Curriculum Guide: Algebra 2/Trig 4 th Quarter GRADE 9-12 Unit of Study: Trigonometric Functions Resources: Textbook: Algebra 2 (Holt, Rinehart & Winston), Ch. 13 Length of Study: Unit of Study: 9 days Trigonometric Graphs and Identities Resources: Textbook: Algebra 2 (Holt, Rinehart & Winston), Ch. 14 Length of Study: 9 days Computation/Estimation Algebraic Concepts Geometry/Spatial Concept Benchmarks MA 12.2.3 The student will perform estimations & computations of real numbers, mentally, with paper & pencil, and with technology Benchmarks MA 12.6.1 The student will graph and interpret algebraic relations and inequalities. Benchmarks MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures. Benchmarks 1
ASSESSMENT RECOMMENDATIONS Computation/Estimation Benchmark MA 12.2.3 The student will perform estimations & computations of real numbers, mentally, with paper & pencil, and with technology. Skills Skills Skills Skills Multiply & divide rational expressions Add & subtract & complex fractions Solve rational equations Possible Assessments FOR Learning Multiply & divide by simplifying expressions Add & subtract by finding LCD s Suggestion Solve rational equations by eliminating denominators & cross-multiplying Required Assessments OF Learning Selected Response Multiple choice (choose correct solutions) Essay Assessment Multiply, divide, add, subtract rational expressions and complex fractions. Solve rational equations. Personal Communication 2
Computation/Estimation Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Graphing calculator use graphs to determine solutions MA 12.2.3 The student will perform estimations & computations of real numbers, mentally, with paper & pencil, and with technology. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Provide more problems without common denominators Skills (): Simplify rational expressions by multiplying, dividing, adding & subtracting Solve rational equations Homework & practice Cooperative learning AVERAGE PERFORMING STUDENT Activities: Provide more problems with common denominators, crossmultiplying LOW PERFORMING STUDENT Activities: Work together to find LCD s to simplify and solve rational expressions and equations. Cooperative learning ELL Activities: Work together to find LCD s to simplify and solve rational expressions and equations. 3
ASSESSMENT RECOMMENDATIONS Algebraic Concepts Benchmark MA 12.6.1 The student will graph and interpret algebraic relations and inequalities. Skills Skills Skills Skills Graph simple & general rational functions Graph sine, cosine, & tangent functions s Possible Assessments FOR Learning Selected response Graph rational functions by finding intercepts & asymptotes Match graphs with equations Required Assessments OF Learning Selected Response matching Essay Assessment Graph functions Personal Communication 4
Benchmark: Algebraic Concepts SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Graphing calculator activity MA 12.6.1 The student will graph and interpret algebraic relations and inequalities. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Provide more graphing problems Skills (): Graph simple and general rational functions Graph sine, cosine, and tangent functions Homework & practice Questions, cues, advance organizers AVERAGE PERFORMING STUDENT Activities: Provide problems where students only identify intercepts and asymptotes, amplitude and period. LOW PERFORMING STUDENT Activities: Have students match graphs with equations Nonlinguistic representation ELL Activities: Provide graphs of similar functions to compare with. 5
ASSESSMENT RECOMMENDATIONS Geometry/Spatial Concept Benchmark MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures. Skills Skills Skills Skills Evaluate trigonometry ratios Solve triangles Evaluate trigonometry expressions Possible Assessments FOR Learning Evaluate the 6 trig. Ratios of any angle, in radius & degrees. Use law of sines & cosines to solve triangles. Evaluate trig. expressions & solve trig. Equations. Required Assessments OF Learning Selected Response Essay Assessment Evaluate trig. ratios Solve triangles Solve trig. equations Personal Communication 6
Benchmark: Geometry/Spatial Concept SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Graphing calculator activity MA 12.4.5 The student will apply right triangle trigonometry to find length and angle measures. Homework & practice HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Provide problems in degrees and radians, some problems solve without a calculator Skills (): Evaluate trig. ratios Solve triangles Evaluate trig. expressions Solve trig. equations Homework & practice Questions, cues, advance organizers AVERAGE PERFORMING STUDENT Activities: Provide problems students can solve with a calculator LOW PERFORMING STUDENT Activities: Provide formulas for trig. ratios, law of sines & cosines, area formulas, double & half angle formulas Questions, cues, advance organizers ELL Activities: Provide formulas for trig. ratios, law of sines & cosines, area formulas, double & half angle formulas 7
ASSESSMENT RECOMMENDATIONS Data Analysis Benchmark MA 12.5.2 The student will write equations and make predictions from sets of data. Skills Skills Skills Skills Make scatter plots & bestfit lines Make predictions from equations. Interpret results Explanation Interpretation Possible Assessments FOR Learning Essay Use Excel to create scatter plots & best-fit lines. Use equations to predict future. Discuss predictions & which ones make most sense. Required Assessments OF Learning Selected Response Essay Write 500-word essay on each stage of project and interpret results. Assessment Personal Communication 8
Data Analysis Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Sample graphs and predictions MA 12.5.2 The student will write equations and make predictions from sets of data. Generating & testing hypothesis HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Have students discuss end behaviors of equations and determine which best fits the data. Skills (): Make scatter plot Explanation Make predictions using best-fit equations Interpretation Interpret results Homework & practice Questions, cues, advance organizers Questions, cues, advance organizers AVERAGE PERFORMING STUDENT Activities: Have students use best-fit equations (provided by Excel) to come up with predictions. LOW PERFORMING STUDENT Activities: Help student pick data that will work best with project. ELL Activities: Help student pick data that will work best with project. 9
REQUIRED KEY CONTENT WORDS Rational function Hyperbole Complex fraction Cross-multiplying Sine, cosine, tangent Cosecant, secant, cotangent Radian Sector Inverse trigonometry Law of sines Law of cosines Heron s formula Quadrant angle Conterminal angle Reference angle Periodic function Cycle Period Amplitude Trigonometric identities Double & half angle formulas Frequency 10