Overview of Math Standards

Transcription

1 Manhattan-Ogden USD 383 Math Year at a Glance Algebra 2 Algebra 2 Welcome to math curriculum design maps for Manhattan- Ogden USD 383, striving to produce learners who are: Effective Communicators who clearly express ideas and effectively communicate with diverse audiences, Quality Producers who create intellectual, artistic and practical products which reflect high standards Complex Thinkers who identify, access, integrate, and use available resources Collaborative Workers who use effective leadership and group skills to develop positive relationships within diverse settings. Community Contributors who use time, energies and talents to improve the welfare of others Self-Directed Learners who create a positive vision for their future, set priorities and assume responsibility for their actions. Click here for more. Overview of Math Teams of teachers and administrators comprised the pk-12+ Vertical Alignment Team to draft the maps below. The full set of Kansas College and Career () for Math, adopted in 2010, can be found here. To reach these standards, teachers use Holt curriculum, resources, assessments and supplemented instructional interventions. of Mathematical Practice 1: Make sense of problems and persevere in solving them 2: Reason abstractly and quantitatively 3: Construct viable arguments and critique the reasoning of others 4: Model with mathematics 5: Use appropriate tools strategically 6: Attend to precision 7: Look for and make use of structure 8: Look for and express regularity in repeated reasoning. Click here for more. Additionally, educators strive to provide math instruction centered on: 1: Focus - Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. 2: Coherence - Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations. 3: Fluency - Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. 4: Deep Understanding - Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. 5: Application - Students are expected to use math concepts and choose the appropriate strategy for application even when they are not prompted. 6: Dual Intensity - Students are practicing and understanding. There is more than a balance between these two things in the classroom both are occurring with intensity. Click here for more. 1

2 When appropriate: Manhattan-Ogden USD 383 Math Year at a Glance Algebra 2 Use multiple representations to enforce concepts (graph, table, equation). Model real life situations that complement the mathematical techniques. Notes: Vocabulary terms are listed only in the unit they are first introduced. Bold text = content difference for Algebra 2 and Advanced Algebra 2; see notes for greater detail 1. Linear Functions 1.1 Parent Functions & Transformations 1.2 Transformations of Linear & Absolute Value Functions 1.3 Modeling with Linear Functions 1.4 Solving Linear Systems F-BF.B.3 SA-CED.A.2 SF-IF.C.9 SF-BF.A.1a SF-LE.A.2 S-ID.B.6a A-CED.A.3 A-REI.C.6 Function Domain Range Slope Intercept Parent function Transformation Translation Reflection Vertical stretch, shrink Linear system Ordered pairs, triples Line of best fit Correlation coefficient (Students should also be familiar with forms of a line) What are some basic characteristics of the eight basic parent functions, specifically ff(xx) = xx and ff(xx) = xx? How do transformations affect the graphs of ff(xx) = xx and ff(xx) = xx? How can you use a linear function to model and analyze a real-life situation? How do you determine the number of solutions to a linear system, as well as find the solutions? Big Ideas math series (for all units). Other resources given specifically in unit notes/teacher notes (separate documents). Graph and describe (in particular domain and range) the eight basic parent functions. Apply one or more transformation to any parent function, with particular focus on linear and absolute value functions. Write a linear function to model real life data. See separate document (for all units). 1

3 Using technology: find a line of best fit, make predictions, and interpret the correlation coefficient. 2. Quadratic Functions 2.1 Transformations of Quadratic Functions 2.2 Characteristics of Quadratic Functions 2.4 Modeling with Quadratic Equations F-IF.C.7c F-BF.B.3 F-IF.B.4 F-IF.C.9 A-APR.B.3 A-CED.A.2 F-IF.B.6 S-BF.A.1a S-ID.B.6a Quadratic function Parabola Vertex (maximum and minimum values) Vertex form Axis of symmetry Standard form Intercept form How do the transformations affect the graph ff(xx) = xx 2? What are the characteristics of a quadratic function? In particular, what type of symmetry is present? How can you use a quadratic function to model and analyze a real-life situation? Solve and interpret a system of linear equations in 2 or 3 variables....apply multiple transformations to create quadratic equations and graphs. Analyze a quadratic function in multiple forms (intercept, vertex, and standard). Write a quadratic function (with and without 2

4 technology) to model real life situations. 3. Quadratic Equations & Complex Numbers 3.1 Solving Quadratic Equations 3.2 Complex Numbers 3.3 Completing the Square 3.4 Using the Quadratic Formula 3.5 Solving Nonlinear Systems 3.6 Quadratic Inequalities A-SSE.A.2 A-REI.B.4b F-IF.C.8a N-CN.A.1 N-CN.A.2 N-CN.C.7 A-CED.A.3 A-REI.C.7 A-REI.D.11 A-CED.A.1 Quadratic equation Root Zero Imaginary unit Imaginary number Complex number Conjugate Complete the square Quadratic formula Discriminant System of nonlinear functions Quadratic inequality How does the graph of a quadratic equation relate to the number of real solutions? How is the complex number system organized? What methods can be used to solve quadratic equations? How do the methods differ? How do you determine the number of solutions to a nonlinear system, as well as find the solutions? How do you solve and interpret the solution to a quadratic inequality in one or two variables? Determine the number and type of solutions to a quadratic equation. Perform the three (or four) basic operations on complex numbers. Analyze (solve, graph, describe) a quadratic equation in different forms, noting the advantages and disadvantages of each form. Describe the possible number of solutions to a nonlinear system, write and draw 3

5 systems with a given number of solutions, and find the solutions to the system. 4. Polynomial Functions 4.1 Graphing Polynomial Functions 4.2 Adding, Subtracting, and Multiplying Polynomials 4.3 Dividing Polynomials 4.4 Factoring Polynomials 4.5 Solving Polynomial Equations 4.6 The Fundamental Theorem of Algebra 4.7 Transformations of Polynomial Functions F-IF.B.4 F-IF.C.7c A-APR.A.1 A-APR.C.4 A-APR.C.5 A-APR.B.2 A-APR.B.3 N-CN.C.8 N-CN.C.9 F-BF.B.3 A-CED.A.2 F-BF.A.1a Polynomial Polynomial function End behavior Synthetic division Complex conjugates Even function Odd function Local max/min Turning point Increasing Decreasing What are the characteristics of polynomial functions? How are the four basic operations performed on polynomial expressions? What methods can be used to solve a polynomial equation? How do you know if a polynomial equation has real or imaginary solutions? How do transformations affect the graphs of polynomial functions? Graph quadratic inequalities in one or two variables to show the solution set. Add, subtract, multiply and divide polynomial expressions. Analyze a polynomial function when given a graph or an equation, in particular finding zeros. Differentiate among polynomial functions with 4

6 4.8 Analyzing Graphs of Polynomial Functions 4.9 Modeling with Polynomial Functions How can you use a polynomial function to model and analyze a real-life situation? real and nonreal zeros. Transform polynomial functions. 5. Rational Exponents & Radical Functions 5.1 n th Roots & Rational Exponents 5.2 Properties of Rational Exponents & Radicals 5.3 Graphing Radical Functions 5.4 Solving Radical Equations & Inequalities 5.5 Performing Function Operations 5.6 Inverses of a Function **END OF SEMESTER** 5 N-RN.A.1 N-RN.A.2 F-IF.C.7b N-BF.B.3 A-REI.A.1 A-REI.A.2 F-BF.A.1b A-CED.A.4 F-BF.B.4a n th root Index of radical Conjugate Radical function Radical equation Extraneous solution How are rational exponents, powers, and radicals related? How do you perform the four basic operations on radical expressions? What are the characteristics of radical functions? How do you solve radical equations? How do you perform the four basic operations on various functions? When does a function have an inverse, and how do you find it? Use polynomial functions to model real life situations. Convert between radical notation and rational exponent notation. Add, subtract, multiply and divide radical expressions. Analyze a radical function (including graphing and solving). Add, subtract, multiply and divide

7 polynomial and radical functions and analyze the resulting function. 6. Exponential & Logarithmic Functions 6.1 Exponential Growth & Decay Functions 6.2 The Natural Base e 6.3 Logarithms & Logarithmic Functions 6.4 Transformations of Exponential & Logarithmic Functions 6.5 Properties of Logarithms 6.6 Solving Exponential & Logarithmic Functions 6.7 Modeling with Exponential & Logarithmic Functions A-SSE.B.3c F-IF.C.7e F-IF.C.8b F-LE.A.2 F-LE.B.5 F-BF.B.4a F-LE.A.4 F-BF.B.3 A-SSE.A.2 F-LE.A.4 A-REI.A.1 A-CED.A.2 F-BF.A.1z Exponential function Exponential growth, decay Asymptote Growth, decay factor Base e Logarithm Common logarithm Natural logarithm Logarithmic function What are the characteristics of exponential functions? Logarithmic functions? What is the role of the number e in mathematics? What are the properties of logarithms? How do you solve exponential and logarithmic equations? How are logarithmic and exponential functions used in real life situations? Determine if a function has an inverse, find its inverse, and compare a function with its inverse. Convert between logarithmic and exponential notation. Analyze logarithmic and exponential functions (including graphing and solving). Transform logarithmic and 6

8 exponential functions. Combine and expand logarithmic expressions. Model real life situations with logarithmic and exponential functions. 7. Rational Functions 7.1 Inverse Variation 7.2 Graphing Rational Functions 7.3 Multiplying and Dividing Rational Expressions 7.4 Adding and Subtracting Rational Expressions 7.5 Solving Rational Equations A-CED.A.1 A-CED.A.2 A-CED.A.3 A-APR.D.6 F-BF.B.3 A-APR.D.7 A-CED.A.4 A-REI.A.1 A-REI.A.2 Direct variation Inverse variation Constant of variation Rational function Rational expression Complex fraction How do you recognize when two quantities vary directly or inversely? What are the characteristics of a rational function? How do you perform the four basic operations on rational expressions? How do you solve a rational equation? Determine if (and what type of) variation exists between quantities. Analyze a rational function (including graphing and solving). Simplify rational 7

9 expressions using the four basic operations. 8. Sequences & Series 8.1 Defining & Using Sequences & Series 8.2 Analyzing Arithmetic Sequences & Series 8.3 Analyzing Geometric Sequences & Series 8.4 Finding Sums of Infinite Geometric Series 8.5 Using Recursive Rules with Sequences 8 F-IF.A.3 F-BF.A.2 F-LE.A.2 A-SSE.B.4 F-BF.A.1a Sequence Term (of a sequence) Series Summation notation Sigma notation Arithmetic sequence Arithmetic series Common difference Geometric sequence Geometric series Common ratio Partial sum Explicit rule Recursive rule 10. Probability S-CP.A.1 Probability experiment How do you find a rule for the n th term of a sequence? What conditions are necessary for a sequence to be considered arithmetic? Geometric? Why can you find the sum of certain infinite geometric series? How does an explicit rule differ from a recursive rule? How many outcomes are in a sample space? Write an explicit rule for arithmetic and geometric sequences. Find the sum of a series using either technology or summing formulas. Explain/show the distinguishing features of both arithmetic and geometric sequences. Determine if an infinite geometric series can be summed, and if so, find its sum. Determine the number of.

10 10.1 Sample Spaces & Probability 10.2 Independent & Dependent Events 10.3 Two-Way Tables & Probability 10.4 Probability of Disjoint & Overlapping Events 10.5 Permutations & Combinations 10.6 Binomial Distributions S-CP.A.2 S-CP.A.3 S-CP.A.5 S-CP.B.6 S-CP.B.8 S-CP.A.4 S-CP.B.7 A-APR.C.5 S-CP.B.9 Outcome Event Sample space Probability (of event) Theoretical probability Experimental probability Geometric probability Independent event Dependent event Conditional probability Two-way table Compound event Overlapping event Mutually exclusive events (disjoint) Permutation Combination Factorial Binomial theorem Probability distribution Binomial distribution Binomial experiment How is probability calculated for independent and dependent events? Disjoint and overlapping events? How can data be organized in tables and diagrams to assist in calculating probability? How do you find the probability of various outcomes in a binomial experiment? possible outcomes in a sample space, including those that require a combination or permutation. Create a model to organize sample spaces and probabilities. Calculate the probability of independent and dependent events, and disjoint and overlapping events. Create a binomial distribution using combinations and Pascal s Triangle. TBD (9, 12, both) 9