Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations.

Transcription

1 POASD Math (SEC) Algebra 2 Timeframe Big Idea(s) Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations. Data can be modeled and used to make inferences. Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions. Patterns exhibit relationships that can be extended, described, and generalized. Week 1 - Week 15 Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations. Data can be modeled and used to make inferences.

2 Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions. Patterns exhibit relationships that can be extended, described, and generalized. Week 16 - Week 29 Geometric relationships can be described, analyzed, and classified based on spatial reasoning and/or visualization. Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions.

3 Measurement attributes can be quantified and estimated using customary and noncustomary units of measure. Week 30 - Week 33 Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations. Numerical quantities, calculations, and measurements can be estimated or analyzed by using appropriate strategies and tools. Measurement attributes can be quantified and estimated using customary and noncustomary units of measure. Patterns exhibit relationships that can be extended, described, and generalized.

4 Week 34 - Week 36

5 Essential Question(s) Concepts How are relationships represented mathematically? How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations? Linear Functions, Notations, and Graphs. Direct, Inverse, and Combined Variation. How does the type of data influence the choice of display? Systems of Lines and Inequalities. Linear Programming. How can probability and data analysis be used to make predictions? How can data be organized and represented to provide insight into the relationship between quantities? How can patterns be used to describe relationships in mathematical situations? How can recognizing repetition or regularity assist in solving-problems more efficiently? How are relationships represented mathematically? How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?

6 How does the type of data influence the choice of display? How can probability and data analysis be used to make predictions? How can data be organized and represented to provide insight into the relationship between quantities? How can patterns be used to describe relationships in mathematical situations? How can recognizing repetition or regularity assist in solving-problems more efficiently? Standard vs. Vertex form of Quadratics and Translations. Projectile Motion. Imaginary and Complex Numbers. Quadratic Formula and Completing the Square. Power Functions, Compound Interest, Rational Exponents. Inverse and Root Functions. Rationalizing the Denominator. Exponential and Logarithmic Functions: Growth, Decay, the number "e". Common Logs and Natural Logs, conversion with exponentials. Regression models. How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems? How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving? How can geometric properties and theorems be used to describe, model, and analyze situations?

7 How can data be organized and represented to provide insight into the relationship between quantities? Why does what we measure influence how we measure? In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted? How precise do measurements and calculations need to be? Polynomial Multiplication, Roots, Factoring, and Graphing. Long and Synthetic Division. Solving Equations of Polynomials. How are relationships represented mathematically? How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations? What does it mean to estimate or analyze numerical quantities? When is it appropriate to estimate versus calculate? What makes a tool and/or strategy appropriate for a given task? Why does what we measure influence how we measure?

8 In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted? How precise do measurements and calculations need to be? How can patterns be used to describe relationships in mathematical situations? How can recognizing repetition or regularity assist in solving-problems more efficiently? Right Triangle Trig, Definitions of Trig, Applications of Trig. Law of Sines and Cosines

9 Competencies Vocabulary Writing Function Definitions and Notations, Drawing Graphs, and Evaluating Functions. Finding/Limiting the Domain and Range of a Function. Solving Equations and Re-writing Formulas. Creating Direct, Inverse, Joint, and Combined Variations and their graphs. Finding Models from data. Solving Systems of equations. Graphing Piecewise functions. Relation, Function, f(x) notation, Domain, Range, Constant of variation, Inverse variation, Hyperbola, Model, Combined Variation, Joint Variation, Recursive formula, Explicit Formula, Arithmetic Sequence, Stepfunction, Piece-wise Function, System of Equations or Inequalities, Substitution Method, Elimination Method, Consistent & Inconsistent systems, Half-plane, Feasible region, Linear Programming, Vertical Line Test.

10 Changing Forms of Quadratics, Translating Quadratics. Calculating Imaginary and Complex Numbers. Using the Quadratic Formula and Completing the Square. Using/Interpreting the Compound Interest Formula. Manipulating Rational Exponents for Equivalence. Graping Quadratic, Inverse, Root, Exponential and Logarithmic Functions. Rationalizing the Denominator. Comparing Regression models. Quadratic expression, Absolute Value, Square root, Vertex Form, Axis of Symmetry, Minimum, Maximum, Trinomial, Complete the Square, Quadratic Regression, Imaginary Number, Complex Number, Complex Conjugate, Nth Power Function, Compound Interest, Geometric Sequence, Cube Root, nth root and Radical Sign, Composite Functions, Horizontal line test, Inverses, Geometric Mean, Extraneous Solution.

11 Multiplying binomials and trinomials. Finding Rational Roots, Degrees, Leading Coefficients, Multiplicity. Graphing and Solving Polynomial Functions. Creating Regression Equations. Polynomial, Degree, Zeroes, Roots, Multiplicity, Synthetic Division, Rational Roots, Dividing Polynomials, Finite Differences, End Behavior.

12 Finding Measures of Sides and Angles of Triangles. Sine, Cosine, Tangent, Angle of elevation, Inverse Functions, Angle of depression. Theta, Alpha, Beta, Law of Sines, Law of Cosines.

13 Standard(s) Eligible Content Assessment(s) CC.2.2.HS.C.1 CC.2.2.HS.C.2 A A CC.2.2.HS.C.3 CC.2.2.HS.D.10 A A CC.2.2.HS.D.7 CC.2.2.HS.D.9 A A CC.2.4.HS.B.2 CC.2.4.HS.B.3 A A Worksheets, Projects, Oral and Written Assessments CC.2.1.HS.F.6 CC.2.1.HS.F.7 A A CC.2.2.HS.C.1 A

14 CC.2.2.HS.C.2 A CC.2.2.HS.C.3 CC.2.2.HS.C.4 A A CC.2.2.HS.C.5 CC.2.2.HS.C.6 A A CC.2.2.HS.D.2 CC.2.2.HS.D.7 A A CC.2.2.HS.D.8 CC.2.2.HS.D.9 A A CC.2.4.HS.B.2 A A A A A A A A A A Worksheets, Projects, Oral and Written Assessments CC.2.1.HS.F.1 A CC.2.1.HS.F.2 A CC.2.1.HS.F.7 A

15 CC.2.2.HS.C.1 A CC.2.2.HS.C.2 CC.2.2.HS.C.3 CC.2.2.HS.C.4 A A A CC.2.2.HS.D.3 A CC.2.2.HS.D.4 CC.2.2.HS.D.5 CC.2.2.HS.D.6 CC.2.2.HS.D.9 CC.2.3.HS.A.12 Worksheets, Projects, Oral and Written Assessments CC.2.2.HS.C.9 A CC.2.2.HS.D.2 A CC.2.2.HS.D.6 CC.2.3.HS.A.3 A G CC.2.3.HS.A.7 G

16 Worksheets, Projects, Oral and Written Assessments

17 Educational Resources Differentiation Advanced Algebra Textbook Small Group Instruction, Alternate Assessments, Additional Time, Use of Alternate Resources.

18 Advanced Algebra Textbook Small Group Instruction, Alternate Assessments, Additional Time, Use of Alternate Resources.

19 Advanced Algebra Textbook Small Group Instruction, Alternate Assessments, Additional Time, Use of Alternate Resources.

20 Advanced Algebra Textbook Small Group Instruction, Alternate Assessments, Additional Time, Use of Alternate Resources.