Transcript Math II
MATH II An overview of the new math II course and a comparison to the traditional geometry course MATH II CONTENT Topics of study Functions, graphs and operations Systems of linear and non-linear equations Transformations of graphs and objects on a graph Triangle congruence and proofs Right triangle trig Law of Sines and Cosines Complex functions Graphing functions Independent and dependent probability Rules of probability GEOMETRY VS. MATH II Geometry by Units Unit 1: Basic Geometric Terms Points, lines, and planes Rays Segment and Angle Addition Graphing on the coordinate plane Writing linear equations Parallel and Perpendicular lines Unit 2: Parallel lines cut by a transversal Special angle relationships Geometric proofs Algebraic properties Unit 1: Math II by Units Function notation Function operations Function structure Literal Equations Domain and Range (linear, exponential, quadratic, absolute value) Graphically and equations Graphing equations in 2 variables Building functions Systems of equations (linear and linear) Systems of equations (linear and quadratic) Writing and solving inequalities Systems of inequalities GEOMETRY VS. MATH II Geometry Cont. Unit 3: Triangle Congruence Triangle Congruence Proofs CPCTC and proofs Unit 4: Triangle angle sum Triangle properties Angles and Sides Exterior angle of triangles Triangle Proofs Math II Cont. Unit 2: Isometry Translations, Dilations, Reflections, and Rotations Combinations of transformations Transformation of functions (linear quadratics) Write functions from vertex to standard form GEOMETRY VS. MATH II Geometry cont. Math II cont. Unit 5: Unit 3: Polygon angle sums Algebraic proofs Triangle segments Triangle Angle Sum Triangle midsegments Triangle Congruence Points of Concurrency Congruence Proofs Graphing triangle segments Dividing Segments into portions Construct triangle, square, and hexagon GEOMETRY VS. MATH II Geometry cont. Unit 6: Properties of parallelograms Parallelogram Rectangle Rhombus Square Trapezoids Kites Quadrilaterals Math II cont. Unit 4: Right triangle trig Sine and Cosine complements Law of Sines Law of Cosines Area of Triangle (A= 1/2absinC) GEOMETRY VS. MATH II Geometry cont. Math II cont. Unit 7: Special Right Triangles Area of quadrilaterals Area of regular polygons Geometric Probability Unit 8: Similar figures Triangle similarity Similarity proofs Unit 5: Complex Functions Graphing Exponential Logs Quadratics Sine Cosine Tangent Circles Solving for Zeros Inverse Functions GEOMETRY VS. MATH II Geometry cont. Math II cont. Unit 9: Unit 6: Right Triangle Trig Angle of elevation and depression Area of regular polygons Unit 10: Volume, Surface Area, and Lateral Area Independent and Conditional Probability Addition Rule of Probability Multiplication Rule of Probability Permutations and Combinations Two way frequency tables GEOMETRY VS. MATH II Geometry cont. Unit 11: Circles Segments and angles Arcs and lengths Unit 12: Transformations Reflections, Rotations, Translations, Dilations Math II cont. FINAL EXAM INFORMATION State will provide us with a Common Exam/MSL The exam will count as 25% of the overall grade There will be no exam exemptions An overview of the geometry in Math II Number and Operations N-RN.2 Geometry topics include: • Congruence • Congruence proofs • Similarity of triangles • Similarity of transformed objects • • Right Triangles Trigonometry • • Laws of Sines and Cosines Graphing trigonometric functions • Modeling given situations • Probability • Conditional probability • Rules of probability Quantities* N-Q.1* N-Q.2* N-Q.3* Statistics and Probability Interpreting Functions Congruence Making Inferences & Justifying Conclusions S-IC.2 Functions M Real Numbers Geometry Algebra Seeing Structure in Expressions A-SSE.1.a* A-SSE.1.b* A-SSE.2 A-SSE.3.c* Arithmetic with Polynomials and Rational Expressions O D E L I N G F-IF.2 G-CO.2 F-IF.4* G-CO.3 S-IC.6 F-IF.5* G-CO.4 F-IF.7.b* G-CO.5 Conditional Probability and the Rules of Probability F-IF.7.e* G-CO.6 S-CP.1 F-IF.8.a G-CO.7 S-CP.2 F-IF.9 G-CO.8 S-CP.3 A-APR.1 Building Functions G-CO.10 S-CP.4 A-APR.3 F-BF.1.a* G-CO.13 S-CP.5 F-BF.1.b* Creating Equations* F-BF.3 Similarity, Right Triangles, & Trigonometry S-CP.6 S-CP.7 A-CED.1* G-SRT.1.a S-CP.8 A-CED.2* G-SRT.1.b S-CP.9 A-CED.3* G-SRT.6 A.CED.4* Reasoning with Equations and Inequalities A-REI.1 A-REI.2 G-SRT.7 G-SRT.8* G-SRT.9 G-SRT.11 A-REI.4.b Expressing Geometric Properties with Equations A-REI.7 G-GPE.1 G-GPE.6 A-REI.10 A-REI.11* Geometric Measurement and Dimension G-GMD.4 Modeling with Geometry G-MG.1* G-MG.2* G-MG.3* WHERE IS ALL THE GEOMETRY NOW? The traditional geometry material is spread over the curriculum from grades 6 – 11. The integrated math approach is introducing students to the strands of geometry as it applies to algebraic concepts. For example: Math II continues a progression of the standards established in Math I. In addition to these standards, Math II includes polynomials, congruence and similarity of figures, trigonometry with triangles, modeling with geometry, probability, making inferences and justifying conclusions. WHAT IS THE NEXT COURSE? Students are on a graduation track that has Math III as the next course. Math III will not be offered until next year. The integrated curriculum of Math II overlaps with the traditional Algebra II curriculum. Students will gain more of the topics of geometry in Math III If students are planning to go into chemistry next semester, math II will meet the requirements of algebra 2. (No need to double up for science) An overview to show the geometry in Math III Number and Operations Algebra M Functions O D E L I N Geometry Statistics and Probability G Real Numbers Seeing Structure in Expressions Interpreting Functions Congruence Interpreting Categorical and Quantitative Data N-RN.3 A-SSE.1.a* F-IF.2 G-CO.1 S-ID.4 A-SSE.1.b* F-IF.4* G-CO.9 A-SSE.2 F-IF.5* G-CO.10 Making Inferences & Justifying Conclusions N-Q.1* A-SSE.3.b* F-IF.7.c G-CO.11 S-IC.1 N-Q.2* A-SSE.4* F-IF.7.e* G-CO.12 S-IC.3 Similarity, Right Triangles, & Trigonometry S-IC.4 The Complex Number System Arithmetic with Polynomials and Rational Expressions F-IF.8.a* N-CN.1 A-APR.1 • Circles N-CN.2 A-APR.2 F-BF.1.a* G-SRT.3 Using Probability to Make Decisions N-CN.7 A-APR.3 F-BF.1.b* G-SRT.4 S-MD.6 • Geometric properties and N-CN.9 A-APR.4 F-BF.2* G-SRT.5 S-MD.7 A-APR.6 F-BF.3 Circles A.APR.7 F-BF.4a G-C.1 G-C.2 Creating Equations* Linear, Quadratic, and Exponential Models* A-CED.1* F-LE.3* G-C.5 • Proofs A-CED.2* F-LE.4* A-CED.3* Expressing Geometric Properties with Equations • Trigonometric Functions A.CED.4* Trigonometric Functions Reasoning with Equations and Inequalities F-TF.1 G-GPE.1 F-TF.2 G-GPE.2 A-REI.1 F-TF.5 A-REI.2 F-TF.8 Modeling with Geometry • Congruence • Similarity • Right Triangles • Trigonometry equations • Modeling with geometry Quantities* N-Q.3* A-REI.4.a A-REI.4.b A-REI.10 F-IF.9 Building Functions G-SRT.2 G-C.3 G-MG.3* S-IC.5 S-IC.6 QUESTIONS????