Overview of Math Standards


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1 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 SelfDirected Learners who create a positive vision for their future, set priorities and assume responsibility for their actions. Click here for more. Overview of Math Standards Teams of teachers and administrators comprised the pk12+ Vertical Alignment Team to draft the maps below. The full set of Kansas College and Career Standards (KCCRS) for Math, adopted in 2010, can be found here. To reach these standards, teachers use Holt curriculum, resources, assessments and supplemented instructional interventions. Standards 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 1. Set of Numbers; Properties of Real Numbers; Square Roots; Simplifying Algebraic Expressions; Properties of Exponents; Relations and Functions; Function Notation; Exploring Transformations; Parent Functions 2. Solving Linear Equations; Proportional Reasoning; Graphing Linear Functions; Writing Linear Functions; Linear Equations in Two Variables; Transforming Linear Variables; Curve Fitting with Linear; Solving AbsoluteValue Equations and Inequalities; Absolute Value Functions 3. Using Graphs and Tables to Solve Linear Functions; Using Algebraic Methods to Solve Linear Systems; Solving Systems of Linear Inequalities; Linear FIF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. FIF.2. Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Reasoning with Equations and Inequalities AREI.1. Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. AREI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Interpreting Functions AREI.3. Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients by letters. AREI.10. Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve. AREI.11. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). domain element function radical range subset transformation absolute value correlation identity line of best fit linear function proportion rate regression intercept scale factor slope constraint elimination feasible region linear programming linear system substitution system of equations How are functions used to represent How do we identify/graph/interpret a variety of functions and their transformations? How are linear functions used to represent How do we graph/transform linear and absolute value functions? Why is it useful to create models for linear data? How can we decide which method to use to solve a system? How can we use systems to model and solve real world 1
3 Programming; Linear Equations in Three Dimensions; Solving Systems in Three Variables 4. Matrices and Data; Multiplying Matrices; Using Matrices to Transform Geometric Figures; Determinants and Cramer s Rule; Matrix Inverses and Solving Systems; Row Operations and Augmented Matrices 2 AREI.12. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. FIF.4. Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs. FIF.5. Relate the domain of a function to its graph and to the quantitative relationship it describes. FIF.6. Calculate and interpret the average FIF.7. Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. AREI.8. Represent a system of linear equations as a single matrix equation in a vector variable. AREI.9. Find the inverse of a matrix if it exists and use it to solve systems of linear equations. AREI.6. Perform operations on matrices and use matrices in applications; represent/manipulate data. AREI.7. Multiply matrices by scalars to produce new matrices. AREI.8. Add, subtract, and multiply matrices of appropriate dimensions. AREI.9. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. AREI.10. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant system of linear inequalities threedimensional system address entry dimensions main diagonal matrix row operation scalar square matrix When is it suitable to use matrices to model information?
4 5. Using Transformations to Graph Quadratic Functions; Properties of Quadratic Functions in Standard Form; Quadratic Equations by Graphing and Factoring; Completing the Square; Complex Numbers and Roots; The Quadratic Formula; Solving Quadratic Inequalities; Curve Fitting 6. Polynomials; Multiplying and Dividing Polynomials; Factoring Polynomials; Finding Real Roots of Polynomial Equations; Fundamental Theorem of Algebra; Investigating Graphs of Polynomial Functions; of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. AREI.11. Multiply a vector by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. AREI.12. Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. AREI.4. Solve quadratic equations in one variable. Arithmetic with Polynomials and Rational Expressions AAPR.1. Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. AAPR.2. Understand the relationship between zeros and factors of polynomials. Know and apply the Remainder Theorem. absolute value of complex number complex conjugate imaginary number maximum value minimum value parabola quadratic function vertex form zero of a function end behavior leading coefficient local maximum minimum monomial multiplicity polynomial polynomial function synthetic division turning point How can we use quadratics to represent real world How can we decide which method to use to solve a quadratic equation? How are polynomials used to represent 3
5 Transforming Polynomial Functions; Curve Fitting with Polynomial Models 7. Exponential Functions; Growth and Decay; Inverse Relations and Functions; Logarithmic Function; Properties of Logarithms; Exponential and Logarithmic Equations and Inequalities; The Natural Base e; Transforming Exponential and Logarithmic Functions; Curve Fitting with Exponential and Logarithmic Models 8. Variation Functions; Multiplying and Dividing Rational Expressions; Adding and Subtracting Rational Expressions; 4 AAPR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. AAPR.4. Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. Linear, Quadratic, and Exponential Model FLQE.1. Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. FLQE.2. Construct linear and exponential functions, including arithmetic and geometric sequences. FLQE.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, or as a polynomial function. FLQE.4. For exponential models, express as a logarithm the solution; evaluate the logarithm using technology. FLQE.5. Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear, quadratic, or exponential function in terms of a context. FLQE.3. Build new functions from existing functions. Identify the effect on the graph; find the value of k. FLQE.4. Find inverse functions. FLQE.5. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. AAPR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. asymptote base common logarithm exponential function inverse function logarithmic function natural logarithm complex fractions constant of variation continuous function direct variation discontinuous function How are exponential used to represent How are logarithms used to represent How are rational functions used to represent real world
6 Rational functions; Solving Rational Equations and Inequalities; Radical Expressions and Rational Exponents; Radical Functions; Solving Radical Equations and Inequalities 9. Multiple Representation of Functions; Piecewise Functions; Transforming Functions; Operations with Functions; Modeling Real World Data AREI.10. Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve. extraneous solutions hole inverse variation radical equation radical function rational equation radical exponent rational function composition of functions onetoone function piecewise function step function Why should we use mathematics to model the real world? 10. Solving Nonlinear Systems 11. Permutations and Combinations; Theoretical and Experimental Probability; Independent and Dependent Events; Compound Events; AREI.10. Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve. Conditional Probability and the Rules of Probability SCP.1. Understand independence and conditional probability and use them to interpret data. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events. circle conic section ellipse foci focus hyperbola nonlinear system tangent line vertices binomial experiment combination conditional probability dependent events experimental probability factorial How can conic sections be used to represent the real world? How can we use probability to model situations in the real world? 5
7 Measures of Central Tendency and Variation; Binomial Distributions 12. Introduction to Sequences; Series and Summation Notation; Arithmetic Sequences and Series; Geometric Sequences and Series; SCP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. SCP.3. Understand the conditional probability. SCP.4. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. SCP.5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. SCP 6. Use the rules of probability to compute probabilities of compound events in uniform probability. SCP 7. Apply the Addition Rule and interpret the answer. SCP 8. Apply the general Multiplication Rule in a uniform probability model and interpret the answer. SCP 9. Use permutations and combinations to compute probabilities of compound events and solve problems. Building Functions FBF.2. Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. FIF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. independent events outcome permutation theoretical probability converge explicit formula diverge finite sequence infinite sequence iteration limit recursive formula sequence series terms of a sequence How can we use sequences and series to model 6
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