First State Military Academy Mathematics Flow Chart 2018 – 2019 *A math course MUST be taken during senior year. th th th 9 Grade 10 Grade 11 Grade 12th Grade Algebra I Algebra II Geometry Precalculus or or or or Geometry Honors Algebra II Honors Geometry Calculus or or or PreCalculus Honors Geometry Algebra II or Honors Algebra II Curriculum Framework for School: First State Military Academy Course: ​Algebra 2 Course Description: ​Algebra II continues the study of quadratic functions and introduces students to polynomial functions, logarithmic functions and trigonometric functions. Advanced features of the graphing calculator are incorporated into the course work. Real world problem solving and applications of algebra in various fields such as engineering and the sciences are a focal point of ​ instruction. Content is aligned to the Delaware Core Standards and the new SAT. Big Idea: To provide all cadets the knowledge, skills, and attributes, to thrive in post-secondary education, work, and civic life. Standards Alignment Unit Concepts/Big Ideas Driving Questions/Learning Assessments Targets Unit One: Expressions, Linear Equations, and Absolute Value Timeline: 4 weeks CCSS.Math.Content.ASSE.1a - Concepts: Driving Questions: Summative: ​ Interpret parts of an expression, Variables - How are symbols useful in - Party Project or Trip Project such as terms, factors, and Algebraic Expressions mathematics? - Wall Activity for Absolute coefficients. Order of Operations - What mathematical symbols Value Formula do you know? - Quiz CCSS.Math.Content.ASSE.1b - Real Numbers ​ Interpret complicated expressions Rational Numbers Learning Targets: Formative: by viewing one or more of their Irrational Numbers - Use the order of operations to - Workshop Practice parts as a single entity. For Integers evaluate expressions - Classwork/Homework example, interpret P(1+r)n as the Whole Numbers - Use formulas Assignments product of P and a factor not Natural Numbers - Classify real numbers - Warm-Ups depending on P. Open Sentence - Use the properties of real Equation numbers to evaluate CCSS. Math.Content.ASSE.2 - Solution expressions ​ Use the structure of an Absolute Value - Translate verbal expressions expression to identify ways to Empty Set into algebraic expressions and 4 rewrite it. For example, see x ​ - Extraneous Solution equations, and vice versa 4 2 2 2 2 ​ y ​ as (x )​ ​ - (y )​ ,​ thus - Solve equations using the ​ ​ ​ ​ ​ recognizing it as a difference Big Ideas: Properties of Equality of squares that can be factored - Use the real properties of real - Evaluate expressions involving 2 2 2 2 as (x ​ - y )​ (x ​ + y )​ . numbers to evaluate absolute values ​ ​ ​ ​ expressions and formulas - Solve absolute value CCSS.Math.Content.A-CED.1 - - Classify real numbers equations ​ Create equations and inequalities - Use the properties of equality in one variable and use them to to solve equations solve problems. Include equations - Solve absolute value arising from linear and equations exponential functions. Unit Two: Compound and Absolute Value Inequalities Timeline: 4 weeks CCSS.Math.Content.A-CED.1 - Concepts: Driving Questions: Summative: ​ Create equations and inequalities Compound Inequality - How are symbols useful in - Size Project or Prom Project in one variable and use them to Intersection mathematics? - Quiz solve problems. Include equations Infinity - What mathematical symbols arising from linear and do you know? Formative: exponential functions. Big Ideas: - Workshop Practice - Solve inequalities, compound Learning Targets: - Classwork/Homework CCSS.Math.Content.A-CED.3. - inequalities, and absolute - To solve one-step inequalities Assignments ​ Represent constraints by value inequalities - To solve multi-step inequalities - Warm-Ups equations or inequalities, and by - Graph inequalities, compound - To solve compound systems of equations and/or inequalities, and absolute inequalities inequalities, and interpret value inequalities - To solve absolute value solutions as viable or nonviable inequalities options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Unit Three: Linear Relations and Functions Timeline: 5 weeks CCSS.Math.Content.F-IF.4 - For Concepts: Driving Questions: Summative: ​ a function that models a One-to-one Functions - How can mathematical ideas - Winter Decoration Project relationship between two Onto Function be represented? - Quiz quantities, interpret key features Discrete Relation of graphs and tables in terms of Continuous Relation Learning Targets: Formative: the quantities, and sketch graphs Vertical Line Test - Analyze relations and - Workshop Practice showing key features given a Independent Variable functions - Classwork/Homework verbal description of the Dependent Variable - Use equations of relations and Assignments relationship. Function Notation functions - Warm-Ups Linear Relations - Use discrete and continuous CCSS.Math.Content.F-IF.5 - Linear Equation functions to solve real-world ​ Relate the domain of a function to Linear Function problems its graph and, where applicable, Standard Form - Identify linear relations and to the quantitative relationship it Y-intercept functions describes. For example, if the X-intercept - Write linear equations in function h(n) gives the number of Rate of Change standard form person-hours it takes to assemble Slope - Find rate of change n engines in a factory, then the Slope-intercept Form - Determine the slope of a line positive integers would be an Point-slope Form - Write an equation of a line appropriate domain for the Parallel given the slope and a point on function Perpendicular the line Scatter Plot - Write an equation of a line CCSS.Math.Content.F-IF.9. - Positive Correlation parallel or perpendicular to a Compare properties of two Negative Correlation given line functions each represented in a Line of Fit - Use scatter plots and different way (algebraically, Prediction Equation prediction equations graphically, numerically in tables, Regression Line - Model data using lines of or by verbal descriptions). For Correlation Coefficient regression example, given a graph of one quadratic function and an Big Ideas: algebraic expression for another, - Identify the mathematical say which has the larger domains and ranges of Maximum functions and determine reasonable domain and range CCSS.Math.Content.F-IF.6 - values for continuous and ​ Calculate and interpret the discrete situations average rate of change of a - Identify and sketch graphs of function (presented symbolically linear functions or as a table) over a specified - Collect and organize data, interval. Estimate the rate of make and interpret scatter change from a graph. plots, fit the graph of a function to the data, interpret the CCSS.Math.Content.ASSE.1b - results and proceed to model, ​ Interpret complicated expressions predict and make decisions by viewing one or more of their and critical judgements parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. CCSS.Math.Content.A-CED.2 - ​ Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Unit Four: Quadratics and Complex Numbers Timeline: 9 weeks CCSS.Math.Content.ASSE.1a - Concepts: Driving Questions: Summative: ​ Interpret parts of an expression, Quadratic function - Why do we use different - Throwing a ball Project such as terms, factors, and Quadratic methods to solve math - Quiz coefficients. Linear problems? Constant Terms Formative: CCSS.Math.Content.F-IF.9. - Parabola Learning Targets: - Workshop Practice Compare properties of two Axis of Symmetry - Solve quadratic equations by - Classwork/Homework functions each represented in a Vertex using the Quadratic Formula Assignments different way (algebraically, Maximum Value - Use the discriminant to - Warm-Ups graphically, numerically in tables, Minimum Value determine the number and or by verbal descriptions). For Quadratic Equations type of roots of a quadratic example, given a graph of one Standard Form equation quadratic function and an Root - Use a graphing calculator to algebraic expression for another, Zero investigate changes to say which has the larger Factored Form parabolas Maximum Foil - Write a quadratic function in Imaginary unit the form y = a(x − h) 2 + k CCSS.Math.Content.A-CED.2 - Pure imaginary unit - Transform graphs of quadratic ​ Create equations in two or more Complex Number functions of the form variables to represent Complex Conjugates y = a(x − h)2 + k relationships between quantities; - Investigate the rate of change graph equations on coordinate of a quadratic function by axes with labels and scales. Big Ideas: examining first- and - Determine reasonable domain second-order differences CCSS.Math.Content.F-IF.4 - For and range values of quadratic ​ a function that models a functions relationship between two - Analyze situations involving quantities, interpret key features quadratic functions and of graphs and tables in terms of formulate quadratic equations the quantities, and sketch graphs and inequalities to solve showing key features given a problems verbal description of the - Solve quadratic equations and relationship. inequalities using graphs, tables, and algebraic methods, including the Quadratic Formula - Use complex numbers to describe the solutions of quadratic equations - Determine a quadratic function from its zeros