Course ...



Course: Algebra II Unit of Study: Unit 2: Algebraic Competency & Unit 3: Quadratic Functions and the Complex Number System

Beginning Date: 10/01/12 Ending Date: 10/05/12

State competency goal:

A.APR.6 REWRITE simple rational expressions in different forms; WRITE a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

A.APR.7 Simplify rational expressions by adding, subtracting, multiplying, or dividing.

F.IF.7 Graph linear functions showing intercepts, quadratic functions showing intercepts, maxima, or minima

F.IF.5 Given the graph of a function, determine the practical domain of the function as it relates to the numerical relationship it describes.

F.IF.4 Given a function, identify key features in graphs and tables including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

| | | |Teacher Input | | |

| | | |(2. Presentation) | | |

| | |Activating Strategy/ Emotional Hook | | | |

|Date |Big |(1. Start the lesson) |Student Active Participation |Summarizing Activity |Closure |

| |Question (s): | |(3. Guided practice) |(5. Evaluation) | |

| | | |__________________________ | |________________________ |

| | | |Additional Student Activities | | |

| | | |(4. Independent practice) | |Homework |

| | |Warm- ups: |Instruction: | | |

| |How do I divide a polynomial by|Simplify: |Dividing polynomials |Take-home assessment |Answer the big question |

|10/01/12 |a polynomial or a monomial? |1.[pic] 2.[pic] |Dividing polynomials by long division | | |

| | |3. [pic] |Dividing polynomials by synthetic division |Lesson 4 - polynomial activity (from |Lesson 4 - polynomial activity (from |

| | |4. (2x + 1) - (3x – 4) |Guided Practice: |illuminations) |illuminations) |

| |A.APR.6 / A.APR.7 | |Dividing polynomials Guided notes | | |

| | | |Long division video | | |

| | | |Independent Practice: | | |

| | | |Dividing polynomials ppt examples | | |

|10/02/12 | |Warm- ups: |Instruction: |T.O.D. | |

| |How do I add and subtract |Rewrite the rational exponents as a |Adding and Subtracting Rational Expressions |1. [pic] 2. |Rational Mult Divide Worksheet |

| |rational expressions? |radical; Rewrite the radicals with |Intro to Multiplying and Dividing Rational Expressions |[pic] | |

| | |rational exponents. |Guided Practice: |3. [pic] | |

| |How do I multiply and divide |1. [pic] 2. [pic] 3. Rewrite [pic]in at |Adding and subtracting rational expressions Notes | | |

| |rational expressions? |least three alternate forms. |Adding and Subtracting Rational Expressions | | |

| | | |PowerPoint | | |

| | | |Intro to Multiplying /Dividing Rational expressions notes| | |

| |A.APR.7 | |Independent Practice: | | |

| | | |Practice with Rational Expressions | | |

| |How do I determine the domain, |Warm- ups: |Instruction: | | |

| |range, maximum, minimum, roots,|Activating Strategy-Data Analysis |Intro to Quadratic Functions |1. Find the answer of 1072 by using | |

|10/03/12 |and y-intercept of a quadratic | |Guided Practice: |polynomial identities. |Algebraic Fractions puzzle |

| |function from its graph? | |Intro to Quadratics Activating Strategy |2. Sally calculates (x + 3)2 to be x2 | |

| |How do I use quadratic | |Independent Practice: |+ 9 | |

| |functions to model data? | |Intro to Quadratics FI |a. Examine her answer to see if she is| |

| |F.IF.7/ F.IF.4 | | |correct. | |

| | | | |b. Verify your answer to part (a) by | |

| | | | |looking at the table on your graphing | |

| | | | |calculator | |

| | | | |c. Verify your answer to part (a) by | |

| | | | |substituting in a number for x and | |

| | | | |evaluating the original problem and | |

| | | | |her answer | |

| | | | |d. If she is incorrect, explain her | |

| | | | |mistake. Then verify correct answer | |

| | | | |with methods (b) and (c) | |

| |How do I determine the domain, |Warm- ups: |Instruction: | | |

| |range, maximum, minimum, roots,|1. Which of the following expressions are |Quadratic Functions & Apps | | |

| |and y-intercept of a quadratic |equivalent to (2x+3)2 ; Choose all that | | |Water Fountain Directions |

|10/04/12 |function from its graph? |apply: A) 4x2 +12x + 9 |Guided Practice: |Q & A before testing | |

| | |B) (2x+3)(2x+3) C) 4x2 + 9 |Quadratic Applications PowerPoint |Review of unit 2: algebraic competency| |

| |How do I use quadratic |D) (2x)2 + 2(6x) + 32 |Quadratic Applications GO |with jeopardy | |

| |functions to model data? |: Consider the following algebraic |Independent Practice: | | |

| |F.IF.7 / F.IF.4 |expressions (n+2)2 − 4 and n2 + 4n |Quadratics Applications Intro and PowerPoint Notes | | |

| | |a.) Use the figures below to illustrate | | | |

| | |why the following expressions are | | | |

| | |equivalent: b.) Find some algebraic | | | |

| | |deductions of the same result. | | | |

| | |[pic] | | | |

| | |Warm- ups: |Independent Practice: | | |

| |What are the three forms of a |Factor the following completely: | | | |

|10/05/12 |quadratic function, and how do |a) x3 – 8y3 b) x4 – 16 c) x3 + 10x2 +| |Unit 1/2 Test | |

| |I use the information from each|24x |Unit 1 and 2 Assessments | |n/a |

| |to graph the function? |The graph of the function y = x2 – x – 2 | | | |

| | |is drawn below. | | | |

| | |[pic] | | | |

| | |(a) Write down the coordinates of the | | | |

| | |point C. | | | |

| | |(b) Calculate the coordinates of the | | | |

| | |points A and B. | | | |

|Literacy enhancements/Key Vocabulary: |binomial, coefficient, complex fraction, conjugates, constant, degree, foil method, leading coefficient, like radical expression, like terms, monomial, , nth root, negative |

| |exponent, polynomial, polynomial function, principal root, radical, rational expression, rational exponent, rationalizing the denominator, square root, synthetic division, |

| |term, trinomial, axis of symmetry, completing the square, complex conjugates, complex numbers, constant term, i (imaginary unit), maximum value, minimum value, parabola, |

| |quadratic equation, quadratic form, quadratic formula, quadratic function, quadratic term, root, vertex, vertex form, zeros |

| | |

|Adaptations/Differentiation: | |

|Warm- ups: |

|Simplify: |

|1.[pic] 2.[pic] |

|3. [pic] |

|4. (2x + 1) - (3x – 4) |

|Warm- ups: |

|Rewrite the rational exponents as a radical; Rewrite the radicals with rational exponents. |

|1. [pic] 2. [pic] 3. Rewrite [pic]in at least three alternate forms. |

|Warm- ups: |

|Activating Strategy-Data Analysis |

|Warm- ups: |

|1. Which of the following expressions are equivalent to (2x+3)2 ; Choose all that apply: A) 4x2 +12x + 9 B) (2x+3)(2x+3) C) 4x2 + 9 D) (2x)2 + 2(6x) + 32 |

|2. Consider the following algebraic expressions (n+2)2 − 4 and n2 + 4n |

|a.) Use the figures below to illustrate why the following expressions are equivalent: |

|b.) Find some algebraic deductions of the same result. |

|Warm- ups: |

|Factor the following completely: |

|1) x3 – 8y3 |

|2) x4 – 16 c |

|3) x3 + 10x2 + 24x |

|4) The graph of the function y = x2 – x – 2 is drawn to the right. |

| |

|(a) Write down the coordinates of the point C. |

|(b) Calculate the coordinates of the points A and B. |

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