Algebra III INSTRUCTIONAL PACING GUIDE (Days Based on 90 minutes)

Transcription

1 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. EA, IA, PC-1.7 G-1. G-1.8 G-1.9 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, Communicate knowledge of geometric relationships by using mathematical terminology appropriately Connect geometry with other branches of mathematics. Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, EA-3.5 EA-3.4 EA-5.1 EA-5.3 EA-5.5 EA-4.1 EA-4. EA-4.3 EA-4.6 EA-5.6 EA-4. EA-4.3 EA-4.6 EA-5.8 EA-4.9 IA-.11 EA-4.10 IA-.11 IA-. FIRST NINE WEEKS Graphing Linear Equations (Include Domain & Range) Carry out a procedure to graph parent functions 1 y = x, y = x, y = x, and y = ). x Analyze the graph of a continuous function to determine the domain and range of the function. Carry out a procedure to graph a line when given the equ of the line. Carry out a procedure to graph the line with a given slope y-intercept. Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally. Writing Equation of Lines ( Include Finding Slope) with a given slope and a y-intercept. with a given slope passing through a given point. passing through two given points. Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard). Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally. Parallel and Perpendicular Lines with a given slope passing through a given point. passing through two given points. Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard). Analyze the equations of two lines to determine whether the lines are perpendicular or parallel. Solving Systems of Linear Equations Graphically Carry out a procedure to solve systems of two linear equations graphically. Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function). Solving Systems of Linear Equations Algebraically Carry out a procedure to solve systems of two linear equations Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function). Solving Systems of Linear Inequalities Graphically Carry out a procedure to solve a system of linear inequalities graphically. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

2 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately IA-.3 IA-.4 FIRST NINE WEEKS (CONTINUED) Linear Programming Analyze a problem situation to determine a system of linear inequalities that models the problem situation. Use linear programming to solve contextual problems involving a system of linear inequalities. GRAPHING QUADRATIC EQUATIONS IA-.7 Carry out a procedure to graph translations of parent functions 1 y = x, y = x, y = x, and y = ). x.5 days IA-.8 Carry out a procedure to graph transformations of parent functions y = x, and y = x ). Solving Quadratic Equations by Factoring EA-.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials). IA-3.3 Carry out a procedure to solve quadratic equations days IA-3.5 Analyze given information (including quadratic models) to solve contextual problems. Solving Quadratics by Taking Square Roots & Completing the Square (Include Simplifying Radicals) IA-3.3 Carry out a procedure to solve quadratic equations IA-3.5 Analyze given information (including quadratic models) to solve contextual problems. Complex Numbers & Solving Quadratics by Square Roots with Complex Numbers IA-3.1 IA-3. IA-3.3 IA-3.3 IA-3.4 IA-3.5 Carry out a procedure to simplify expressions involving powers of i. Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division). Carry out a procedure to solve quadratic equations Solving Quadratics by the Quadratic Formula & Examining the Discriminant Carry out a procedure to solve quadratic equations Use the discriminant to determine the number and type of solutions of a quadratic equation. Analyze given information (including quadratic models) to solve contextual problems. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

3 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately EA-3.1 EA-3. EA-3.3 EA-3.4 IA-.10 IA-4. PC-3.1 IA-4.3 IA-4.3 PC-3. PC-3.3 IA-3.6 FIRST NINE WEEKS (CONTINUED) Definition of Function & Function Notation Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph. Use function notation to represent functional relationships. Domain & Range of Functions, Definition of & Evaluating Polynomials Carry out a procedure to evaluate a function for a given element in the domain. Analyze the graph of a continuous function to determine the domain and range of the function. Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions). ADMINISTER TEACHER-MADE INTERIM ASSESSMENT SECOND NINE WEEKS Graphing Polynomials End Behavior, Max, Min Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions. Carry out a procedure to graph quadratic and higherorder polynomial functions by analyzing intercepts and end behavior. Solve Polynomial Equations by Factoring Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes). Solving Polynomial Equations by the Rational Root Theorem Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes). 1.5 days Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation. Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros. Write Equations of Polynomials Given Roots Carry out a procedure to write an equation of a quadratic function when given its roots. 0.5 day IA-4.8 Simplifying Rational Expressions Carry out a procedure to perform operations with rational expressions (including addition, subtraction,.5 days multiplication, and division). RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

4 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately SECOND NINE WEEKS (CONTINUED) Solving Rational Equations IA-4.1 PC-3.8 Carry out a procedure to solve rational equations Carry out a procedure to solve rational equations IA-.7 PC-3.4 EA-. Graphing Rational Functions Carry out a procedure to graph translations of parent functions 1 y = x, y = x, y = x, and y = ). x Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities). TEST Laws of Exponents (Including Rational Exponents) Apply the laws of exponents and roots to solve problems. IA-4.5 IA-4.7 PC-4.5 IA-4.14 PC-4.1 PC-4.3 IA-.6 PC-.8 PC-.9 IA-4.6 Carry out a procedure to simplify algebraic expressions involving rational exponents. Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation). Apply the laws of exponents to solve problems involving rational exponents. Graphing Exponential Functions (Include Domain & Range) Carry out a procedure to graph exponential functions. Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior. Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes). Inverse Functions & Function Composition Apply a procedure to write the equation of a composition of given functions. Carry out a procedure to determine whether the inverse of a function exists. Carry out a procedure to write a rule for the inverse of a function, if it exists. Definition of Logarithm, Evaluating & Simplifying Logarithms Carry out a procedure to simplify algebraic expressions involving logarithms. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

5 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately IA-4.6 SECOND NINE WEEKS (CONTINUED) Laws of Logarithms Carry out a procedure to simplify algebraic expressions involving logarithms. PC-4.7 IA-4.13 Apply the laws of logarithms to solve problems. ADMINISTER INTERIM ASSESSMENT Graphing Logarithmic Functions (Include Domain & Range) Carry out a procedure to graph logarithmic functions. PC-4. PC-4.4 IA-4.10 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior. Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes). Solving Exponential & Logarithmic Functions Carry out a procedure to solve logarithmic equations PC-4.8 PC-4.10 Carry out a procedure to solve exponential equations Carry out a procedure to solve logarithmic equations THIRD NINE WEEKS G-3.10 G-3.11 G-3.1 G-3.10 G-3.11 G-3.1 PC-5.1 PC-5. Pythagorean Theorem Use the Pythagorean theorem and its converse to solve problems. Special Right Triangles & Use the properties of and triangles to solve problems. Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles Solving Right Triangles Introduction to Sine, Cosine, & Tangent Use the Pythagorean theorem and its converse to solve problems Use the properties of and triangles days to solve problems Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles. TEST CONVERTING BETWEEN DEGREES AND RADIANS Understand how angles are measured in either degrees or radians. Carry out a procedure to convert between degree and radian measures. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

6 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately PC-5.6 PC-5.6 PC-5.6 PC-5.5 PC-5.10 THIRD NINE WEEKS (CONTINUED) Coterminal Angles Apply a procedure to evaluate trigonometric expressions. Introduction to Sine, Cosine, and Tangent with the Unit Circle Apply a procedure to evaluate trigonometric expressions. Reference Angles Apply a procedure to evaluate trigonometric expressions. Graphs of Sine, Cosine & Tangent (Include Domain & Range) Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, days intercepts, and asymptotes). Solving Simple Trigonometric Equations Carry out a procedure to solve trigonometric equations days algebraically TEST Area of a Triangle Given Two Sides & Included Angle PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle. Law of Sines & Cosines PC-5.1 Apply the laws of sines and cosines to solve problems. days PC-5.14 PC-5.10 G-6.1 G-6. IA-5.1 ADMINISTER TEACHER-MADE INTERIM ASSESSMENT FOURTH NINE WEEKS Trigonometric Identities (Pythagorean, Reciprocal, Co-Function) Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities. Solving Trigonometric Equations Carry out a procedure to solve trigonometric equations TEST Review Practice for SAT ( days) Distance & Midpoint Formulas Use the distance formula to solve problems. Use the midpoint formula to solve problems. Writing Equations of & Graphing Circles Carry out a procedure to graph the circle whose equation is the form x + y = r. IA-5. PC-6.1 PC-6. PC-6.3 Carry out a procedure to write an equation of a circle centered at the origin when given its radius. Carry out a procedure to graph the circle whose equation is the form (x h) + (y k) = r. Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle. Apply a procedure to calculate the coordinates of points where a line intersects a circle. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011

7 EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. G-1. Communicate knowledge of geometric relationships by using mathematical terminology appropriately IA-5.3 IA-5.4 FOURTH NINE WEEKS (CONTINUED) Writing Equations of & Graphing Ellipses with Center at (0,0) Carry out a procedure to graph the ellipse whose equation is the form x a + y b =1. Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices. IA-5.5 IA-5.6 PC-6.4 PC-6.5 PC-6.6 IA-.11 Writing Equations of & Graphing Hyperbolas with Center at (0,0) Carry out a procedure to graph the hyperbola whose equation is the form x a y b =1. Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices. Writing Equations of & Graphing Ellipses & Hyperbolas Not Centered at (0,0) Carry out a procedure to graph the ellipse whose ( x h) ( equation is the form + y k ) =1. a b days Carry out a procedure to graph the hyperbola whose ( ) ( ) x h y k equation is the form = 1. a b Writing Equations of & Graphing Parabolas Carry out a procedure to graph the parabola whose equation is the form y k = a(x h). Solve Quadratic Systems Graphically and Algebraically Carry out a procedure to solve a system of equations (including two linear functions and one linear function days with one quadratic function). TEST Review Practice for Final Exam (3 days) ADMINISTER FINAL TEACHER-MADE INTERIM ASSESSMENT NOTE: THIS INSTRUCTIONAL GUIDE IS BUILT TO ASSIST IN PROVIDING TIME FOR AND REMEDIATION FOR STATE ASSESSMENT. RICHLAND COUNTY SCHOOL DISTRICT ONE CANNOT BE REPRODUCED WITHOUT PERMISSION CURRICULUM AND INSTRUCTION JUNE 011