Mathematics Curricular Guide ALGEBRA SCHOOL YEAR. Updated: Thursday, December 02, 2010

Transcription

1 Mathematics Curricular Guide ALGEBRA SCHOOL YEAR 1 Updated: Thursday, December 0, 010

2 Pasco School District Algebra School Year MATHEMATICS SCOPE & SEQUENCE Unit Title Dates Page 1. Chapter 1 Equations and Inequalities Chapter - Linear Equations and Functions Chapter 5 Quadratic Functions Chapter 3 Systems of Linear Equations and Inequalities Chapter 6 Polynomials and Polynomial Functions Chapter 1 Probability and Statistics Chapter 7 Powers, Roots, and Radicals Chapter 8 Exponential and Logarithmic Functions Chapter 9 Rational Equations and Functions Chapter 11 Sequences and Series Chapter 13 Trigonometric Ratios and Functions... 3 Updated: Thursday, December 0, 010

3 Pasco School District Algebra School Year Unit Name: Chapter 1 Equations and Inequalities [Starting Date] [Ending Date] A..A Explain how whole, integer, 1.1 Real Numbers and Number This standard is briefly rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved. Operations Identify properties of and use operations with real numbers. Recognize and explain the relationship amongst different number systems. mentioned, but a typical student would not be able to achieve mastery with the available content. A relationship between number systems if not identified. Locate materials to use for instruction and reinforcement. A..B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A.1.A Select and justify functions and equations to model and solve problems. 1. Algebraic Expressions and Models Evaluate algebraic expressions. Simplify algebraic expressions by combining like terms. 1.3 Solving Linear Equations Solve linear equations. Use linear equations to model and solve real-life problems. 1.4 Rewriting Equations and Formulas Rewrite equations with more than one variable. The laws of rational exponents occur in section 7. which will be addressed later in the curriculum. While solving linear equations is not addressed specifically in the PEs, a review of this skill is needed prior to completion of the rest of the curriculum. Refer to 1.3 Practice B and 1.3 Practice C worksheets to find additional application problems. This section is included in anticipation for the unit on solving systems of equations. 3 Updated: Thursday, December 0, 010

4 Pasco School District Algebra School Year A.1.A Select and justify functions and equations to model and solve problems. In anticipation of A.1.B Solve problems that can be represented by systems of equations and inequalities. 1.5 Problem Solving Using Algebraic Models Use a general problem-solving plan to solve real-life problems. Have students write a verbal model, assign labels, write an algebraic model, then solve the algebraic model to solve the problem. 1.6 Solving Linear Inequalities Solve simple inequalities. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 1 common assessment 3 Add three days for review, reteaching, and assessment. 4 Updated: Thursday, December 0, 010

5 Pasco School District Algebra School Year Unit Name: Chapter Linear Equations and Functions [Starting Date] [Ending Date] A.1.A Select and justify functions and.1 Functions and their graphs Be sure to emphasize the equations to model and solve problems. Distinguish between definitions of relation and relations and functions. function. The second objective is included in anticipation of Graph and evaluate linear the section on graphing lines functions. which follows. A.1.A Select and justify functions and. Slope and Rate of Change A basic review of calculating equations to model and solve problems. Use slope to solve real-life slope may be necessary before problems. students are ready to solve problems with rate of change. This section is included to address problem solving with rates of change, to meet the In anticipation of A.1.B Solve problems that can be represented by systems of equations and inequalities. A.1.A Select and justify functions and equations to model and solve problems. 5 Updated: Thursday, December 0, Quick Graphs of Linear Equations Graph linear equations in slope-intercept form..4 Writing Equations of Lines Model functions by writing linear equations..7 Piecewise Functions Represent piecewise functions. Use piecewise functions to model real-life situations..8 Absolute Value Functions Represent absolute value functions. Use absolute value functions to model reallife situations. Sections.7 and.8 do not match PEs. They are included so students will be prepared for the Compass test at CBC. PE.

6 Pasco School District Algebra School Year Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter common assessment 3 Add three days for review, reteaching, and assessment. 6 Updated: Thursday, December 0, 010

7 Pasco School District Algebra School Year Unit Name: Chapter 5 Quadratic Functions [Starting Date] [Ending Date] A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form. 5.1 Graphing Quadratic Functions Graph quadratic functions. Use quadratic functions to solve real-life problems. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. 5. Solving Quadratic Equation by Factoring Factor quadratic expressions Solve quadratic equations by factoring Find solutions (zeros) of quadratic functions. 5.3 Solving Quadratic Equations by Finding Square Roots Solve quadratic equations by finding square roots. Use quadratic equations to solve real-life problems. 5.4 Complex Numbers Solve quadratic equations with complex solutions. 5.5 Completing the Square Solve quadratic equations by completing the square. 7 Updated: Thursday, December 0, 010

8 Pasco School District Algebra School Year A.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form. Use completing the square to write quadratic functions in vertex form. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. 5.6 The Quadratic Formula and the Discriminant Solve quadratic equations using the quadratic formula. Use the quadratic formula in real-life situations. Use the discriminant to determine the number and type of solutions of a quadratic equation. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. 5.7 Graphing and Solving Quadratic Inequalities Graph quadratic inequalities in two variables Solve quadratic inequalities in real-life situations. 5.8 Modeling with Quadratic Functions Write quadratic functions given characteristics of their graphs. 3 Add three days for review, reteaching, and assessment. 8 Updated: Thursday, December 0, 010

9 Pasco School District Algebra School Year Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 5 common assessment 9 Updated: Thursday, December 0, 010

10 Pasco School District Algebra School Year Unit Name: Chapter 3 Systems of Linear Equations and Inequalities [Starting Date] [Ending Date] 10 A.1.B Solve problems that can be represented by systems of equations and inequalities. A.1.B Solve problems that can be represented by systems of equations and inequalities. A.1.B Solve problems that can be represented by systems of equations and inequalities. A.7.A Solve systems of three equations with three variables. Updated: Thursday, December 0, Solving Linear Systems by Graphing Graph and solve systems of linear equations. Use linear systems to solve real-life problems. 3. Solve Linear Systems Algebraically Use algebraic methods to solve linear systems. Use linear systems to model real-life situations. 3.3 Graphing and Solving Systems of Linear Inequalities Graph a system of linear inequalities to find the solutions of the system. Use systems of linear inequalities to solve real-life problems 3.6 Solving Systems of Linear Equations in Three Variables Solve systems of linear equations in three variables.

11 Pasco School District Algebra School Year Use linear systems in three variables to solve real-life problems. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 3 common assessment 3 Add three days for review, reteaching, and assessment. 11 Updated: Thursday, December 0, 010

12 Pasco School District Algebra School Year Unit Name: Chapter 6 Polynomials and Polynomial Functions [Starting Date] [Ending Date] A..B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A..B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax 3 + d as an example of higher order polynomials and solve related equations. 6.1 Using Properties of Exponents Use properties of exponents to evaluate and simplify expressions involving powers. Use exponents to solve reallife problems. 6. Evaluating and Graphing Polynomial Functions Evaluate a polynomial function. Graph a polynomial function. In order to meet the PE, be sure to emphasize the description of the graphs. A..C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions. A.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax 3 + d as an example of higher order polynomials and solve related equations. 1 Updated: Thursday, December 0, Adding, Subtracting and Multiplying Polynomials Add, subtract, and multiply polynomials. Use polynomial operations in real-life problems. 6.4 Factoring and Solving Polynomial Equations Factor polynomial expressions. Use factoring to solve polynomial equations. Use polynomial equations to solve real-life problems.

13 Pasco School District Algebra School Year 3 Add three days for review, reteaching, and assessment. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 6 common assessment 13 Updated: Thursday, December 0, 010

14 Pasco School District Algebra School Year Unit Name: Chapter 1 Probability and Statistics [Starting Date] [Ending Date] A.1.F Solve problems involving combinations and permutations. 1.1 The Fundamental Counting Principle and Permutations Use the fundamental counting principle to count the number of ways an event can happen Use permutations to count the number of ways an event can happen 3 A.6.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events). 14 Updated: Thursday, December 0, Combinations and the Binomial Theorem Use combinations to count the number of ways and event can happen. 1.3 An Introduction to Probability Find theoretical and experimental probabilities. 1.4 Probability of Compound Events Find probabilities of unions and intersections of two events. Use complements to 3

15 Pasco School District Algebra School Year find the probability of an event. A.6.B Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B. A.6.C Compute permutations and combinations, and use the results to calculate probabilities. A..6.D Apply the binomial theorem to solve problems using probability. A.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets. A.6.G and A.7.C Calculate and interpret margin of error and confidence intervals for 1.5 Probability of Independent and Dependent Events Find the probability of independent events Find the probability of dependent events. 1.6 Binomial Distributions Find binomial probabilities and analyze binomial distributions. 7.7 Statistics and Statistical Graphs Use measures of central tendency and measures of dispersion to describe data sets. 1.7 Normal Distributions Calculate probabilities using normal distributions. Use normal distributions to approximate binomial distributions. ***MISSING! 15 Updated: Thursday, December 0, 010

16 Pasco School District Algebra School Year population proportions. 3 Add three days for review, reteaching, and assessment. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 1 common assessment 16 Updated: Thursday, December 0, 010

17 Pasco School District Algebra School Year Unit Name: Chapter 7 Powers, Roots, and Radicals [Starting Date] [Ending Date] A..B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A.5.A Construct new functions using the transformations f(x h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s). ***The construction of new functions using transformations is missing for this PE. In anticipation of A.4.A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them. A.5.B Plot points, sketch, and describe the graphs of functions of the form f(x) = a (x c) + d, and solve related equations. 7. Properties of Rational Exponents Use properties of rational exponents to evaluate and simplify expressions. Use properties of rational exponents to solve reallife problems. 7.3 Power Functions and Function Operations Perform operations with functions including power functions. Use power functions and function operations. 7.4 Inverse Functions Find inverses of linear functions. Find inverses of nonlinear functions. 7.5 Graphing Square Root and Cube Root Functions Graph square root and cube root functions. Use square root and cube root functions to find real-life quantities. ***The construction of new functions using transformations is missing for this PE. While composition of functions is not a PE, this skill is needed for the Compass test at CBC. 17 Updated: Thursday, December 0, 010

18 Pasco School District Algebra School Year A.5.B Plot points, sketch, and describe the graphs of functions of the form f(x) = a (x c) + d, and solve related equations. A.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets. 7.6 Solving Radical Equations Solve equations that contain radicals or rational exponents. Use radical equations to solve real-life problems. 7.7 Statistics and Statistical Graphs Use measures of dispersion to describe data sets. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 7 common assessment 3 Add three days for review, reteaching, and assessment. 18 Updated: Thursday, December 0, 010

19 Pasco School District Algebra School Year Unit Name: Chapter 8 Exponential and Logarithmic Functions [Starting Date] [Ending Date] A.4.C equations. Solve exponential and logarithmic 8.1 Exponential Growth Graph exponential growth functions Use exponential growth functions to model real-life situations A.4.C equations. Solve exponential and logarithmic A.1.D Solve problems that can be represented by exponential and logarithmic functions and equations. A.1.D Solve problems that can be represented by exponential and logarithmic functions and equations. A.1.D Solve problems that can be represented by exponential and logarithmic functions and equations. 8. Exponential Decay Graph exponential decay functions Use exponential decay functions to model real-life situations 8.3 Using the Number e Use the number e as the base of exponential functions. Use the natural base e in real-life situations. 8.4 Logarithmic Functions Evaluate logarithmic functions. Graph logarithmic functions. Use logarithmic functions to model real-life situations. 8.5 Properties of Logarithms Use properties of logarithms. Use properties of logarithms to solve real-life problems. 19 Updated: Thursday, December 0, 010

20 Pasco School District Algebra School Year A.1.D Solve problems that can be represented by exponential and logarithmic functions and equations. 8.6 Solving Exponential and Logarithmic Equations Solve exponential equations in real-life situations Solve logarithmic equations in real-life situations A.1.D Solve problems that can be represented by exponential and logarithmic functions and equations. 8.7 Modeling with Exponential and Power Functions Model data with exponential functions. Model data with power functions. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 8 common assessment 3 Add three days for review, reteaching, and assessment. 0 Updated: Thursday, December 0, 010

21 Pasco School District Algebra School Year Unit Name: Chapter 9 Rational Equations and Functions [Starting Date] [Ending Date] A.1.E Solve problems that can be represented by inverse variations of the forms f(x) = (a/x) + b, f(x) = (a/x ) + b, and f(x) = a/(bx+c). 9.1 Inverse and Joint Variation Write and use inverse variation models. A..C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions. A..C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions. A.5.C Plot points, sketch, and describe the graphs of functions of the form f(x) = (a/x) + b, f(x) = (a/x ) + b, and f(x) = a/(bx+c), and solve related equations. 9.4 Multiplying and Dividing Rational Expressions Multiply and divide rational expressions Use rational expressions to model real-life quantities. 9.5 Addition, Subtraction, and Complex Fractions Add and subtract rational expressions. 9.6 Solving Rational Equations Solve rational equations. Use rational equations to solve real-life problems. Complex fractions are not part of the PE. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 9 common assessment 3 Add three days for review, reteaching, and assessment. 1 Updated: Thursday, December 0, 010

22 Pasco School District Algebra School Year Unit Name: Chapter 11 Sequences and Series [Starting Date] [Ending Date] A.7.B Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series An Introduction to Sequences and Series Use and write sequences. Use summation notation to write series and find sums of series. 11. Arithmetic Sequences and Series Write rules for arithmetic sequences and find sums of arithmetic series Geometric Sequences and Series Write rules for geometric sequences and find sums of geometric series Infinite Geometric Series Find sums of geometric series. Process Standards Addressed: A.8.A Analyze a problem situation and represent it mathematically. Assessment: Chapter 11 common assessment 8 3 Add three days for review, reteaching, and assessment. Updated: Thursday, December 0, 010

23 Pasco School District Algebra School Year Unit Name: Trigonometric Ratios and Functions [Starting Date] [Ending Date] ***NOTE: While this chapter does not meet any State PE s, the committee felt it needed to be included in preparation for Pre-Calculus Right Triangle Trigonometry Use trigonometric relationships to evaluate trigonometric functions of acute angles. Use trigonometric functions to solve reallife problems. 3 Updated: Thursday, December 0, General Angles and Radian Measure Measure angles in standard position using degree measure and radian measure. Calculate arc lengths and areas of sectors Trigonometric Functions of Any Angle Evaluate trigonometric functions of any angle. Use trigonometric functions to solve reallife problems Inverse Trigonometric Functions

24 Pasco School District Algebra School Year Process Standards Addressed: Assessment: Chapter 13 common assessment Evaluate inverse trigonometric functions. Use inverse trigonometric functions to solve reallife problems The Law of Sines Use the law of sines to find the sides and angles of a triangle. Find the area of any triangle The Law of Cosines Use the law of cosines to find the sides and angles of a triangle. Use Heron s formula to find the area of a triangle. 3 Add three days for review, reteaching, and assessment. 4 Updated: Thursday, December 0, 010