apply two methods for simplifying complex fractions. Solve equations and inequalities having fractional coefficients by using equivalent equations with integral coefficients. solve fractional equations and to check for extraneous roots Simplify fractions with exponents. Write expressions in simplest form without negative or zero exponents. Find a onesignificantdigit estimate of each given quotient. Find the domain of each given function and its zeros, if any. Simplify given rational expressions. solve inequality and equations Content Area: Algebra 2 and Trigonometry Unit Title: Analytic Geometry Target Course/Grade Level: Duration: 2 Weeks Description : Distance and midpoint formulas are the first topics introduced. Students discuss and study conic sections in depth as related to the distance formula. Students define circles, parabolas, ellipses and hyperbolas in terms of the distance formula and present them visually. They study their graphs and equations. They solve systems of three equations in three variables using graphing calculators and determinants serve to introduce technology to the students. Students extend and apply these skills to reallife situations. Evaluation of student learning occurs via homework, quizzes and test upon completion of the chapter. Distance and Midpoint Formulas Circles Parabolas Ellipses Hyperbola Central Conics Solving Quadratic Systems in Three Variables using Matrices and Graphing Calculator Ordered pairs are used to find the distance and midpoint of line segments in the coordinate plane. The distance formula is used to define an ellipse and its parts, i.e., the center, foci and intercepts The relationship between the center and radius of a circle and its equation is examined are discussed The use of focus, directrix, vertex and axis of symmetry completes the study of the parabola The distance formula is used to define a hyperbola and its parts.i.e, foci, intercepts and asymptotes The relationship between the foci, intercepts, and asymptotes of a hyperbola Conic sections with centers other than (0,0) are examined. Geometric solutions and algebraic solutions of systems involving conic
PreCalculus. Curriculum (447 topics additional topics)
PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More informationAlgebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards
Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards Standard 2 : Number & Operations CLE 3103.2.1: CLE 3103.2.2: CLE 3103.2.3:
More informationMCPS Algebra II Pacing Guide
Units to be covered 1 st Semester: Units to be covered 2 nd Semester: Vocabulary Semester Class: 10 days Year Long: 20 days OR Unit: Functions & Graphs Include content with individual units SOL AII.6 Recognize
More informationGrade 8 Math Curriculum Map Erin Murphy
Topic 1 Variables and Expressions 2 Weeks Summative Topic Test: Students will be able to (SWBAT) use symbols o represent quantities that are unknown or that vary; demonstrate mathematical phrases and realworld
More informationTopics Covered in Math 115
Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition
More informationIntermediate Algebra
Intermediate Algebra The purpose of this course is to strengthen students foundational conceptual and procedural skills in order to prepare students for collegeandcareer readiness. The course textbook,
More informationMTH306: Algebra II. Course length: Two semesters. Materials: None
MTH306: Algebra II Students are able to gain credit if they have previously completed this course but did not successfully earn credit. For each unit, students take a diagnostic test that assesses their
More informationAlgebra 2 Secondary Mathematics Instructional Guide
Algebra 2 Secondary Mathematics Instructional Guide 20092010 ALGEBRA 2AB (Grade 9, 10 or 11) Prerequisite: Algebra 1AB or Geometry AB 310303 Algebra 2A 310304 Algebra 2B COURSE DESCRIPTION Los Angeles
More information1.9 CC.912.A.REI.4b graph quadratic inequalities find solutions to quadratic inequalities
1 Quadratic Functions and Factoring 1.1 Graph Quadratic Functions in Standard Form 1.2 Graph Quadratic Functions in Vertex or Intercept Form 1.3 Solve by Factoring 1.4 Solve by Factoring 1.5 Solve Quadratic
More informationAldine I.S.D. Benchmark Targets/ Algebra 2 SUMMER 2004
ASSURANCES: By the end of Algebra 2, the student will be able to: 1. Solve systems of equations or inequalities in two or more variables. 2. Graph rational functions and solve rational equations and inequalities.
More informationHow well do I know the content? (scale 1 5)
Page 1 I. Number and Quantity, Algebra, Functions, and Calculus (68%) A. Number and Quantity 1. Understand the properties of exponents of s I will a. perform operations involving exponents, including negative
More informationAlgebra 2. Chapter 4 Exponential and Logarithmic Functions. Chapter 1 Foundations for Functions. Chapter 3 Polynomial Functions
Algebra 2 Chapter 1 Foundations for Chapter 2 Quadratic Chapter 3 Polynomial Chapter 4 Exponential and Logarithmic Chapter 5 Rational and Radical Chapter 6 Properties and Attributes of Chapter 7 Probability
More informationHow do you write and evaluate algebraic expressions? How can algebraic expressions and equations represent actual situations?
Topic: Expressions, Equations and Functions Days: 13 Key Learning: Expressions, equations, tables and graphs are used to model realworld situations. Unit Essential Question(s): How do you write and evaluate
More informationnonadjacent angles that lie on opposite sides of the transversal and between the other two lines.
WORD: Absolute Value DEFINITION: The distance from zero, distance is always positive. WORD: Absolute Value Function DEFINITION: A function whose rule contains an absolute value expression. EXAMPLE(S) COUNTEREXAMPLE(S):
More informationNEW YORK ALGEBRA TABLE OF CONTENTS
NEW YORK ALGEBRA TABLE OF CONTENTS CHAPTER 1 NUMBER SENSE & OPERATIONS TOPIC A: Number Theory: Properties of Real Numbers {A.N.1} PART 1: Closure...1 PART 2: Commutative Property...2 PART 3: Associative
More informationAlgebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.
Standard 1: Relations and Functions Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.
More informationCollege Algebra with Trigonometry
College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (556 topics + 614 additional
More informationAlgebra 2 with Trigonometry
Algebra 2 with Trigonometry This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize
More informationNew Jersey Quality Single Accountability Continuum (NJQSAC) ASSE 12; ACED 1,4; AREI 13, FIF 15, 7a
ALGEBRA 2 HONORS Date: Unit 1, September 430 How do we use functions to solve real world problems? What is the meaning of the domain and range of a function? What is the difference between dependent variable
More informationVirginia UnitSpecific Learning Pathways. Grades 6Algebra I: Standards of Learning
BUI L T F O VIR R G INIA 2014 2015 Virginia Specific Learning Pathways Grades 6Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia
More informationPrentice Hall Algebra Correlated to: Hawaii Mathematics Content and Performances Standards (HCPS) II (Grades 912)
Prentice Hall Hawaii Mathematics Content and Performances Standards (HCPS) II (Grades 912) Hawaii Content and Performance Standards II* NUMBER AND OPERATIONS STANDARD 1: Students understand numbers, ways
More informationCopyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10
Prep for Calculus This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (281 topics + 125 additional topics) Real
More informationThis image cannot currently be displayed. Course Catalog. Algebra II Glynlyon, Inc.
This image cannot currently be displayed. Course Catalog Algebra II 2016 Glynlyon, Inc. Table of Contents COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND
More informationAlgebra 2 Math Curriculum Pacing Guide (Revised 2017) Amherst County Public Schools. Suggested Sequence of Instruction and Pacing
Algebra 2 Math Curriculum Pacing Guide (Revised 2017) Amherst County Public Schools Suggested Sequence of Instruction and Pacing 1st 9weeks Unit 1  Solving Equations and Inequalities (including absolute
More informationFLORIDA STANDARDS TO BOOK CORRELATION
FLORIDA STANDARDS TO BOOK CORRELATION Florida Standards (MAFS.912) Conceptual Category: Number and Quantity Domain: The Real Number System After a standard is introduced, it is revisited many times in
More informationCollege Algebra. Course Text. Course Description. Course Objectives. StraighterLine MAT101: College Algebra
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGrawHill, 2008, ISBN: 9780072867381 [This text is available as an etextbook at
More informationcorrelated to the Washington D.C. Public Schools Learning Standards Algebra II
correlated to the Washington D.C. Public Schools Learning Standards Algebra II McDougal Littell Algebra 2 2007 correlated to the Washington DC Public Schools Learning Standards Algebra II NUMBER SENSE
More informationCurriculum Catalog
20162017 Curriculum Catalog 2016 Glynlyon, Inc. Table of Contents ALGEBRA I FUNDAMENTALS COURSE OVERVIEW... ERROR! BOOKMARK NOT DEFINED. UNIT 1: FOUNDATIONS OF ALGEBRA... ERROR! BOOKMARK NOT DEFINED.
More informationCourse Text. Course Description. Course Objectives. Course Prerequisites. Important Terms. StraighterLine Introductory Algebra
Introductory Algebra Course Text Dugopolski, Mark. Elementary Algebra, 6th edition. McGrawHill, 2009. ISBN 9780077224790 [This text is available as an etextbook at purchase or students may find used,
More informationPre Algebra. Curriculum (634 topics)
Pre Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More informationPrecalculus. Course Text. Course Description. Course Objectives. StraighterLine MAT201: Precalculus
Precalculus Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGrawHill, 2008. ISBN: 9780073312637 [This text is available as an etextbook at purchase
More information, Precalculus, Quarter 1
2017.18, Precalculus, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency
More informationALGEBRA 1B GOALS. 1. The student should be able to use mathematical properties to simplify algebraic expressions.
GOALS 1. The student should be able to use mathematical properties to simplify algebraic expressions. 2. The student should be able to add, subtract, multiply, divide, and compare real numbers. 3. The
More informationAlgebra I Block Curriculum Map Key : Glencoe Algebra I; Glencoe Study Guide (SG) Glencoe Handbook (HB) Aleks (A)
Time frame Unit/Concepts PA Eligible Content Standard Assessments Resources Support Materials Period 1 Preparing for Algebra: Problem solving Number systems and operations A1.1.1.4.1 Use estimation to
More informationIntegrated Mathematics I, II, III 2016 Scope and Sequence
Mathematics I, II, III 2016 Scope and Sequence I Big Ideas Math 2016 Mathematics I, II, and III Scope and Sequence Number and Quantity The Real Number System (NRN) Properties of exponents to rational
More informationMathematics. Algebra II Curriculum Guide. Curriculum Guide Revised 2016
Mathematics Algebra II Curriculum Guide Curriculum Guide Revised 016 Intentionally Left Blank Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction and
More informationTHEIR GRAPHS, AND THEIR
St. Michael Albertville High School Teacher: Kim Benson Algebra 2 (Master) August 2015 CEQs: WHAT RELATIONSHIP S EXIST BETWEEN VARIOUS FUNCTIONS, THEIR GRAPHS, AND THEIR SOLUTION(S)? HOW DO WE SIMPLIFY
More informationAlgebra II. Key Resources: Page 3
Algebra II Course This course includes the study of a variety of functions (linear, quadratic higher order polynomials, exponential, absolute value, logarithmic and rational) learning to graph, compare,
More informationHonors Algebra I. Course of Study
Honors Algebra I Course of Study Findlay City Schools 2007 Week Chapter Topic Indicators 1 n/a Review All previous grades 2 1 Expressions, Equations, and Functions 3 1 Expressions, Equations, and Functions
More informationAlgebra 1. Correlated to the Texas Essential Knowledge and Skills. TEKS Units Lessons
Algebra 1 Correlated to the Texas Essential Knowledge and Skills TEKS Units Lessons A1.1 Mathematical Process Standards The student uses mathematical processes to acquire and demonstrate mathematical understanding.
More informationObservations Homework Checkpoint quizzes Chapter assessments (Possibly Projects) Blocks of Algebra
September The Building Blocks of Algebra Rates, Patterns and Problem Solving Variables and Expressions The Commutative and Associative Properties The Distributive Property Equivalent Expressions Seeing
More informationK12 MATH HIGH ACHIEVEMENT OUTCOMES
K12 MATH HIGH ACHIEVEMENT OUTCOMES Mission Statement: By working individually and cooperatively, students in math will apply mathematical concepts, demonstrate computational skills, and use technological
More informationMathematics: Algebra II Honors Unit 1: Quadratic Functions
Understandings Questions Knowledge Vocabulary Skills Quadratic functions can be used to model reallife situations. What are the properties of Algebra and how are these used to solve quadratic equations?
More informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More informationCK12 Middle School Math Grade 8
CK12 Middle School Math aligned with COMMON CORE MATH STATE STANDARDS INITIATIVE Middle School Standards for Math Content Common Core Math Standards for CK12 Middle School Math The Number System (8.NS)
More informationMontgomery College algebra Equations & Problem Solving *Order of Operations & Simplifying Algebraic. Expressions
Where to go for help with the lessons in the I textbook: www.pearsonsuccessnet.com Username: student id number followed by scpsfl Password: YYYYMMDDscpsfl Click Student Resource Choose the chapter Choose
More informationRange of Competencies
MATHEMATICS l. Content Domain Range of Competencies Mathematical Processes and Number Sense 0001 0003 19% ll. Patterns, Algebra, and Functions 0004 0007 24% lll. Measurement and Geometry 0008 0010 19%
More informationTransitional Algebra. Semester 1 & 2. Length of Unit. Standards: Functions
Semester 1 & 2 MP.1 MP.2 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Length of Unit Progress Monitoring Short cycle Weekly or biweekly formative assessment
More informationALGEBRA 2/MATH 3 COURSE 1
ALGEBRA 2/MATH 3 COURSE 1 TABLE OF CONTENTS NUMBER AND QUANTITY 6 THE REAL NUMBER SYSTEM (N.RN) 6 EXTEND THE PROPERTIES OF EXPONENTS TO RATIONAL EXPONENTS. (N.RN.12) 6 Expectations for Learning 6 Content
More informationALGEBRA & TRIGONOMETRY FOR CALCULUS MATH 1340
ALGEBRA & TRIGONOMETRY FOR CALCULUS Course Description: MATH 1340 A combined algebra and trigonometry course for science and engineering students planning to enroll in Calculus I, MATH 1950. Topics include:
More informationTitle Grade 8 Algebra I 2013
Title Grade 8 Algebra I 2013 Type Essential Document Map Authors Elizabeth Tucker, Deborah Baxter, Kristin Iacobino, Jane Feret, Caryn Trautz, Melissa Cosgrove, Jaclyn Thomas Subject Mathematics Course
More informationStudent Learning Outcomes MATH 100: BEGINNING ALGEBRA
Student Learning Outcomes MATH 100: BEGINNING ALGEBRA I. Real Numbers 1. Perform the basic operations on fractions, reduce, and convert to decimals and percents. 2. Define, classify, and graph real numbers.
More informationNew Jersey Quality Single Accountability Continuum (NJQSAC) ACED 14; AREI 12,57; FIF 12, 45; NQ 13; NRN
New Jersey Quality Single Accountability Continuum (NJQSAC) (former ICM) Date: Unit 1, September 430 How do we use functions to solve real world problems? How can we model a reallife situation with a
More informationGlossary. Glossary Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The
More informationImportant Math 125 Definitions/Formulas/Properties
Exponent Rules (Chapter 3) Important Math 125 Definitions/Formulas/Properties Let m & n be integers and a & b real numbers. Product Property Quotient Property Power to a Power Product to a Power Quotient
More informationPearson Georgia High School Mathematics Advanced Algebra
A Correlation of Pearson Georgia High School Mathematics Advanced Algebra 2014 to the Gwinnett County Academic Knowledge and Skills (AKS) Mathematics Table of Contents A  Process Skills... 1 C  Geometry...
More informationA video College Algebra course & 6 Enrichment videos
A video College Algebra course & 6 Enrichment videos Recorded at the University of Missouri Kansas City in 1998. All times are approximate. About 43 hours total. Available on YouTube at http://www.youtube.com/user/umkc
More informationSubject: Equations Calendar: August/September Timeframe: NA Level/Grade: 10/11 Algebra 2
Subject: Equations Calendar: August/September Timeframe: NA Level/Grade: 10/11 Algebra 2 Chapter: Solving Equations and Inequalities I. Solving Linear Equations II. Solving OneVariable Linear Inequalities
More informationPrealgebra and Elementary Algebra
Prealgebra and Elementary Algebra 9781635450354 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek,
More informationALGEBRA I CCR MATH STANDARDS
RELATIONSHIPS BETWEEN QUANTITIES AND REASONING WITH EQUATIONS M.A1HS.1 M.A1HS.2 M.A1HS.3 M.A1HS.4 M.A1HS.5 M.A1HS.6 M.A1HS.7 M.A1HS.8 M.A1HS.9 M.A1HS.10 Reason quantitatively and use units to solve problems.
More informationMATHEMATICS Video List
LIBRARY SERVICES MATHEMATICS Video List Macon Campus Library June 2010 MATHEMATICS Basic College Mathematics 6e 2009  LEARNING SUPPORT Textbook (DVD, 4 discs) 1. 1.1 Understanding Whole Numbers 1.2 Adding
More informationUnit 1. Revisiting Parent Functions and Graphing
Unit 1 Revisiting Parent Functions and Graphing Revisiting Statistics (Measures of Center and Spread, Standard Deviation, Normal Distribution, and ZScores Graphing abs(f(x)) and f(abs(x)) with the Definition
More informationSaxon Advanced Mathematics Scope and Sequence
hmhco.com Saxon Advanced Mathematics Scope and Sequence Foundations Calculator Perform twovariable analysis Use graphing calculators Find roots of equations Solve systems of equations Exponentials and
More informationBasic ALGEBRA 2 SUMMER PACKET
Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout
More informationAlgebra I Assessment. Eligible Texas Essential Knowledge and Skills
Algebra I Assessment Eligible Texas Essential Knowledge and Skills STAAR Algebra I Assessment Mathematical Process Standards These student expectations will not be listed under a separate reporting category.
More informationAlgebra Readiness. Curriculum (445 topics additional topics)
Algebra Readiness This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize the
More informationBellwoodAntis School District Curriculum Revised on 11/08/12
Course: Alg I Grade Level(s): 8 BellwoodAntis School District Curriculum Revised on 11/08/12 Month Duration Common Core Standards/Anchors Content Assessment Instructional Activities PreRequisite Skills
More informationSequenced Units for Arizona s College and Career Ready Standards MA40 Algebra II
Sequenced Units for Arizona s College and Career Ready Standards MA40 Algebra II Year at a Glance Semester 1 Semester 2 Unit 1: Linear Functions (10 days) Unit 2: Quadratic Functions (10 days) Unit 3:
More informationAlgebraic Connections. Mathematics Curriculum Framework. Revised 2004
Algebraic Connections Mathematics Curriculum Framework Revised 2004 Course Title: Algebraic Connections (Thirdyear Course) Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics
More informationSTEMPrep Pathway SLOs
STEMPrep Pathway SLOs Background: The STEMPrep subgroup of the MMPT adopts a variation of the student learning outcomes for STEM from the courses Reasoning with Functions I and Reasoning with Functions
More informationDoverSherborn High School Mathematics Curriculum Algebra I Level 1 CP/Honors
Mathematics Curriculum A. DESCRIPTION This two semester course is designed to develop a thorough understanding of the framework of algebra, the real number system and related operations and methods of
More informationAlgebra 34 Honors PUHSD Curriculum. PARCC MODEL CONTENT FRAMEWORK FOR ALGEBRA 34 Honors
PARCC MODEL CONTENT FRAMEWORK FOR ALGEBRA 34 Honors Building on their work in Algebra I with linear and quadratic functions, students in Algebra II expand their repertoire by working with rational and
More informationEssential Learning Outcomes for Algebra 2
ALGEBRA 2 ELOs 1 Essential Learning Outcomes for Algebra 2 The following essential learning outcomes (ELOs) represent the 12 skills that students should be able to demonstrate knowledge of upon completion
More informationAlgebra II Assessment. Eligible Texas Essential Knowledge and Skills
Algebra II Assessment Eligible Texas Essential Knowledge and Skills STAAR Algebra II Assessment Mathematical Process Standards These student expectations will not be listed under a separate reporting category.
More informationCurriculum Catalog. Algebra II Glynlyon, Inc Released
Curriculum Catalog Algebra II 2011 Glynlyon, Inc Released 4111 Welcome to SwitchedOn Schoolhouse! We are excited that you are including SwitchedOn Schoolhouse as part of your program of instruction,
More informationDraft. Algebra 1 Lesson Correlation
CC Standard Saxon Algebra 1 Topic On Core N.RN.3 1 Classifying Real Numbers A.SSE.1 2 Understanding Variables and Expression 3 Simplifying Expressions Using the Product Property of Exponents 4 Using Order
More informationAlgebra 2 Pearson High School SY
Chapters Total School Days Algebra 2 Pearson High School 20172018 SY Benchmark Cycle1 Benchmark Cycle2 Benchmark Cycle 3 Cycle 4 September 5 October 31 BM Window Opens Nov 1 Term 1 ends Nov 13 November
More informationMathematics Precalculus: Academic Unit 7: Conics
Understandings Questions Knowledge Vocabulary Skills Conics are models of reallife situations. Conics have many reflective properties that are used in every day situations Conics work can be simplified
More information1: Translating Expressions
Algebra I 20172018 1: Translating Expressions Translate between words and math symbols, such as: The sum of twice a number and 3 Answer: 2n + 3 Also translate math symbols into verbal language. 5(x +
More informationAlgebra 1 Math Year at a Glance
Real Operations Equations/Inequalities Relations/Graphing Systems Exponents/Polynomials Quadratics ISTEP+ Radicals Algebra 1 Math Year at a Glance KEY According to the Indiana Department of Education +
More informationGrade 12 PreCalculus
Albuquerque School of Excellence Math Curriculum Overview Grade 12 PreCalculus Module Complex Numbers and Transformations Module Vectors and Matrices Module Rational and Exponential Functions Module Trigonometry
More informationPrentice Hall Algebra Correlated to: South Dakota Mathematics Standards, (Grades 912)
High School Algebra Indicator 1: Use procedures to transform algebraic expressions. 912.A.1.1. (Comprehension)Write equivalent forms of algebraic expressions using properties of the set of real numbers.
More informationAlgebra III. Mathematics Curriculum Framework. Revised 2004
Algebra III Mathematics Curriculum Framework Revised 2004 Title: Algebra III (Fourthyear Course) Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics Prerequisite: Algebra II
More informationEPPING HIGH SCHOOL ALGEBRA 2 Concepts COURSE SYLLABUS
Course Title: Algebra 2 Concepts Course Description Algebra 2 Concepts is designed for students who wish to take an Algebra 2 course at a non college prep level. The class will begin with a review of Algebra
More informationHonors Algebra II/Trigonometry
Honors Algebra II/Trigonometry Scranton School District Scranton, PA Honors Algebra II/Trigonometry Prerequisite: Successful completion of Geometry or Honors Geometry Be in compliance with the SSD Honors
More informationAlgebra 2 College Prep Curriculum Maps
Algebra 2 College Prep Curriculum Maps Unit 1: Polynomial, Rational, and Radical Relationships Unit 2: Modeling With Functions Unit 3: Inferences and Conclusions from Data Unit 4: Trigonometric Functions
More informationMathematics. Algebra I (PreAP, Pt. 1, Pt. 2) Curriculum Guide. Revised 2016
Mathematics Algebra I (PreAP, Pt. 1, Pt. ) Curriculum Guide Revised 016 Intentionally Left Blank Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction and
More informationCarrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS. Curriculum Map
Carrollton Exempted Village School District Carrollton, Ohio Curriculum Map Course Title: Algebra I Concepts Pacing: 10 days Academic Year: 20132014 Unit 1: Connections to Algebra Essential Questions:
More informationInstructional Unit Conic Sections Pre Calculus #312 Unit Content Objective Performance Performance Task State Standards
Instructional Unit Conic Sections Conic Sections The student will be Define conic sections Homework 2.8.11E Ellipses able to create conic as conic slices and Classwork Hyperbolas sections based on
More informationCopyright 2016 Pearson Education, Inc. or its affiliates. All rights reserved. NES, the NES logo, Pearson, the Pearson logo, and National Evaluation
Mathematics (304) Copyright 2016 Pearson Education, Inc. or its affiliates. All rights reserved. NES, the NES logo, Pearson, the Pearson logo, and National Evaluation Series are trademarks, in the U.S.
More informationPreCalculus and Trigonometry Capacity Matrix
Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational expressions Solve polynomial equations and equations involving rational expressions Review Chapter 1 and their
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationPrecalculus. Represent complex numbers and their operations on the complex plane.
Precalculus Precalculus is designed for students who have successfully completed the Algebra II with Trigonometry course. This course is considered to be a prerequisite for success in calculus and college
More informationQ 1. Richland School District Two 8th Grade Mathematics Pacing Guide. Last Edit: 1/17/17
Overview of Units Pacing Guide Standards and Indicators Suggested Days Q 1 12 Unit 1: Geometry and Measurement: Transformations in the Plane Congruence:  Translations  Reflections  Rotations  Congruent
More informationPA Core Standards For Mathematics 2.2 Algebraic Concepts PreK12
Addition and Represent addition and subtraction with CC.2.2.PREK.A.1 Subtraction objects, fingers, mental images, and drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
More informationHOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS
HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 020 ELEMENTARY ALGEBRA CREDIT HOURS: 0.0 EQUATED HOURS: 4.5 CLASS HOURS: 4.5 PREREQUISITE: REQUIRED TEXTS: MAT 010 or placement on ACCUPLACER MartinGay,
More informationBridge to Algebra II Standards for Mathematical Practice
Bridge to Algebra II Standards for Mathematical Practice The Standards for Mathematical Practices are to be interwoven and should be addressed throughout the year in as many different units and tasks as
More informationPrentice Hall Algebra Correlated to: Illinois Math Assessment Frameworks (Grade 11)
Mathematics State Goal 6: Number Sense Grade 11 Standard 6A Representations and Ordering 6.11.01 Recognize, represent, order, compare real numbers, and locate real numbers on a number line (e.g., π, Ö
More informationAlgebra 2 Mississippi College and Career Readiness Standards for Mathematics RCSD Unit 1 Data Relationships 1st Nine Weeks
1 st Nine Weeks Algebra 2 Mississippi College and Career Readiness Standards for Mathematics Unit 1 Data Relationships Level 4: I can interpret key features of graphs and tables in terms of the quantities.
More information