Mathematics Curriculum Map

Grade Level: 9th – 12th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 9 blocks (RTI – highlighted in red) Pre-AP 7 days Unit: Piecewise Functions

Enduring Understanding: a. Patterns are structures that are repeated in a variety of applications. b. Change is inevitable. It happens at different rates in different situations.

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Name examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future?

Vocabulary Instructional Activities/ Concept/Topic Indicators Development Assessment Strategies Extension Activities Resources Piecewise review of absolute value inequalities Absolute Review solving absolute value Calculator use Functions Value equations. http://regentsprep.org/Regents/math/algtrig/ma | | Review solving absolute value th-algtrig.htm#m6 inequalities. * 1.7 C 1.7 Parent IA-2.7 Carry out a procedure to graph Parent Review graphing (translations and Calculator use Functions translations of parent function transformations) of line equations. www.mastermathmentor.com Piecewise functions (including Piecewise Graph y = | x – h | and discuss the http://online.math.uh.edu/Math1310/ functions y= x, y = x , ). function changes in the absolute value parent * 2.8 Vertex function. C 2.7 Vertical Graph y = | x | + k and discuss the translation changes in the absolute value parent Horizontal function. translation

0277647377067a9437e9f85780ce0f6f.doc 8/2/10 1 300 South Catawba Street, Lancaster SC 29720 Mathematics Curriculum Map

Vocabulary Instructional Activities/ Concept/Topic Indicators Development Assessment Strategies Extension Activities Resources Parent IA-2.8 Carry out a procedure to Wider Review graphing (translations and Calculator use Functions graph transformations of (shrink) transformations) of line equations. www.mastermathmentor.com Piecewise parent Narrower Graph y = a| x | and discuss the http://online.math.uh.edu/Math1310/ functions functions (including y = x and y = |x|). (stretch) changes in the absolute value parent * 2.8 Condensed function. C 2.7 Elongated Graph y =a | x – h | + k and discuss the changes in the absolute value parent function. Piecewise IA-2.9 Carry out a procedure to Function Graph piecewise functions. Calculator use functions graph discontinuous notation Graph step functions. www.mastermathmentor.com functions Step Function * 2.7 (including piecewise and step [[ ]] C EXT p130 functions).

Parent IA-2.10 Carry out a procedure to Domain Find the domain of the function Calculator Functions determine the domain and range of Range graphically and algebraically. www.mastermathmentor.com Piecewise discontinuous functions (including Find the range of the function * 2.7 functions piecewise and step functions) graphically and algebraically. C EXT p130 Unit Test * Chapter 1 Resource Book Chapter 2 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 6 blocks (RTI – highlighted in red) Pre-AP 15 days Unit: Systems of Linear Inequalities

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future?

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Systems of IA-2.2 Carry out a procedure to Linear Review graphing linear equations. Calculator inequalities solve a system of linear inequalities Inequality Graph systems of linear inequalities http://www.kutasoftware.com/freeia2.html graphically. Solution with graph paper and the graphing http://regentsprep.org/Regents/math/ALGEBR Graph calculator. A/math- Half-planes ALGEBRA.htm#Equations_and_Inequalities_ _ * 2.6,3.3 C 2.8,3.3

Systems of IA-2.1 Carry out a procedure to System of http://www.kutasoftware.com/freeia2.html inequalities solve a system of linear inequalities linear * 2.6,3.3 algebraically. inequalities C 2.8,3.3

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Systems of IA-2.3 Analyze a problem Write inequalities from an http://www.kutasoftware.com/freeia2.html inequalities situation to determine a application problem. * 2.6,3.3 system of C 2.8,3.3 linear inequalities that models the problem situation.

Systems of IA-2.4 Use linear programming to Optimization Graph the system of linear * 3.4 inequalities solve contextual problems Linear inequalities. C EXT p174 involving a system of linear programming Find the vertices. inequalities Objective Determine the maximum and function minimum by substituting the Constraints vertices into the optimization Feasibility equation. region Unit Test *Chapter 2 Resource Book Chapter 3 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 10 blocks

(RTI – highlighted in red) Pre-AP 20 days Unit: Complex Numbers/Quadratic Functions

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Name examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future?

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies

Complex numbers IA-3.1 Carry out a procedure to Imaginary Simplify a variety of imaginary http://www.kutasoftware.com/freeia2.html simplify expressions unit expressions involving exponents. http://regentsprep.org/Regents/math/algtrig/ma involving powers of i. th-algtrig.htm#m6 * 5.4 C 4.6 Complex numbers IA-3.2 Carry out a procedure to Complex number Add, subtract, and multiply http://www.kutasoftware.com/freeia2.html perform operations Standard form complex numbers. * 5.4 Imaginary with complex numbers (including number Rationalize the denominator C 4.6 addition, subtraction, Pure imaginary (divide) of a fraction formed by 2 multiplication, and division). number complex numbers. Complex plane Complex

conjugates

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Graphing quadratic IA-2.7 Carry out a procedure to Quadratic Graph y = x² on graph paper (use the Calculator use equations graph translations of parent functions function calculator to make a table) and the www.mastermathmentor.com (including y= x²). Parabola calculator. *5.1 Vertex Graph y = (x – h)² and discuss the C4.1 Axis of effect of h on the position of the graph. symmetry Graph y = x ² + k and discuss the effect Standard form of k on the position of the graph. Vertex form Intercept form Quadratic equations IA-2.8 Carry out a procedure to Graph y = ax ² and discuss the effect of Calculator use graph transformations a on the change in the graph. www.mastermathmentor.com of parent functions (including y= x²). Graph y = a(x – h) ² + k and discuss http://regentsprep.org/Regents/math/ALGEBRA/m the effect of a, h, and k on the change ath-ALGEBRA.htm#Equations_and_Inequalities__ in the graph. * 5.1 C 4.1,4.2 Quadratic equations IA-3.3 Carry out a procedure to Binomial Solve equations by factoring. http://www.kutasoftware.com/freeia2.html solve quadratic equations Trinomial Solve equations by completing the http://regentsprep.org/Regents/math/algtrig/math- algebraically (including factoring, Factoring square. algtrig.htm#m6 completing the square, and Monomial Solve equations using the quadratic http://online.math.uh.edu/Math1310/ applying the quadratic formula). Quadratic formula. * 5.2,5.3,6.6 equation Standard form Solutions should include rational, C 4.3 -4.5, 4.7-4.8 Zeros irrational and complex numbers. Square root Radical sign Radicand Radical Rationalizing the denominator Completing the square Quadratic

formula

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Quadratic IA-4.3 Carry out a procedure to Factor by Solve equations using factoring by * 5.2, 5.3, 6.6, p346 equations solve grouping grouping and factoring special C 4.3 -4.5, 4.7-4.8, p354 polynomial(quadratic) Difference of products. equations (including factoring by 2 squares grouping, factoring the difference between two squares). Quadratic IA-3.4 Use the discriminant to Discriminant Use the discriminant to determine http://www.kutasoftware.com/freeia2.html equations determine the number and the number and type * 5.6 type of solutions of a quadratic equation. C 4.8 of solutions of a quadratic equation. Quadratic IA-3.6 Carry out a procedure to Given the rational, irrational and * 5.6 equations write an equation of a complex roots write the equation of C 4.8 quadratic a quadratic function. function when given its roots. Quadratic IA-3.5 Analyze given information Find the solution to an application * Chapter 5 equations (including quadratic problem when the formula is given. models) to solve contextual Write the equation for an problems. application problem and solve based on the given information. Carry out a procedure to solve Review solving quadratic *5.7 quadratic inequalities inequalities both graphically and C 4.9 algebraically. IA-2.11 Carry out a procedure to Review solving systems of linear * 3.1,3,2, Supplement Systems solve a system of equations equations. (including two linear functions and Solve a system that includes a C 3.1, 3.2 one linear function with linear and a quadratic function both

one graphically and algebraically. quadratic function). Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Systems Carry out a procedure to solve a Ordered Solve a 3 equation system *3.4 system of 3 equations in 3 Triple algebraically. C variables. Unit Test * Chapter 3 Resource Book Chapter 5 Resource Book Chapter 6 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 13 blocks (RTI – highlighted in red) Pre-AP 20 days Unit: Polynomial Functions

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future?

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Polynomials IA-4.1 Carry out a procedure to Polynomial Review Laws of Exponents. http://www.kutasoftware.com/freeia2.html perform operations function Review adding and subtracting www.mastermathmentor.com (including multiplication, Leading polynomial expressions. http://regentsprep.org/Regents/math/algtrig/ma exponentiation, and coefficient Multiply polynomial expressions. th-algtrig.htm#m6 division) Constant term Exponentiate polynomial http://online.math.uh.edu/Math1310/ with polynomial expressions Degree expressions. * 6.1, 6. 2,6.3-6.5 Standard form Divide polynomial expressions both C 5.3-5.5 Synthetic with long division and synthetic substitution division. Polynomial long division Synthetic

division

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Polynomials IA-2.5 Carry out procedures to Power Review function notation. http://www.kutasoftware.com/freeia2.html perform operations function Using function notation, add, http://online.math.uh.edu/Math1310/ on polynomial functions (including subtract, multiply and divide * 7.3 f(x) + g(x), f(x) – g(x), polynomial functions. C 6.3 f(x) • g(x), and f(x)/g(x)). Polynomials IA-2.6 Apply a procedure to write Composition Using function notation, find the * 7.3 the equation of a composition of functions. C 6.3 composition of given functions.

Polynomials IA-4.3 Carry out a procedure to End behavior Solve polynomial functions by http://www.kutasoftware.com/freeia2.html solve polynomial Quadratic factoring. * 6.6,6.7 equations (including factoring by form grouping, factoring the C5.6 difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes).

Polynomials IA-4.2 Carry out a procedure to Local Find the zeros of a function, Calculator use determine specified maximum algebraically and graphically (with www.mastermathmentor.com points (including zeros, maximums, Local both graph paper and the graphing * 6.8 and minimums) of minimum calculator). C 5.8 polynomial functions. Extrema Find the local extrema ( local maximums and local minimums) both algebraically and with the graphing calculator.

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Polynomials IA-4.4 Analyze given information Solve application problems given * 6.8 (including polynomial the formula. C 5.8 models) to solve contextual Solve application problems writing problems. the equation from the problem.

Unit Test * Chapter 6 Resource Book Chapter 7 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 11 blocks (RTI – highlighted in red) Pre-AP 20 days Unit: Rational Functions

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future? Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Rational IA-4.8 Carry out a procedure to Rational Add, subtract, multiply and divide http://www.kutasoftware.com/freeia2.html Functions perform operations function rational expressions. www.mastermathmentor.com with rational expressions (including Hyperbola http://online.math.uh.edu/Math1310/ addition, subtraction, Branches * 8.4, 8.5 multiplication, and division). Asymptote C 9.4 – 9.5 Simplified form Complex fraction Rational IA-4.12 Carry out a procedure to Cross Solve rational equations using cross http://www.kutasoftware.com/freeia2.html Functions solve rational multiplying multiplication. http://regentsprep.org/Regents/math/algtrig/ma equations algebraically. Solve rational equations th-algtrig.htm#m6 multiplying by the LCD. * 8.6

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Rational IA-2.7 Carry out a procedure to Graph rational functions. http://www.kutasoftware.com/freeia2.html Functions graph translations Find horizontal and vertical www.mastermathmentor.com of parent functions asymptotes. http://online.math.uh.edu/Math1310/

2 1 * 8.3, 8.3 y  x, y  x , y  x , y  x , and y  x C 9.3, 9.3 Unit Test * Chapter 9 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 10 blocks (RTI – highlighted in red) Pre-AP 22 days Unit: Rational Functions

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future? Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Rational IA-4.5 Carry out a procedure to n th root of a Change rational expressions to http://www.kutasoftware.com/freeia2.html exponents simplify algebraic Index radical expressions and vice versa * 7.1 expressions involving rational Simplest form Simplify expressions. C 6.1 exponents Like radicals

IA-4.7 Carry out a procedure to Add, subtract, multiply, divide, and http://www.kutasoftware.com/freeia2.html perform operations with exponentiate expressions with *7.2 expressions involving rational exponents. C 6.2 rational exponents (including addition, subtraction, multiplication, division, and exponentiation).

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Radical Equations IA-4.9 Carry out a procedure to Radical Solve radical equations. http://www.kutasoftware.com/freeia2.html solve radical functions Determine if roots are extraneous. www.mastermathmentor.com equations algebraically. Extraneous http://regentsprep.org/Regents/math/algtrig/ma solution th-algtrig.htm#m6 * 7.6 C 6.6 Radical Functions IA-2.7 Carry out a procedure to Graph radical functions. www.mastermathmentor.com graph translations http://online.math.uh.edu/Math1310/ of parent functions * 7.5 1 C 6.5 y  x, y  x2 , y  x, y  x , and y  x .

Unit Test * Chapter 7 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 11 blocks (RTI – highlighted in red) Pre-AP 23 days Unit: Exponential and Logarithmic Functions

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future? Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Exponential IA-4.14 Carry out a procedure Exponential Graph exponential functions, http://www.kutasoftware.com/freeia2.html functions to graph exponential function including base e. www.mastermathmentor.com functions. Base http://regentsprep.org/Regents/math/ALGEBR Asymptote A/math- Exponential ALGEBRA.htm#Equations_and_Inequalities_ growth _ function http://regentsprep.org/Regents/math/algtrig/ma Exponential th-algtrig.htm#m6 decay http://online.math.uh.edu/Math1310/ function * 8.1 – 8.3 Growth factor C 7.1 – 7.3 Decay factor Natural base e, Euler

number Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Logarithmic IA-4.13 Carry out a procedure to graph Inverse Graph logarithmic functions, including Calculator use Functions logarithmic Function ln. http://www.kutasoftware.com/freeia2.html functions. Logarithm of y www.mastermathmentor.com with base b http://regentsprep.org/Regents/math/algtrig/math- Common algtrig.htm#m6 logarithm http://online.math.uh.edu/Math1310/ Natural * 7.4, 8.4 logarithm C 6.4, 7.4

Logarithmic IA-4.11 Carry out a procedure to solve Find the zeros of the logarithmic Calculator use Functions logarithmic functions graphically. * 8.4 equations graphically C 7.4 Logarithmic IA-4.6 Carry out a procedure to Use the Properties of Logarithms to http://www.kutasoftware.com/freeia2.html Functions simplify algebraic rewrite algebraic expressions involving * 8.6, 8.5 expressions involving logarithms. logarithms (both expanding and C 7.6, 7.5 condensing). Logarithmic IA-4.10 Carry out a procedure to solve Logistic growth Solve logarithmic functions using the http://www.kutasoftware.com/freeia2.html Functions logarithmic function Properties of Logarithms. * 8.6 equations algebraically. C 7.6

Unit Test * Chapter 7 Resource Book Chapter 8 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 10 blocks (RTI – highlighted in red) Pre-AP 20 days Unit: Conic Sections

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future? Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Conic Sections IA-5.1 Carry out a procedure to Distance Find the distance between 2 points. Calculator use graph the circle whose formula Find the midpoint of a line http://mathworld.wolfram.com/ConicSection.h equation is the form Midpoint segment. tml x 2  y 2  r 2 . formula Graph a circle from the center and http://math2.org/math/algebra/conics.htm Circle radius. http://www.personal.psu.edu/smh408/home.ht Center m Radius http://www.kutasoftware.com/freeia2.html  http://www.regentsprep.org/Regents/math/geo metry/math-GEOMETRY.htm#m6 * 10.3, 10.1 C 9.3, 9.1 Conic Sections IA-5.2 Carry out a procedure to Standard form Write the equation of a circle with a http://regentsprep.org/Regents/math/algtrig/ma write an equation of a of the given radius. th-algtrig.htm#m6 circle centered at the origin equation of a * 10.3

when given its radius. circle C 9.3 Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Developme Assessment Extension Activities nt Strategies Circles PC-6.1 Carry out a procedure to Graph a circle with center at (h, k). http://edhelper.com/conics.htm graph the circle whose Supplement (Pre-Calculus Book) equation is the form (x  h)2  (y  k)2  r2. Parabola PC-6.6 Carry out a procedure to Directrix Graph a parabola and its focus and http://edhelper.com/conics.htm graph the parabola whose Focus directrix. Supplement (Pre-Calculus Book) equation is the form  y  k  a(x  h)2 . Conic Sections IA-5.3 Carry out a procedure to Ellipse Graph an ellipse using vertices, co- Calculator use graph the ellipse whose Foci vertices, foci, etc. * 10.4 equation is the form Vertices C 9.4  x 2 y 2 Major axis   1 . a 2 b 2 Center Co-vertices Minor axis

 Conic Sections IA-5.4 Carry out a procedure to Standard form Given key parts of the ellipse, write http://edhelper.com/conics.htm write an equation of an of the the equation of the ellipse in * 10.4 ellipse centered at the equation of an standard form. C 9.4 origin when given ellipse information from among length of major axis, length of minor axis, and vertices.

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Ellipse PC-6.4 Carry out a procedure to Graph an ellipse with the center at http://edhelper.com/conics.htm graph the ellipse whose (h, k). Supplement (Pre-Calculus Book) equation is the form x  h 2 y  k 2   1 . a 2 b 2 Conic Sections IA-5.5 Carry out a procedure to Hyperbola Graph a hyperbola using vertices, http://edhelper.com/conics.htm graph the hyperbola Foci foci, and asymptotes. Calculator use Vertices * 10.5,9.1 whose equation is the form Transverse C 9.5, 8.1 x 2 y 2   1 . axis a 2 b 2 Center Conic Sections IA-5.6 Carry out a procedure to Standard form Given key parts of the hyperbola, http://edhelper.com/conics.htm write an equation of a of the write the equation of the hyperbola * 10.5  equation of a in standard form. C 9.5 hyperbola centered at the origin with hyperbola specified vertices. Hyperbola PC-6.5 Carry out a procedure to Graph a hyperbola with the center http://edhelper.com/conics.htm graph the hyperbola whose at (h, k). Supplement (Pre-Calculus Book) equation is the form x  h2 y  k2   1. a2 b2

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Conic Sections IA-5.7 Match the equation of a Conic Using the discriminant, determine http://www.anderson3.k12.sc.us/crescent/Alex conic section with its sections the type of graph from the equation ander/lesson-template1.htm (conics) without graphing. http://www2.latech.edu/~slk/Webquest/Webqu graph. General Using the coefficients of the est1.htm second degree squared terms, determine the type http://teacherlink.ed.usu.edu/tlresources/units/ equation of graph from the equation without HodgesFall2005/RichardWalker/Conic Discriminant graphing. %20Sections%20Webquest.pdf http://edhelper.com/conics.htm * 10.6 C 9.6 Unit Test * Chapter 9 Resource Book Chapter 10 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

Grade Level: 9th Title: Algebra 2 (optional PreAP materials – highlighted in green) Time Frame: CP 10 blocks (RTI – highlighted in red) Pre-AP 15 days Unit: Sequences and Series

Essential Questions: a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific process learned in this unit. Explain how this process is similar to one learned in an earlier unit? b. 1. Give examples of things that change. How do they differ from one another? 2. Which models can we use to represent different types of change? 3. How can we apply these models to make decisions about the future? Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Developme Assessment Extension Activities nt Strategies Sequences and IA-6.1 Categorize a sequence as Terms Find the pattern in a sequence. http://www.kutasoftware.com/freeia2.html Series arithmetic, geometric, Sequence Determine if the type of sequence . http://regentsprep.org/Regents/math/algtrig/ma or neither. Finite th-algtrig.htm#m6 sequence * 11.1 – 11.3 Infinite C 12.1 – 12.3 sequence Arithmetic sequence Common difference Geometric sequence Common ratio

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Sequences and IA-6.2 Carry out a procedure to Find the nth term using formulas . http://www.kutasoftware.com/freeia2.html Series write a specified term http://regentsprep.org/Regents/math/algtrig/ma of an arithmetic or geometric th-algtrig.htm#m6 sequence when given the * 11.2 – 11.3 nth C 12.2 – 12.3 term of the sequence. Sequences and IA-6.3 Carry out a procedure to Given a list of consecutive terms, http://www.kutasoftware.com/freeia2.html Series write a formula for write the formula for the nth term http://regentsprep.org/Regents/math/algtrig/ma the nth term of an arithmetic or of the sequence. th-algtrig.htm#m6 geometric sequence when * 11.2 – 11.3 given at least four consecutive terms C 12.2 – 12.3 of the sequence.

Sequences and IA-6.4 Carry out a procedure to Given 4 nonconsecutive terms, http://www.kutasoftware.com/freeia2.html Series write a formula for the write the formula for the nth term. http://regentsprep.org/Regents/math/algtrig/ma nth term of an arithmetic or th-algtrig.htm#m6 geometric sequence when * 11.2 – 11.3 given C 12.2 – 12.3 at least four terms of the sequence. Sequences and IA-6.5 Represent an arithmetic or Series Write a series using sigma notation. http://www.kutasoftware.com/freeia2.html Series geometric series by Sigma http://regentsprep.org/Regents/math/algtrig/ma using sigma notation. notation th-algtrig.htm#m6 Arithmetic * 11.2 – 11.4 series C 12.2 – 12.4 Geometric series

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Sequences and IA-6.6 Carry out a procedure to Find the sum of a series written in http://www.kutasoftware.com/freeia2.html Series calculate the sum of an sigma notation. http://regentsprep.org/Regents/math/algtrig/ma arithmetic or geometric series written th-algtrig.htm#m6 in sigma notation. * 11.2 – 11.4 C 12.2 – 12.4

Sequences and IA-6.7 Carry out a procedure to Write a sequence from recursive http://www.kutasoftware.com/freeia2.html Series determine consecutive equation. http://regentsprep.org/Regents/math/algtrig/ma terms of a sequence that is defined th-algtrig.htm#m6 recursively. * 11.5 C 12.5

Sequences and IA-6.8 Carry out a procedure to Write the recursive equation for a http://www.kutasoftware.com/freeia2.html Series define a sequence given sequence. http://regentsprep.org/Regents/math/algtrig/ma recursively when given four or more th-algtrig.htm#m6 consecutive terms * 11.5 of the sequence. C 12.5

Sequences and IA-6.9 Translate between the Explicit rule Rewrite the equation of a sequence http://www.kutasoftware.com/freeia2.html Series explicit form and the Recursive rule changing a recursive equation in http://regentsprep.org/Regents/math/algtrig/ma recursive form of sequences. Factorial explicit form, and vice versa. th-algtrig.htm#m6 * 11.5 C 12.5

Vocabulary Instructional Activities/ Resources Concept/Topic Indicators Development Assessment Extension Activities Strategies Unit Test * Chapter 11 Resource Book Standardized Test Practice Workbook * Old version of textbook C New adoption of textbook

0277647377067a9437e9f85780ce0f6f.doc 8/2/10 25 300 South Catawba Street, Lancaster SC 29720