San Jose Unified School District. Algebra 2 Pacing Calendar

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1 San Jose Unified School District Algebra 2 Pacing Calendar SJUSD ALGEBRA 2 TIMELINE Page 1 of 10

2 SJUSD ALGEBRA 2 PACING GUIDE FOR The Algebra 2 curriculum has been broken into logical units of study called Benchmark Periods (BMPs), as outlined below. Each benchmark period is followed by a benchmark assessment. Each of the four benchmark tests is each designed to be completed in two periods. Several days of review have been built into the calendar prior to each assessment, and five days after the assessment to re-teach, review and enrich missed material. Each exam emphasizes all of the state content standards. The first benchmark assessment is to be used as a baseline test. The fourth benchmark assessment is designed to identify areas of focus for the CST review sessions. There will be 4 benchmark periods over the course of the year. They will be administered over two days (as determined by the school site) during the following testing periods: Benchmark 1: August two-period exam Benchmark 2: October 5-9 two-period exam Benchmark 3: November 30 December 4 two-period exam (Dec. 16, 17, 18 Final exams for high schools) Benchmark 4: February 8-12 two-period exam (June 1, 2, 3 Final exams for high schools) No calculators of any kind may be used on any of the benchmark exams. Starred standards make up 70 percent of the CST. Spiraling will be a major key to success on student achievement and on CST exams. The purpose of the pacing calendar and benchmark tests is to promote standards based teaching in preparation for the STAR/CST. SJUSD ALGEBRA 2 TIMELINE Page 2 of 10

3 CLARIFICATIONS Calculators and Technology: Calculators are prohibited on all benchmark exams as calculators are not permitted on the CST. Use of graphing calculators throughout the year for exploration and demonstration purposes is highly recommended. Geometer s Sketchpad can be used to develop skills and aid in visualization in the context of the course content. Word Problems: Word problem questions make up between 20% and 25% percent of the CST and should be incorporated into the course and emphasized on a regular basis. Spiraling Curriculum: A spiral approach to developing skills and concepts is suggested since students may not reach mastery in the time allotted. Continuous review will facilitate student retention of concepts. Textbook Alignment: This pacing guideline is designed to be independent of any text. Material is divided and taught in thematic groupings to facilitate student learning. Need to Supplement the Textbook: The Algebra 2 text will need to be supplemented heavily when working on analysis and critical thinking. Most of the texts offer limited experience with problem solving and word problems necessitating the use of additional sources. SJUSD ALGEBRA 2 TIMELINE Page 3 of 10

4 VOCABULARY The CST and CAHSEE use a predictable set of vocabulary. Teachers should use appropriate terminology and force their students to do the same. Catchy mnemonics can be useful when introducing a concept, but students need to be fully conversant in mathematical language. The following is not an exhaustive list, but it provides a thorough foundation. VOCABULARY FROM ALGEBRA 2: absolute value additive, multiplicative identity additive, multiplicative inverse algebraic proof counterexample, justification cross multiplication, proportion distributive, associative, commutative domain, range exponential functions function, relation, function notation hypothesis, conclusion inductive, deductive reasoning intersection point inverse operations linear combination linear, quadratic logarithmic functions model with a graph and/or an equation monomial, binomial, polynomial ordered pair parallel, perpendicular perfect square, square root point-slope form power, exponent, degree, base rate of change, slope rational, irrational numbers reciprocal, negative, opposite root, solution, x-intercept slope-intercept form solution to linear system standard form of a quadratic equation standard form of the equation of a line system of equations, inequalities term, coefficient, constant valid, invalid argument vertex form of quadratic equation vertical change, horizontal change x-intercept(s), y-intercept zeros of a function SJUSD ALGEBRA 2 TIMELINE Page 4 of 10

5 HOW TO READ THE TIMELINE CA Standards from which a section s content are drawn (Starred standards make up 70 percent of the CST; an A indicates a standard drawn from Algebra I, and a dash ( ) indicates foundational material not specifically tested on the CST.) Section number within the pacing calendar (This does not correspond to a section in a textbook.) Checkbox UNIT 1: Algebra Review Std Days 1.1 Solve proportions using cross-multiplication ( 8.1) A Write the equation of a parallel line through a 17* 1 specific point ( 3.6) 1.3 Write the equation of a perpendicular line through a specific point ( 3.7) 17* Multiply radicals with integer coefficients A Reduce a radical expression to lowest terms A 1 Clear radicals from the denominators of fractions A 1.5 Factor a quadratic to find its roots A Use the quadratic formula to find the roots of a A 1 quadratic TOTAL 5 Discrete, measurable content or skill objective Section in the Geometry Text that contains the specific content or skill (Note: These notations do not suggest that the specific objective is covered to the depth required by the CST. Please supplement as often as possible, but those sections marked with a plus sign (+) require particular attention because the textbook is deficient in some way. If an objective is not paired with a textbook section, you will have to supplement with other materials.) Number of 50-minute instructional days the calendar recommends be spent on a section Textbook sections marked with a plus sign (+) require supplementary materials and/or lessons in order to cover the required concept. SJUSD ALGEBRA 2 TIMELINE Page 5 of 10

6 BENCHMARK 1: ALGEBRAIC THINKING 7 DAYS This benchmark period starts with reviewing Algebra I content. Baseline Benchmark 0 is given between August *Weave in standards 24.0 and 25.0 throughout the year as applicable. Unit 1a: (CA Algebra 1, CA Algebra 2 Standards 1.0, 2.0) Std Days 1.1 Review of Algebra 1 skills (Chapter 1) Alg1 5 TOTAL 5 Teaching: 5 days Assessment: 2 days BENCHMARK PERIOD 1 TOTAL: 7 DAYS Algebra 2 Benchmark 1 Assessment Date: 2 days during August SJUSD ALGEBRA 2 TIMELINE Page 6 of 10

7 BENCHMARK 2: LINEAR FUNCTIONS, SYSTEMS, QUADRATICS 34 DAYS In Benchmark Period 2, students will learn how to solve systems of equations with 3 variables. In unit two, students review factoring trinomials and simplifying radicals. Students then review solving quadratic equations by completing the square and factoring before moving into the new concept of complex numbers and their graphs. *Weave in standards 24.0 and 25.0 throughout the year as applicable. Unit 1b: (CA Algebra 1, CA Algebra 2 Standards 1.0, 2.0) Std Days 1.2 Absolute value equations and inequalities ( 2-8) Review graphing & slope/intercept ( 3-1) Alg Solving system of equations by graphing, substitution, elimination, word 2 5 problems ( 3-2) Solving system of inequalities by graphing ( 3-3) Solving systems with 3 variables by elimination, word problems ( 3-6) 2 2 TOTAL 13 Unit 2: (CA Algebra 2 Standards 5.0, 8.0, 9.0, 10.0) Std Days 2.1 Graphs of quadratic as a parent function with translations and dilations ( 5.1) 9,10 Parabolas,Equations in standard form, vertex form, more word problems ( 5-2) 9,10 5 Connect factoring quadratic equations to x-intercepts of the parabolas ( 5-3) 9, General factoring of all types of trinomials, factor by grouping ( 5-4) Solving quadratic equation by factoring ( 5-4) 8 5 Review simplifying square roots Alg Solve quadratic equations by completing the square ( 5-4) Imaginary numbers, complex numbers, and their graphs ( 5-5) 8 1 TOTAL 14 Review and Assessment: 7 days (Assessment: 2 days; Review/Re-teach/Enrich: 5 days) BENCHMARK PERIOD 2 TOTAL: 34 DAYS Algebra 2 Benchmark 2 Assessment Date: 2 days during October 5-9, 2009 Although all content standards will be tested, focus on the following standards during review: 1.0, 2.0, 4.0, 8.0, 24.0, 25.0 SJUSD ALGEBRA 2 TIMELINE Page 7 of 10

8 BENCHMARK 3: QUADRATICS, POLYNOMIALS, RATIONAL EXPRESSIONS, AND EXPONENTS 40 DAYS In this benchmark period the concept of complex numbers is taught, including all operations. Move into graphing parabolas and connect solutions to the intercepts of the graph, including imaginary solutions. After factoring the sum and difference of two cubes, students then review long division of polynomials, and connecting divisors and quotients with factors. Synthetic division is optional and may be taught if time permits. However, it is not a California Algebra 2 standard, so do not spend unnecessary time on it. End the benchmark period with simplifying, multiplying and dividing rational expressions, rational exponents, and composition of functions. *Continue to weave in standards 24.0 and 25.0 throughout the year as applicable. Unit 3: (CA Algebra 2 Standards 3.0, 6.0, 8.0) Std Days 3.1 Solve quadratic equations using the quadratic formula ( 5-6) Solving Word Problems using all 3 quadratic methods Add, subtract, multiply complex numbers ( 5-9) 6 4 Divide complex numbers, Graphing complex numbers( 5-9) 3.4 Introduction to polynomials, adding and subtracting polynomials 3 3 Multiplying polynomials ( 6-2) TOTAL 11 Unit 4: (CA Algebra 2 Standards 3.0, 4.0, 7.0, 12.0, 24.0) Std Days 4.1 Connect expanding polynomials to factoring diff of 2 squares & perfect sq 3, 4 2 trinomials ( 6 2, 6 4) 4.2 Sum, difference of 2 cubes ( 6 4) Long Division of polynomials, connect to factoring ( 6 3) Simplifying rational expressions ( 8 2) 7 1 Multiplying, dividing rational expressions ( 8 2) 7 2 Add, subtract rational expressions with like denominators ( 8 3) 7 1 Add, subtract rational expressions with like denominators with UNLIKE denominators ( 8 3) Rational exponents ( 8 6) More on Rational Exponents, Composition of Functions ( 8 7, 9 4) 12, 24 2 TOTAL 17 BMP Review and Assessment: 12 days (Assessment: 5 days, including 3 days for finals; Review/Re-teach/Enrich: 7 days) BENCHMARK PERIOD 3 TOTAL: 35 DAYS Algebra 2 Benchmark 3 Assessment Date: 2 days during December 1-4, 2009 Although all content standards will be tested, focus on the following standards during review: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 24.0, 25.0 First Semester Teacher-Made Final Exams: December 16-18, 2009 SJUSD ALGEBRA 2 TIMELINE Page 8 of 10

9 BENCHMARK 4: EXPONENTS AND LOGARITHMS, PROBABILITY 33 DAYS Continue to weave in standards 24.0 and 25.0 throughout the year as applicable. These reasoning standards will be especially useful as students begin learning the new topics of inverse relations and composite functions and logarithms. Spend time insuring student understanding of the applications of logarithms. This application section will need to be supplemented heavily. Unit 6 is designed to cover combinations, permutations and the probability and statistics standards before moving into conic sections. Unit 5: (CA Algebra 2 Standards 11.1, 11.2, 12.0, 13.0, 14.0, 15.0, 24.0) Std Days 5.1 Inverse of relations ( 7-2, 9-5) Graphs of exponential and log functions (as parent functions) ( 7-3) Properties of logarithms, change of base formula ( 7-4) 11.2, 13 2 Simplify logarithmic expressions & identify their approximate values 14 ( 7-4) 2 Natural Log, and the number e ( 7-5, 7-6) Applications of logarithms and exponents including growth and decay 12,13,15 functions (Chapter 7) 3 TOTAL 13 Unit 6: (CA Algebra 2 Standards 18, 19, 20, PS 1, 2, 7) Std Days 6.1 Counting principles, Permutations, Combinations ( 11-1) Theoretical and Experimental Probability ( 11-2) Probability of Independent, Dependent Events ( 11-3) PS:1 2 Compound probability including binomial probability, complements ( 11-4) 19 Conditional Probability, use in infinite sample spaces ( 11 3) PS: Standard deviation & variance ( 11 5) PS: Binomial Expansion( 11-6) 20 2 TOTAL 13 BMP Review and Assessment: 7 days (Assessment: 2 days; Review/Re-teach/Enrich : 5 days) BENCHMARK PERIOD 4 TOTAL: 33 DAYS Algebra 2 Benchmark 4 Assessment Date: 2 days during February 8-12, 2010 Although all content standards will be tested, focus on the following standards during review: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.1, 11.2, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 24.0, 25.0, Probability & Statistics Standards: PS1, PS2, PS7 SJUSD ALGEBRA 2 TIMELINE Page 9 of 10

10 CST PREP: SEQUENCES, SERIES, CONICS, CST REVIEW 24 DAYS This unit is designed to front-load Pre-calculus concepts to give students a head start on next year s course content. Students learn arithmetic, geometric, and infinite geometric sequences and series. End the unit with conics. Unit 7: (CA Algebra 2 Standards 16.0, 17.0, 22.0, 23.0) Std Days 7.1 Sequences and Recursion ( 12 1) Arithmetic sequences and series ( 12 3) Geometric sequences and series ( 12 4) Summation Notation ( 12 2) Infinite geometric series ( 12 5) Conic sections: Circles centered at the origin and translation ( 10 2) 16,17 1 Conic sections: Ellipses centered at the origin and translations ( 10 3) 16,17 2 Conic sections: Hyperbolas centered at the origin and translations ( 10 4) 16,17 2 Review Completing the square. Identify conics from equations. ( 10 6) 16,17 1 Review of parabolas, all conics with vertex centered at the origin, and their 16,17 translations ( 10 5) 1 TOTAL 15 CST PREP TOTAL: 24 DAYS (CST Review and Assessment: 9 days) PREPARING FOR PRE-CALCULUS 23 DAYS This unit continues to front-load Pre-calculus concepts. This early accessibility to polynomial functions, theorems about roots and Descartes Rule of Signs to facilitate graphing polynomials should give the Pre-calculus teacher more time to cover concepts in depth next year and should also allow more time to explore limits in preparation for AP Calculus. Continue Unit 7: (CA Algebra 2 Standard 21.0) Std Days 7.5 Mathematical Induction ( 12 5) 21 2 Reasoning Strategies Polynomials, polynomial functions ( 6 7) Remainder, factor theorems ( 6 3) 2 Theorems about roots ( 6 6) 2 Rational Roots ( 6 5) 2 Decartes Rule of Signs 2 Graphs of polynomial functions ( 6 7) 3 TOTAL 16 Post-CST Review and Assessment: 7 days (Assessment: 3 days; Review: 4 days) POST-CST TOTAL: 23 DAYS Second Semester Teacher-Made Final Exams: June 1-3, 2010 SJUSD ALGEBRA 2 TIMELINE Page 10 of 10

San Jose Unified School District. Algebra 1 Pacing Calendar

San Jose Unified School District Algebra 1 Pacing Calendar 2009-2010 SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 1 of 9 SJUSD ALGEBRA 1 PACING GUIDE FOR 2009-2010 The Algebra 1 curriculum has been broken into