Algebraic Concepts Algebraic Concepts Writing

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1 Curriculum Guide: Algebra 2/Trig (AR) 2 nd Quarter 8/7/ nd Quarter, Grade 9-12 GRADE 9-12 Unit of Study: Matrices Resources: Textbook: Algebra 2 (Holt, Rinehart & Winston), Ch. 4 Length of Study: Unit of Study: 6 days Quadratic Functions Resources: Textbook: Algebra 2 (Holt, Rinehart & Winston), Ch. 5 Length of Study: Unit of Study: 9 days Polynomials Functions Resources: Textbook: Algebra 2 (Holt, Rinehart & Winston), Ch. 6 Length of Study: 9 days Writing Benchmarks MA The student will solve problems involving equations and inequalities. Benchmarks MA The student will solve problems using patterns and functions. Benchmarks MA The student will solve problems involving systems of two equations, and systems of two or more inequalities. Benchmarks Interpret results of a prediction using equations of best fit (quadratic) 1

2 ASSESSMENT RECOMMENDATIONS 8/7/ nd Quarter, Grade 9-12 Benchmark MA The student will solve problems involving equations and inequalities. Skills Skills Skills Skills Solve quadratic equations Factor & solve polynomial equations Possible Assessments FOR Learning Solve quadratics by factoring & finding square roots. Solve polynomial functions by synthetic division. Suggestion Required Assessments OF Learning Selected Response Matching graphs with equations Multiple choice Essay Use equation of best fit to make and interpret a prediction (communication-writing) Assessment Graph polynom. Functions Solve equations by factoring Solve by completing the square Solve using synthetic division Find real & rational zeroes Personal Communication 2

3 8/7/ nd Quarter, Grade 9-12 Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Find rational zeroes of functions. MA The student will solve problems involving equations and inequalities. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Same as average students Skills (): Solve quadratic equations by various methods Solve polynomial equations by various methods. Homework & practice Identify similarities & differences AVERAGE PERFORMING STUDENT Activities: Graph quadratic functions Solve quadratic equations by factoring, square roots, complete the square. Factor and solve polynomial equations LOW PERFORMING STUDENT Activities: Compare long division with synthetic division Nonlinguistic representation ELL Activities: Provide formulas 3

4 ASSESSMENT RECOMMENDATIONS 8/7/ nd Quarter, Grade 9-12 Benchmark MA The student will solve problems involving systems of two equations, and systems of two or more inequalities. Skills Skills Skills Skills Use matrices to solve systems. Possible Assessments FOR Learning Use determinants, Cramer s Rule, inverse matrices to solve systems. Required Assessments OF Learning Selected Response Match matrix operations with correct solutions. Essay Assessment Solve a system using inverses. Find determinants Use determinants and Cramer s Rule to solve systems. Personal Communication 4

5 8/7/ nd Quarter, Grade 9-12 Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: MA The student will solve problems involving systems of two equations, and systems of two or more inequalities. Summarizing & note taking HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Identify steps involved in using Cramer s Rule or inverse matrices Skills (): Solve systems using matrices Homework & practice Identify similarities & differences AVERAGE PERFORMING STUDENT Activities: Provide problems using Cramer s Rule and inverse matrices to solve systems. LOW PERFORMING STUDENT Activities: Determine whether a product of matrices is defined by comparing dimensions Nonlinguistic representations ELL Activities: Provide examples of completed problems. 5

6 ASSESSMENT RECOMMENDATIONS 8/7/ nd Quarter, Grade 9-12 Benchmark MA The student will solve problems using patterns and functions. Skills Skills Skills Skills Graph polynomial functions Graph quadratic equations & inequalities Explanation Possible Assessments FOR Learning Determine end behaviors of graphs Graph quadratic equations in standard, vertex, & intercepts form. Required Assessments OF Learning Selected Response Match graphs with polynom. functions of various degrees. Essay Assessment Find end behaviors Graph quadratic equations using various forms. Personal Communication 6

7 8/7/ nd Quarter, Grade 9-12 SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Benchmark: MA The student will solve problems using patterns and functions. Determine end behaviors of polynomial functions of odd degree, even degree, when leading coefficients is positive, negative. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Same as average students Skills (): Explanation Determining end behaviors Graphing quadratics Homework & practice Identify similarities & differences AVERAGE PERFORMING STUDENT Activities: Provide examples of polynomials of various degrees, determine end behaviors. Given quadratics in standard vertex & intercepts form, students graph. LOW PERFORMING STUDENT Activities: Discuss similarities of end behaviors for polynomials of even degrees, odd degrees Look at effect of a negative reading coefficient on graphs. Nonlinguistic representations ELL Activities: Provide examples of graphs, function dance show end behaviors with arms. 7

8 8/7/ nd Quarter, Grade 9-12 REQUIRED KEY CONTENT WORDS Matrix Scalar Determinant Cramer s Rule Identify matrix Inverse matrix Parabola Quadratic function Zero of a function Complex number Imaginary number Completing the square Best-fit quadratic model Vertex form Intercept form Polynomial function End behavior Polynomial long division Synthetic division Rational zero theorem Local maximum & minimum 8