First State Military Academy Mathematics Flow Chart 2018 – 2019 *A Math Course MUST Be Taken During Senior Year

$First State Military Academy Mathematics Flow Chart 2018 – 2019 *A Math Course MUST Be Taken During Senior Year$

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: A lgebra 2

Course Description: A lgebra 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 - Identify and sketch graphs of parent functions, including quadratic functions

Unit Five:Polynomials and Analyzing Graphs Timeline: 6 weeks CCSS.Math.Content.A-CED.1 - Concepts: Driving Questions: Summative: Create equations and inequalities Prime Polynomials - Why is math used to model - Roller Coaster Project in one variable and use them to Quadratic Form real-world situations? - Quiz solve problems. Include equations Identity arising from linear and Polynomial Identity Learning Targets: Formative: exponential functions Synthetic Substitution - Factor Polynomials - Workshop Practice Depressed Polynomial - Solve polynomial equations by - Classwork/Homework CCSS.Math.Content.A-APR.4 - factoring Assignments Prove polynomial identities and - Prove polynomial identities - Warm-Ups use them to describe numerical Big Ideas: - Evaluate functions by using relationships. For example, the - Use tools including factoring synthetic substitution polynomial identity (x2 + y2)2 = and properties of exponents to - Determine whether a binomial (x2 – y2)2 + (2xy)2 can be used simplify expressions and to is a factor of a polynomial by to generate Pythagorean triples transform and solve equations using synthetic substitution - Identify the mathematical - Determine the number and CCSS.Math.Content.A-APR.2 - domains and ranges of type of roots for a polynomial Know and apply the Remainder functions equation Theorem: For a polynomial p(x) - Determine the reasonable - Find the zeros of a polynomial and a number a, the remainder on domain and range values for function division by x – a is p(a), so p(a) = continuous situations - Use a graphing calculator to 0 if and only if (x – a) is a factor of analyze polynomial functions p(x). - Identify possible rational zeros of a polynomial function CCSS.Math.Content.F-IF.7 - - Find all of the rational zeros of Graph functions expressed a polynomial function symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

CCSS.Math.Content.A-APR.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.

CCSS.Math.Content.N-CN.9 - (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

CCSS.Math.Content.A-REI.11 - Explain why the x-coordinates 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); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★

Unit Six: Inverses and Radical Functions and Relations Timeline: 4 weeks

CCSS.Math.Content.F-IF.9 - Concepts: Driving Questions: Summative: Compare properties of two Composition of Functions - How can you choose a model - Driving in Style Project functions each represented in a Inverse Relation to represent a set of data? - Quiz different way (algebraically, Inverse Function graphically, numerically in tables, Square Root Function Learning Targets: Formative: or by verbal descriptions). For Radical Function - Find the sum, difference, - Workshop Practice example, given a graph of one Square Root Inequality product, and quotient of - Classwork/Homework quadratic function and an Nth root functions Assignments algebraic expression for another, Radical sign - Find the composition of - Warm-Ups say which has the larger Index functions maximum Radicand - Find the inverse of a function Principal Root or relation CCSS.Math.Content.F-BF.1 - Rationalizing the Denominator - Determine whether two Write a function that describes a Like radical expressions functions or relations are relationship between two Conjugate inverses quantities.★ Radical Equation - Compare a functions and its Extraneous solution inverse using a graphing b. Combine standard function Radical Inequality calculator types using arithmetic operations. - Graph and analyze square root For example, build a function that Big Ideas: functions models the temperature of a - Relate representations of - Graph square root inequalities cooling body by adding a constant square root functions - Simplify radicals function to a decaying - Connect inverses of square - Use a calculator to exponential, and relate these root functions with quadratic approximate radicals functions to the model. functions - Use a graphing calculator to - Determine solutions of square graph nth root functions CCSS.Math.Content.F-IF.4 - For root equations and inequalities - Simplify radical expressions a function that models a using graphs, tables, and - Add, subtract, multiply, and relationship between two algebraic methods divide radical expressions quantities, interpret key features - Determine the reasonable - Write expressions with rational of graphs and tables in terms of domain and range values of exponents in radical form and the quantities, and sketch graphs square root functions, and vice versa. showing key features given a interpret and determine the - Simplify expressions in verbal description of the reasonableness of solutions to exponential or radical form relationship. Key features include: square root equations and - Solve equations containing intercepts; intervals where the inequalities radicals function is increasing, decreasing, - Use the parent function to - Solve inequalities containing positive, or negative; relative investigate, describe, and radicals maximums and minimums; predict the effects of - Use a graphing calculator to symmetries; end behavior; and parameter changes on graphs solve radical equations and periodicity. of square root functions and inequalities describe limitations on the CCSS.Math.Content.F-BF.4 - domains and ranges Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x 1.

CCSS.Math.Content.F-IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.

CCSS.Math.Content.F-BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

CCSS.Math.Content.A-SSE.2. - Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

CCSS.Math.Content.A-REI.2. - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Unit Seven: Exponential and Logarithmic Functions and Relations Timeline: 5 weeks

CCSS.Math.Content.F-IF.7. - Concepts: Driving Questions: Summative: Graph functions expressed Exponential Function - How can you make good - Population Puzzle Project symbolically and show key Exponential Growth decisions? - Quiz features of the graph, by hand in Asymptote - What factors can affect good simple cases and using Growth Factor decision making? Formative: technology for more complicated Exponential Decay - Workshop Practice cases.★ Decay Factor Learning Targets: - Classwork/Homework Exponential Equation - Graph exponential growth Assignments e. Graph exponential and Compound Interest functions - Warm-Ups logarithmic functions, showing Exponential Inequality - Graph exponential decay intercepts and end behavior, and Logarithm functions trigonometric functions, showing Logarithmic Function - Use a graphing calculator to period, midline, and amplitude. Logarithmic Equation solve exponential equations by Logarithmic Inequality graphing or by using the table CCSS.Math.Content.F-IF.8. - Common Logarithm feature Write a function defined by an Change of Base Formula - Solve exponential equations expression in different but Natural Base, e - Solve exponential inequalities equivalent forms to reveal and Natural Base Exponential - Evaluate logarithmic explain different properties of the Function expressions function. Natural Logarithm - Graph logarithmic functions Rate of Continuous Growth - Use a graphing calculator to b. Use the properties of Rate of Continuous Decay find an equation of best fit for exponents to interpret Logistic Growth Model exponential and logarithmic expressions for exponential functions functions. For example, identify - Solve logarithmic equations percent rate of change in Big Ideas: - Solve logarithmic inequalities functions such as y = (1.02)t, y = - Analyze a situation modeled - Simplify and evaluate (0.97)t, y = (1.01)12t, y = by an exponential function, expressions using the (1.2)t/10, and classify them as formulate an equation or properties of logarithms representing exponential growth inequality, and solve the - Solve logarithmic equations or decay. problem using the properties of - Develop the definition of logarithms CCSS.Math.Content.A-REI.11. - logarithms by exploring and - Solve exponential equations Explain why the x-coordinates of describing the relationships and inequalities using common the points where the graphs of the between exponential functions logarithms equations y = f(x) and y = g(x) and their inverses - Evaluate logarithmic intersect are the solutions of the - Use parent functions to expressions using the Change equation f(x) = g(x); find the investigate, describe and of Base Formula solutions approximately, e.g., predict the effects of - Use a graphing calculator to using technology to graph the parameter changes on the solve exponential and functions, make tables of values, graphs of exponential and logarithmic equations and or find successive logarithmic functions, describe inequalities approximations. Include cases limitations on the domains and - Evaluate expressions involving where f(x) and/or g(x) are linear, ranges, and examine the natural base and natural polynomial, rational, absolute asymptotic behavior logarithm value, exponential, and - Determine solutions of - Solve exponential equations logarithmic functions.★ exponential and logarithmic and inequalities using natural equations using graphs, logarithms CCSS.Math.Content.A-CED.1. - tables, and algebraic methods - Use a spreadsheet to display Create equations and inequalities - Interpret and determine the the growth of an investment in one variable and use them to reasonableness of solutions to over time solve problems. Include equations exponential and logarithmic - Use logarithms to solve arising from linear and equations and inequalities problems involving exponential exponential functions. growth and decay - Use logarithms to solve CCSS.Math.Content.F-LE..4. - problems involving logistic For exponential models, express growth as a logarithm the solution to abct =d where a, c, and d are numbers and the base b is 2,10,or e; evaluate the logarithm using technology.

CCSS.Math.Content.F-IF.7. - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

CCSS.Math.Content.F-BF.3. - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

CCSS.Math.Content.A-CED.1. - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions.

Unit Eight: Rational Functions and Relations Timeline: 4 weeks

CCSS.Math.Content.A-APR.7. - Concepts: Driving Questions: Summative: (+) Understand that rational Rational expression - Why are graphs useful? - Financial Literacy Project expressions form a system Complex fraction - Quiz analogous to the rational Reciprocal function Learning Targets: numbers, closed under addition, Hyperbola - Simplify rational expressions Formative: subtraction, multiplication, and Asymptote - Simplify complex fractions - Workshop Practice division by a nonzero rational Rational function - Determine the LCM of - Classwork/Homework expression; add, subtract, Point discontinuity polynomials Assignments multiply, and divide rational Direct variation - Add and subtract rational - Warm-Ups expressions. Constant of variation expressions Rational equations - Determine properties of CCSS.Math.Content.A-CED.2. - Rational inequalities reciprocal functions Create equations in two or more Weighted average - Graph transformations of variables to represent reciprocal functions relationships between quantities; - Graph rational functions with graph equations on coordinate Big Ideas: vertical and horizontal axes with labels and scales. - Determine properties of asymptotes reciprocal functions and graph - Graph rational functions with CCSS.Math.Content.F-BF.3. - their transformations oblique asymptotes and point Identify the effect on the graph of - Use quotients of polynomials discontinuity replacing f(x) by f(x) + k, k f(x), to describe the graphs of - Use a graphing calculator to f(kx), and f(x + k) for specific rational functions, describe explore the graphs of rational values of k (both positive and limitations on the domains and functions negative); find the value of k ranges, and examine - Recognize and solve direct given the graphs. Experiment with asymptotic behavior and joint variation problems cases and illustrate an - Determine the reasonable - Recognize and solve inverse explanation of the effects on the domain and range values of and combined variation graph using technology. Include rational functions and problems recognizing even and odd determine the reasonableness - Solve rational equations functions from their graphs and of solutions to rational - Solve rational inequalities algebraic expressions for them. equations and inequalities - Use a graphing calculator to - Analyze a situation modeled solve rational equations by CCSS.Math.Content.F-IF.9. - by a rational function, graphing or by using the table Compare properties of two formulate an equation feature functions each represented in a composed of a linear or different way (algebraically, quadratic function, and solve graphically, numerically in tables, the problem or by verbal descriptions). For - Use functions to model and example, given a graph of one make predictions in problem quadratic function and an situations involving direct and algebraic exp inverse variation

CCSS.Math.Content.A-REI.2. - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

CCSS.Math.Content.A-CED.1. - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions.

CCSS.Math.Content.A-REI.11. - Explain why the x-coordinates 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); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★

Unit Nine: Timeline:

CCSS.Math.Content. Concepts: Driving Questions: Summative: - - - Quiz Big Ideas: Learning Targets: - - Formative: - Workshop Practice - Classwork/Homework Assignments - Warm-Ups

Algebra 2 Maria Collier [email protected] [email protected]

Expectations: 1. Use proper salutations. 2. Wear your uniform properly 3. Come prepared with a notebook, writing utensil, your computer, and homework if necessary. 4. Contribute during class discussion. 5. Stay on task while working in partners or groups.

Materials Needed Everyday: Spiral Notebook Writing Utensil Computer

Topics to be covered: Unit 1: Equations and Inequalities Unit 2: Linear Relations and Functions Unit 3: Systems of Equations and Inequalities Unit 4: Quadratic Functions and Relations Unit 5: Polynomials Unit 6: Inverses and Radical Functions Unit 7: Exponential and Logarithmic Functions Unit 8: Rational Functions Unit 9: Conic Sections

Assignment Headings When you turn in work electronically, I need you to put a heading on your assignments so that it is easier to keep track of the assignments along with the members of your group.

Last name: Assignment Title Collier: Order of Operations HW

Group Work Last name: Group members: Assignment Title Collier: Cook, Garton, Irwin: Order of Operation Project

Make-up Work: Every student has the ability to check his or her assignments from home as long as Wi-Fi is available. Make-up work will be taken care of on an individual basis, but students that aren’t in school will be expected to contact their groups to make sure that they are contributing as much as possible to help the group run smoothly to finish the projects. Absent students need to check the Agenda to see if there are any daily assignments that need to be accomplished before they come back to school. Assignments will only be accepted up to 5 school days late unless a plan has been created with the teacher.

Late Work A student has the ability to turn in work up until 5 days after the due date for the assignment. This is for when a student needs to finish an assignment that might not be quite done at the time it is supposed to be turned in. The student will lose points off of his or her grade each day that the assignment is late. The assignment will not be accepted on the 6th day for a grade. The assignment will automatically turn to a 0.

Grading System: The assignments will be graded on a scale so that Content and Knowledge are worth 50%, Written Communication is 15%, Oral Communication is 15%, Agency is 10%, and Collaboration is 10%.

100 – 93 A 92 – 85 B 84 – 77 C 76 – 70 D 69 – below F

We are looking forward to an exciting year where everyone is learning and growing together.

Sincerely,

Mrs. Collier

Curriculum Framework for:

School: First State Military Academy Course: Algebra I

Course Description: This course applies critical thinking skills needed to solve real world problems. It covers patterns and sequences, all types of linear equations and inequalities in one variable, systems of equations, quadratic functions, and an introduction to exponential functions. Coordinate geometry will be integrated into the investigation of these functions. Students learn how to use a graphing calculator in order to stay current with modern technological trends. 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, Equations, and Functions Timeline: 14 Days

CCSS.A.SSE.1a - Interpret parts of Concepts: Driving Questions: Summative: an expression, such as terms, factors, Algebraic Expressions - How can mathematical ideas be - Car Project and coefficients. Variable represented? - Quiz Term CCSS.A.SSE.2 - Use the structure of Power Learning Targets: an expression to identify ways to Exponent - To write verbal expressions for Formative: rewrite it. Base algebraic expressions - Workshop Practice Evaluate - To write algebraic expressions for - Classwork/Homework CCSS.A.SSE.1b - Interpret Order of Operations verbal expressions Assignments complicated expressions by viewing Equivalent Expressions - To evaluate numerical expressions - Warm-Ups one or more of their parts as a single Reciprocal by using the order of operations entity. Like Terms - To evaluate algebraic expressions Simplest Form by using the order of operations CCSS.A.CED.1 - Create equations Distributive Property - To use the distributive property to and inequalities in one variable and Coefficient evaluate and simplify expressions use them to solve problems. Equation - To solve equations with one and Solving two variables CCSS.A.REI.3 - Solve linear Solution - To represent and interpret graphs equations and inequalities in one Coordinate Plane of relations variable, including equations with X- and y-axes - To determine whether a relation is coefficients represented by letters. Origin a function Ordered Pair - To identify function values CCSS.A.REI.10 - Understand that the X- and y-coordinates graph of an equation in two variables Relation is the set of all its solutions plotted in Domain the coordinate plane, often forming a Range curve (which could be a line). Independent Variable Dependent Variable CCSS.F.IF.1 - Understand that a Function function from one set (called the Vertical Line Test domain) to another set (called the Function Notation range) assigns to each element of the domain exactly one element of the Big Ideas: range. - Represent relationships among quantities using tables, graphs, CCSS.F.IF.2 - Use function notation, verbal descriptions, and evaluate functions for inputs in their inequalities domains, and interpret statements - Use symbols to represent that use function notation in terms of a unknowns and variables context. - Find specific function values and solve equations in problem situations - Describe independent and dependent quantities in functional relationships - Identify mathematical domains and ranges and determine reasonable domain and range values for given situations - Connect equation notation with function notation

Unit Two: Linear Equations Timeline: 20 Days

CCSS.A.CED.1 - Create equations Concepts: Driving Questions: Summative: and inequalities in one variable and Formula - Why is it helpful to represent the - Central Park Desmos use them to solve problems. Solve an Equation same mathematical idea in - Pepsi Points Problem Equivalent Equations different ways? - Bottomless Coffee CCSS.A.REI.1 - Explain each step in Multi-Step Equations - Quiz solving a simple equation as following Addition Property of Equality Learning Targets: from the equality of numbers asserted Subtraction Property of Equality - To translate sentences into Formative: at the previous step, starting from the Multiplication Property of Equality equations - Penny Balance Problem assumption that the original equation Division Property of Equality - To translate equations into - Basketball Overboard Problem has a solution. Construct a viable Consecutive Integers sentences - Workshop Practice argument to justify a solution method - To solve equations by using - Classwork/Homework Big Ideas: addition, subtraction, multiplication, Assignments CCSS.A.REI.3 - Solve linear - Describe functional relationships and division - Warm-Ups equations and inequalities in one for given problem situations and - To solve equations involving more variable, including equations with write equations to answer than one operation coefficients represented by letters. questions arising from the - To solve equations involving situations consecutive integers - Represent relationships among - To solve equations with the quantities using diagrams, verbal variable on each side descriptions, and equations - To solve equations involving - Find specific function values, and grouping symbols transform and solve equations in problem situations - Use the Properties to simplify expressions

Unit Three: Linear Functions Timeline: 12 days

CCSS.F.IF.4 - For a function that Concepts: Driving Questions: Summative: models a relationship between two Linear Equation - Why are graphs useful? - Roller Coaster Project quantities, interpret key features of Standard Form - Quiz graphs and tables in terms of the Constant Learning Targets: quantities, and sketch graphs showing X-intercept - To identify linear equations, Formative: key features given a verbal Y-intercept intercepts, and zeros. - Function Research description of the relationship. Key Linear function - To graph and write linear - Leo the Rabbit features include: intercepts; intervals Rate of change equations. - Foundations of Functions where the function is increasing, Slope - To use rate of change to solve Worksheet decreasing, positive, or negative; Direct variation problems. - Workshop Practice relative maximums and minimums; - Classwork/Homework symmetries; end behavior; and Big Ideas: Assignments periodicity.* - Create, use, translate, and make - Warm-Ups connections among algebraic, CCSS.F.IF.7a - Graph linear and tabular, graphical, or verbal quadratic functions and show descriptions of linear functions. intercepts, maxima, and minima. - Interpret the meaning of intercepts in situations using data, symbolic CCSS.A.REI.10 - Understand that the representations, or graphs graph of an equation in two variables - Determine the intercepts of the is the set of all its solutions plotted in graphs of linear functions and the coordinate plane, often forming a zeros of linear functions from curve (which could be a line). graphs, tables, and algebraic representations CCSS.F.IF.6 - Calculate and interpret - Look for patterns and represent the average rate of change of a generalizations algebraically function (presented symbolically or as - Develop the concept of slope as a table) over a specified interval. rate of change and determine the Estimate the rate of change from a slope from graphs, tables, and graph.* algebraic representations - Interpret the meaning of slope in situations using data, symbolic CCSS.F.LE.1a - Distinguish between representation situations that can be modeled with linear functions and with exponential functions.

Unit Four: Equations of Linear Functions Timeline: 16 Days

CCSS.F.IF.7a - Graph linear and Concepts: Driving Questions: Summative: quadratic functions and show Slope-intercept form - Why is math used to model - Lost in Space Project intercepts, maxima, and minima. Constant function real-world situations? - Quiz CCSS.S.ID.7 - Interpret the slope Constraint (rate of change) and the intercept Linear extrapolation Learning Targets: Formative: (constant term) of a linear model in Point-slope form - To write and graph linear - Investigating T-shirt offers the context of the data. Parallel lines equations in various forms. - Workshop Practice CCSS.F.BF.1 - Write a function that Perpendicular lines - To find inverse linear functions. - Classwork/Homework describes a relationship between two Inverse relation Assignments quantities Inverse function - Warm-Ups CCSS.F.LE.2 - Construct linear and exponential functions, including Big Ideas: arithmetic and geometric sequences, - Write equations of lines given given a graph, a description of a specific characteristics relationship, or two input-output pairs - Interpret and predict the effects of (include reading these from a table). changing the slope and y-intercept CCSS.F.IF.2 - Use function notation, in applied situations evaluate functions for inputs in their - Interpret and make decisions, domains, and interpret statements predictions, and critical judgments that use function notation in terms of a from functional relationships context. - Solve an equation of the form f(x) CCSS.A.CED.2 - Create equations in = c for a simple function f that has two or more variables to represent an inverse and write an expression relationships between quantities; for the inverse. graph equations on coordinate axes with labels and scales. CCSS.F.BF.4a - Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Unit Five: Linear Inequalities Timeline: 12 Days

CCSS.A.CED.1 - Create equations Concepts: Driving Questions: Summative: and inequalities in one variable and Set-Builder Notation - How are symbols useful in - Equations and inequalities project use them to solve problems. Include Compound Inequality mathematics? - Quiz equations arising from linear and Intersection - What mathematical symbols do quadratic functions, and simple Union you know? Formative: rational and exponential functions. Boundary - Workshop Practice CCSS.A.REI.3 - Solve linear Half-Plane Closed Learning Targets: - Classwork/Homework equations and inequalities in one Half-Plane Open - To solve one-step and multi-step Assignments variable, including equations with inequalities - Warm-Ups coefficients represented by letters. Big Ideas: - To solve compound inequalities CCSS.A.REI.12 - Graph the solutions - Formulate linear inequalities to and inequalities involving absolute to a linear inequality in two variables solve problems value. as a half-plane (excluding the - Investigate methods for solving - To graph inequalities in two boundary in the case of a strict linear inequalities using the variables. inequality), and graph the solution set Properties of Inequality to a system of linear inequalities in - Solve linear inequalities two variables as the intersection of - Interpret and determine the the corresponding half-planes. reasonableness of solutions to linear inequalities

Unit Six: Systems of Linear Equations and Inequalities Timeline: 12 Days

CCSS.A.CED.2 - Create equations in Concepts: Driving Questions: Summative: two or more variables to represent Systems of equations - How can you find the solution to a - Netflix, Redbox, or Apple TV relationships between quantities; Consistent math problem? - Star Wars vs. Avengers graph equations on coordinate axes Independent - How can you use system of - Quiz with labels and scales. Dependent equations to solve real-world CCSS.A.REI.6 - Solve systems of Inconsistent problems? Formative: linear equations exactly and Substitution - Workshop Practice approximately (e.g., with graphs), Elimination Learning Targets: - Classwork/Homework focusing on pairs of linear equations - To solve systems of linear Assignments in two variables. Big Ideas: equations by graphing, - Warm-Ups CCSS.A.REI.5 - Prove that, given a - Analyze situations and formulate substitution, and elimination. system of two equations in two systems of linear equations in two variables, replacing one equation by unknowns to solve problems. the sum of that equation and a - Solve systems of linear equations multiple of the other produces a using graphs and algebraic system with the same solutions methods - Interpret and determine the reasonableness of solutions to systems of linear equations.

Unit Seven: Exponents and Exponential Functions Timeline: 14 Days

CCSS.A.SSE.2 - Use the structure of Concepts: Driving Questions: Summative: an expression to identify ways to Monomial - How can you make good - Exponential Functions Project: rewrite it. For example, see x4 – y4 as Constant decisions? Math with a Message. (x2)2 – (y2)2, thus recognizing it as a Zero Exponents - What factors can affect good - Quiz difference of squares that can be Negative Exponent decision making? factored as (x2 – y2)(x2 + y2). Order of Magnitude Formative: CCSS.F.IF.8b - Write a function Rational Exponent Learning Targets: - Workshop Practice defined by an expression in different Cube Root - To simplify and perform operations - Classwork/Homework but equivalent forms to reveal and nth Root on expressions involving Assignments explain different properties of the Exponential Equation exponents. - Warm-Ups function. Scientific Notation - To extend the properties of integer CCSS.N.RN.1 - Explain how the Exponential Function exponents to rational exponents. definition of the meaning of rational Exponential Growth Function - To use scientific notation. exponents follows from extending the Exponential Decay Function - To graph and use exponential properties of integer exponents to Compound Interest functions those values, allowing for a notation Geometric Sequence for radicals in terms of rational Common Ratio exponents. For example, we define Recursive Formula 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so Big Ideas: (51/3)3 must equal 5. - Simplify polynomial expressions CCSS.N.RN.2 - Rewrite expressions and apply the laws of exponents in involving radicals and rational problem-solving situations exponents using the properties of - Graph and analyze exponential exponents. functions CCSS.F.IF.7e - Graph exponential - Analyze data and represent and logarithmic functions, showing situations involving exponential intercepts and end behavior, and growth and decay using tables, trigonometric functions, showing graphs, or algebraic methods period, midline, and amplitude. - Relate geometric sequences to CCSS.F.LE.2 - Construct linear and exponential functions, and write exponential functions, including recursive formulas to represent arithmetic and geometric sequences, sequences given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). CCSS.REI.11 - Explain why the x-coordinates 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); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CCSS.F.BF.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* CCSS.F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Unit Eight: Quadratic Expressions and Equations Timeline: 18 Days

CCSS.A.SSE.1a - Interpret parts of Concepts: Driving Questions: Summative: an expression, such as terms, factors, Factoring - When could a nonlinear function - “How To” Quadratics Project and coefficients. Factoring by grouping be used to model a real-world - Quiz CCSS.A.APR.1 - Understand that Zero Product Property situation? polynomials form a system analogous Quadratic Equation Formative: to the integers, namely, they are Prime Polynomial Learning Targets: - Workshop Practice closed under the operations of Difference of Two Squares - To add, subtract, and multiply - Classwork/Homework addition, subtraction, and Perfect Square Trinomial polynomials Assignments multiplication; add, subtract, and - To factor trinomials - Warm-Ups multiply polynomials. - To factor differences of squares CCSS.A.SSE.2 - Use the structure of Big Ideas: - To graph quadratic functions an expression to identify ways to - Add, subtract, and multiply - To solve quadratic equations rewrite it. For example, see x4 – y4 as polynomials (x2)2 – (y2)2, thus recognizing it as a - Factor as necessary in problem difference of squares that can be situations factored as (x2 – y2)(x2 + y2). - Solve quadratic equations using CCSS.A.SSE.3a - Factor a quadratic concrete models, tables, graphs, expression to reveal the zeros of the and algebraic methods function it defines. CCSS.A.REI.4b - Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CCSS.A.REI.1 - 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.

Unit Nine: Quadratic Functions and Equations Timeline: 18 Days

CCSS.F.IF.4 - For a function that Concepts: Driving Questions: Summative: models a relationship between two Quadratic Function - Why do we use different methods - Quadratic functions project - quantities, interpret key features of Standard form to solve math problems? Parabola Selfie graphs and tables in terms of the Parabola - Quiz quantities, and sketch graphs showing Axis of Symmetry Learning Targets: key features given a verbal Vertex - To solve quadratic equations by Formative: description of the relationship. Minimum graphing, completing the square, - Workshop Practice CCSS.F.IF.7a - Graph linear and Maximum and using the Quadratic Formula - Classwork/Homework quadratic functions and show Double root - To analyze functions with Assignments intercepts, maxima, and minima. Transformation successive differences and ratios - Warm-Ups CCSS.A.REI.4b - Solve quadratic Translation - To identify and graph special 2 equations by inspection (e.g., for x = Dilation functions 49), taking square roots, completing Reflection the square, the quadratic formula and Vertex Form factoring, as appropriate to the initial Completing the square form of the equation. Quadratic Formula CCSS.A.SSE.3b - Complete the square in a quadratic expression to Big Ideas: reveal the maximum or minimum - To identify and sketch the general value of the function it defines. forms of quadratic parent functions CCSS.A.REI.4 - Solve quadratic - Analyze graphs of quadratic equations in one variable. functions and draw conclusions CCSS.F.IF.8a - Use the process of - Make connections among the factoring and completing the square in solutions of quadratic equations, a quadratic function to show zeros, the zeros of their related functions, extreme values, and symmetry of the and the horizontal intercepts of the graph, and interpret these in terms of graph of the function a context. - Solve quadratic equations using CCSS.F.IF.6 - Calculate and interpret concrete models, tables, graphs, the average rate of change of a and algebraic methods function (presented symbolically or as - Analyze functions with successive a table) over a specified interval. differences and ratios Estimate the rate of change from a - Identify and graph special graph. functions CCSS.F.LE.1 -Distinguish between situations that can be modeled with linear functions and with exponential functions.

Unit Ten: Radical Functions and Geometry Timeline: 16 Days

CCSS.F.BF.4a - Solve an equation of Concepts: Driving Questions: Summative: the form f(x) = c for a simple function f Square Root Function - How can you choose a model to - Radical Functions - Modeling the that has an inverse and write an Radical Function represent a real-world situation? Speed of Tsunamis expression for the inverse. Redicand - Quiz CCSS.F.IF.4 - For a function that Radical Expression Learning Targets models a relationship between two Rationalizing the denominator - To graph and transform radical Formative: quantities, interpret key features of Conjugate functions. - Workshop Practice graphs and tables in terms of the Closed - To simplify, add, subtract, and - Classwork/Homework quantities, and sketch graphs showing nth Root multiply, radical expressions. Assignments key features given a verbal Index - To solve radical equations. - Warm-Ups description of the relationship. Radical Equations - To use the Pythagorean Theorem. CCSS.F.IF.7b - Graph functions Extraneous Solutions - To find trigonometric ratios. expressed symbolically and show key Hypotenuse features of the graph, by hand in Legs simple cases and using technology for Converse more complicated cases Pythagorean Triple CCSS.A.REI.4a - Use the method of Distance Formula completing the square to transform Midpoint any quadratic equation in x into an Trigonometry equation of the form (x – p)2 = q that Trigonometric Ratio has the same solutions. Derive the Sine quadratic formula from this form. Cosine CCSS.N.NR.2 - Rewrite expressions Tangent involving radicals and rational Solving the Triangle exponents using the properties of Inverse sine exponents. Inverse Cosine CCSS.A.CED.2 - Create equations in Inverse Tangent two or more variables to represent relationships between quantities; Big Ideas: graph equations on coordinate axes - Add, subtract, multiply, and with labels and scales. simplify radical expressions - Solve radical equations - Use Pythagorean Theorem and and trigonometric ratios to solve problems.

Unit Eleven: Rational Functions and Equations Timeline: 14 Days

CCSS.A.CED.2 - Create equations in Concepts: Driving Questions: Summative: two or more variables to represent Inverse Variation - How can simplifying mathematical - Rational Functions Project - Crime relationships between quantities; Product Rule expressions be useful? Scene Investigation graph equations on coordinate axes Rational Function Learning Targets - Quiz with labels and scales. Excluded Value - To identify and graph inverse Formative: CCSS.A.REI.11 - Explain why the Asymptote variations - Workshop Practice x-coordinates of the points where the Rational Expression - To identify extended values of - Classwork/Homework graphs of the equations y = f(x) and y Least Common Multiple rational functions Assignments = g(x) intersect are the solutions of Least Common Denominator - To multiply, divide, and add - Warm-Ups the equation f(x) = g(x); find the Mixed Expression rational expressions solutions approximately, e.g., using Complex Fraction - To divide polynomials technology to graph the functions, Rational Equation - To solve rational equations make tables of values, or find Extraneous Solution successive approximations. Include Work and Rate Problems cases where f(x) and/or g(x) are linear, polynomial, rational, absolute Big Ideas: value, exponential, and logarithmic - Analyze data and represent functions.* situation involving inverse variation using tables, graphs, or algebraic methods - Graph and analyze rational functions - Identify excluded values from rational expressions and simplify rational expressions - Multiply and divide rational expressions and use dimensional analysis - Divide a polynomial by a monomial or binomial - Add and subtract rational expressions with like and unlike denominators - Solve rational equations and eliminate extraneous roots

Unit Twelve: Statistics and Probability Timeline: 14 Days

CCSS.S.ID.2 - Use statistics Concepts: Driving Questions: Summative: appropriate to the shape of the data Population - How are statistics and probability - Independent Study distribution to compare center Sample used in the real world? - Quiz (median, mean) and spread Simple random sample (interquartile range, standard Systematic sample Learning Targets Formative: deviation) of two or more different Self-selected sample - To design surveys and evaluate - Workshop Practice data sets. Convenience sample results - Classwork/Homework CCSS.S.ID.3 - Interpret differences in Stratified sample - To use permutations and Assignments shape, center, and spread in the Bias combinations - Warm-Ups context of the data sets, accounting Survey - To design and use simulations for possible effects of extreme data Observational study points (outliers). Experiment CCSS.S.ID.5 - Summarize categorical Statistical inference data for two categories in two-way Statistic frequency tables. Interpret relative Parameter frequencies in the context of the data Mean absolute deviation (MAD) (including joint, marginal, and Standard deviation conditional relative frequencies). Variance Recognize possible associations and Distribution trends in the data. Negatively skewed distribution Symmetric distribution Positively skewed distribution Linear transformation Theoretical probability Experimental probability Relative frequency Simulation Probability model Permutation Factorial Combination Compound event Joint probability Independent events Dependent events Mutually exclusive events Random variable Discrete random variable Probability distribution Probability graph Expected value

Big Ideas: - Identify various sampling techniques and recognize a biased sample - Count outcomes using the Fundamental Counting Principle - Use combinations and permutations to determine probabilities - Find the probability of two independent events or dependent events, and find the probability of two mutually exclusive or inclusive events - Use random variables to compute probability, and use probability distributions to solve real-world problems - Use probability simulations to model real-world situations

Algebra 1 Cassandra Garton [email protected] [email protected]

Expectations:

1. Use proper salutations.

2. Wear your uniform properly

3. Come prepared with a notebook, writing utensil, your computer, and homework if necessary.

4. Contribute during class discussion.

5. Stay on task while working in partners or groups.

Materials Needed Everyday: Spiral Notebook Writing Utensil Computer

Topics to be covered: Unit 1: Functions, Equations, and Expressions Unit 2: Linear Equations Unit 3: Linear Functions Unit 4: Equations of Linear Functions Unit 5: Linear Inequalities Unit 6: Systems of Linear Equations and Inequalities Unit 7: Exponents and Exponential Functions Unit 8: Quadratic Expressions and Equations Unit 9: Quadratic Functions and Equations

Late Work A student has the ability to turn in work up until 5 days after the due date for the assignment. This is for when a student needs to finish an assignment that might not be quite done at the time it is supposed to be turned in. The student will lose 7% of his or her grade each day that the assignment is late. The assignment will not be accepted on the 6th day for a grade. The assignment will automatically turn to a 0.

100 – 93 A 92 – 85 B 84 – 77 C 76 – 70 D 69 – below F

We are looking forward to an exciting year where everyone is learning and growing together.

Sincerely,

Ms. Garton

Curriculum Framework for

School: First State Military Academy Course: C alculus

This course includes the in-depth study of functions, analysis of graphs, limits, continuity, derivatives at a Course Description: point and of functions, second derivatives and applications and computation of derivatives: interpretations and properties of definite integrals, applications of integrals, including volumes of solids of revolution, disks, and washer, and the approximations to definite integrals. All topics are covered algebraically, geometrically, and analytically.

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: Prerequisites for Calculus Timeline: 2 weeks

CCSS.MATH.CONTENT.HSA.CE Concepts: Driving Questions: Summative: D.A.1 Increments - How are linear equations used - Isotope Project Slope of a Line extensively in business and - Quiz CCSS.MATH.CONTENT.HSA.CE Parallel and Perpendicular Lines economic applications? D.A.2 Equations of Lines - How are functions and graphs Formative: Functions used to form the basis for - Workshop Practice CCSS.MATH.CONTENT.HSA.CE Domains and Ranges understanding mathematics? - Classwork/Homework D.A.4 Viewing and Interpreting Graphs - How do exponential functions Assignments Even Functions and Odd model growth patterns? - Warm-Ups CCSS.MATH.CONTENT.HSA.RE Functions-Symmetry - How do parametric equations I.A.10 Functions Defined in Pieces create graphs of relations and The Absolute Value Function functions? CCSS.MATH.CONTENT.HSA.CE Composite Functions - How are logarithmic functions D.A.11 Exponential Growth used in real-life applications? Exponential Decay - How do trigonometric functions CCSS.MATH.CONTENT.HSF.IF. The Number e model periodic behavior? A.1 Relations Circles CCSS.MATH.CONTENT.HSF.IF. Ellipses Learning Targets: A.2 Lines and Other Curves - Use increments to calculate One-to-One Functions slopes CCSS.MATH.CONTENT.HSF.IF. Inverses - Write an equation and sketch a A.5 Finding Inverses graph of a line given specific Logarithmic Functions information CCSS.MATH.CONTENT.HSF.IF. Properties of Logarithms - Identify the relationships A.7a Radian Measure between parallel lines, Graphs of Trigonometric perpendicular lines, and slopes CCSS.MATH.CONTENT.HSF.IF. Functions - Use linear regression A.7b Periodicity equations to solve problems Even and Odd Trigonometric - Identify the domain and range CCSS.MATH.CONTENT.HSF.IF. Functions of a function using its graph or A.7e Transformations of Trigonometric equation Graphs - Recognize even functions and CCSS.MATH.CONTENT.HSF.IF. Inverse Trigonometric Functions odd functions using equations A.8b and graphs Big Ideas: - Interpret and find formulas for CCSS.MATH.CONTENT.HSF.BF - Review the most important piecewise defined functions .A.1b topics necessary to start - Write and evaluate learning Calculus compositions of two functions CCSS.MATH.CONTENT.HSF.BF - Introduce a graphing utility as - Determine the domain, range, .A.1c an investigative tool to support and graph of an exponential analytic work function CCSS.MATH.CONTENT.HSF.BF - Solve problems with numerical - Solve problems involving .A.3 and graphical methods exponential growth and decay - Functions and parametric - Use exponential regression CCSS.MATH.CONTENT.HSF.BF equations are major tools to equations to solve problems .A.4 describe real world situations - Graph curves that are - Learn the different functions described, using parametric CCSS.MATH.CONTENT.HSF.BF and the behaviors they can equations .A.5 describe - Find parameterizations of - Trigonometric functions circles, ellipses, line segments, CCSS.MATH.CONTENT.HSF.LE. describe cyclic and repetitive and other curves A.1 activity - Identify a one-to-one function - Exponential, logarithmic, and - Determine the algebraic CCSS.MATH.CONTENT.HSF.LE. logistic functions describe representation and the A.3 growth and decay graphical representation of a - Polynomial functions can function and its inverse CCSS.MATH.CONTENT.HSF.LE. approximate these and most - Use parametric equations to A.4 other functions graph inverse functions - Convert between radians and CCSS.MATH.CONTENT.HSF.LE. degrees, and find arc length A.5 - Identify the periodicity and even-odd properties of the CCSS.MATH.CONTENT.HSF.TF. trigonometric functions A.1 - Find values of trigonometric functions CCSS.MATH.CONTENT.HSF.TF. - Generate graphs for A.2 trigonometric functions and explore various CCSS.MATH.CONTENT.HSF.TF. transformations A.4 - Use the inverse trigonometric functions to solve problems CCSS.MATH.CONTENT.HSF.TF. A.5

CCSS.MATH.CONTENT.HSF.TF. A.6

CCSS.MATH.CONTENT.HSF.TF. A.7

CCSS.MATH.CONTENT.HSS.ID. B.6

CCSS.MATH.CONTENT.HSS.ID. B.7

CCSS.MATH.CONTENT.HSS.ID. B.8 Unit Two: Limits and Continuity Timeline: 4 weeks

CCSS.MATH.CONTENT.HSA.SS Concepts: Driving Questions: Summative: E.A.1 Average and Instantaneous - How can limits be used to - Insect Population Project Speed describe continuity, the - Quiz CCSS.MATH.CONTENT.HSA.SS Definition of Limit derivative, and the integral? E.B.3 Properties of Limits - How can limits be used to Formative: One-sided Limits describe the behavior of - Workshop Practice CCSS.MATH.CONTENT.HSA.AP Two-sided Limits functions for numbers in - Classwork/Homework R.C.4 Sandwich Theorem absolute value? Assignments Finite Limits as x →± ∞ - How do continuous functions - Warm-Ups CCSS.MATH.CONTENT.HSA.AP Infinite Limits as x → a describe how a body moves R.D.6 End Behavior Models through space? Continuity as a Point - How does a tangent line CCSS.MATH.CONTENT.HSA.CE Continuous Functions describe points of motion? D.A.4 Algebraic Combinations Composites CCSS.MATH.CONTENT.HSF.IF. Intermediate Value Theorem for Learning Targets: B.6 Continuous Functions - Calculate average and Average Rates of Change instantaneous speeds CCSS.MATH.CONTENT.HSF.IF. Tangent to a Curve - Define and calculate limits for C.7 Slope of a Curve function values and apply the Normal to a Curve properties of limits - Use the Sandwich Theorem to find certain limits indirectly Big Ideas: - Find and verify end behavior - To understand the concept of models for various functions limit - Calculate limits as x →± ∞ and - To define and calculate limits to identify vertical and of function values horizontal asymptotes - Use substitution, graphical - Identify the intervals upon investigation, numerical which a given functions is approximation, algebra, or continuous and understand the some combination to solve meaning of continuous limits function - Use limits to test for continuity - Remove removable discontinuities by extending or modifying a function - Apply the Intermediate Value Theorem and the properties of algebraic combination and composites of continuous functions - Apply directly the definition of the slope of a curve in order to calculate slopes - Find the equations of the tangent line and normal line to a curve at a given point - Find the average rate of change of a function

Unit Three: Derivatives Timeline: 4 weeks

Concepts: Driving Questions: Summative: Derivative - How can we use the derivative - Medicine Dosage Project Notation to model the instantaneous - Quiz Relationships between the change? Graphs of f and f′ - How can we create a graph Formative: Graphing the Derivative from when you know the tangent - Workshop Practice Data lines at multiple points? - Classwork/Homework One-sided Derivatives - How do you use the rules for Assignments How f′(a) Might Fail to Exist differentiation to analyze - Warm-Ups Differentiability Implies Local functions quickly? Linearity - How do derivatives give Numerical Derivatives on a different rates at which things Calculator change? Differentiability Implies Continuity - How can sine and cosine Intermediate Value Theorem for graphs describe periodic Derivatives change? Positive Integer Powers, Multiples, Sums, and Learning Targets: Differences - Calculate slopes and Products and Quotients derivatives using the definition Negative Integer Powers of x of the derivative Second and Higher Order - Graph f from the graph of f′ , Derivatives graph f′ from the graph of f , Instantaneous Rates of Change and graph the derivative of a Motion Along a Line function given numerically with Sensitivity to Change data Derivatives in Economics - Find where a function is not Derivative of the Sine Function differentiable and distinguish Derivative of the Cosine Function between corners, cusps, Simple Harmonic Motion discontinuities, and vertical Jerk tangents. Derivatives of the Other Basic - Approximate derivatives Trigonometric Functions numerically and graphically - Use the rules of differentiation Big Ideas: to calculate derivatives, - Calculate the instantaneous including second and higher rate of change at any point order derivatives - Study the rates of change - Use the derivative to calculate of functions the instantaneous rate of - Find out what a derivative change is - Use derivatives to analyze - Learn how derivatives work straight line motion and solve other problems involving rates of change - Use the rules of differentiating the six basic trigonometric functions

Unit Four: More Derivatives Timeline: 4 weeks

Concepts: Driving Questions: Summative: Chain Rule - How does the Chain Rule help - Professor Project Implicit Differentiation you differentiate functions? - Quiz Inverse Function - How does implicit Inverse Cofunction Identities differentiation allow us to find Formative: Logarithmic Differentiation derivatives of functions? - Workshop Practice Normal to the Surface - How do graphs of functions - Classwork/Homework Orthogonal Curves and inverses relate to their Assignments Orthogonal Families derivatives? - Warm-Ups Power Chain Rule - How do exponential rates Power Rule for Arbitrary Real model growth rates in the real Powers world? Power Rule for Rational Powers of x Learning Targets: - Differentiate composite Big Ideas: functions using the Chain Rule - Exploring the Chain Rule - Find slopes of parameterized - Use the Chain Rule curves - Create a derivative for a - Find derivatives using implicit composite function differentiation - Create derivatives of - Find derivatives using the trigonometric functions and Power Rule for Rational their inverses Powers of x - Calculate derivatives of - Calculate derivatives of exponential and logarithmic functions involving the inverse functions trigonometric functions - Use implicit differentiation to - Calculate derivatives of find derivatives exponential and logarithmic - Use the Power Rule to find functions derivatives -

Unit Five:Applications of Derivatives Timeline: 6 weeks

Concepts: Driving Questions: Summative: Absolute change - How do you find optimization? - Gas Mileage Project Absolute maximum value - How does the Mean Value - Quiz Absolute minimum value Theorem connect average and Antiderivative instantaneous rates of Formative: Antidifferentiation change? - Workshop Practice Arithmetic mean - How do you use differential - Classwork/Homework Average cost calculus to analyze functions? Assignments Center of Linear Approximation - How does optimization explain - Warm-Ups Concave down real world applications? Concave up - How can we use Concavity Test approximation techniques to Critical point explain practical applications? Decreasing function - How can we use related rate Differential problems to explain Differential estimate of change mechanics? Differential of a function Extrema Learning Targets: Extreme Value Theorem - Determine the local and global First Derivative Test extreme values of a function Geometric mean - Apply the Mean Value Global maximum value Theorem and find the intervals Global minimum value on which a function is Increasing function increasing or decreasing Linear approximation - Use the First and Second Linearization Derivative Tests to determine Local linearity the local extreme values of a Local maximum value function Local minimum value - Determine the concavity of a Logistic or life cycle curve function and locate the points Logistic regression of inflection by analyzing the Marginal analysis second derivative Marginal cost and revenue - Graph f using information Mean Value Theorem about f′ Monotonic function - Solve application problems Newton’s method involving finding minimum or Optimization maximum values of functions Percentage change - Find linearizations and use Point of inflection Profit Newton’s method to Quadratic approximation approximate the zeros of a Related rates function Relative change - Estimate the change in a Relative extrema function using differentials Rolle’s Theorem - Solve related rate problems Second Derivative Test Standard linear approximation Stationary point

Big Ideas: - Drawing conclusions from derivatives about extreme values and the general shape - See how tangent lines capture the shape of a curve near a point of tangency - Deducing rates of change we cannot measure from rates of change we already know - Finding functions from the first derivative and a point - Use the Mean Value Theorem to recover functions from derivatives

Unit Six: The Definite Integral Timeline: 6 weeks

Concepts: Driving Questions: Summative: Area under a curve - How do you estimate with finite - Lottery Project Average value sums? - Quiz Bounded function - What happens to a limit when Cardiac output the numbers are infinitely small Formative: Characteristic function of the or infinitely large? - Workshop Practice rationals - How can we connect - Classwork/Homework Definite integral derivatives and definite Assignments Differential calculus integrals? - Warm-Ups Dummy variable - How can we use trapezoids to Error bounds create numerical Fundamental Theorem of approximations? Calculus Integrable function Integral calculus Learning Targets: Integral Evaluation Theorem - Approximate the area under Integral of f from a to b the graph of a nonnegative Integral sign continuous function by using Integrand rectangle approximation Lower bound methods Lower limit of integration - Interpret the area under a LRAM graph as a net accumulation of Mean value a rate of change Mean Value Theorem for Definite - Express the area under a Integrals curve as a definite integral and MRAM as a limit of Riemann sums Net area NINT - Compute the area under a Norm of a partition curve using a numerical Partition integration procedure RAM - Apply rules for definite Regular partition integrals and find the average Riemann sum value of a function over a Riemann sum for f on the [a, b] closed interval RRAM - Apply the Fundamental Sigma notation Theorem of Calculus Simpson’s Rule - Understand the relationship Subinterval between the derivative and Total area definite integral as expressed Trapezoidal Rule in both parts of the Upper bound Fundamental Theorem of Upper limit of integration Calculus Variable of integration - Approximate the definite integral by using the trapezoidal Rule and by using Big Ideas: Simpson’s Rule. - Calculate instantaneous rates - Estimate the error in using the of change Trapezoidal and Simpson’s - Investigate slopes of tangent Rules lines - Investigate areas under curves - Prove how slopes of tangents and areas under curves are connected

Unit Seven: Differential Equations and Mathematical Modeling Timeline: 4 weeks

Concepts: Driving Questions: Summative: CCSS.MATH.CONTENT.HSN.Q. Antidifferentiation by parts - How can we model problems - Population Project A.1 Antidifferentiation by substitution of motion using derivatives? - Quiz Arbitrary constant of integration - How can we find the Use units as a way to understand Carbon-14 dating antiderivative of f ? Formative: problems and to guide the Carrying capacity - How does the Product Rule - Workshop Practice solution of multi-step problems; Compounded continuously relate derivatives? - Classwork/Homework choose and interpret units Constant of integration - How does the differential Assignments consistently in formulas; choose Continuous interest rate dy - Warm-Ups equation dx = ky give insight and interpret the scale and the Decay constant into exponential growth and origin in graphs and data Differential equation decay? displays. Direction field - How do real world populations Euler’s Method grow logistically over extended CCSS.MATH.CONTENT.HSN.Q. Evaluate an integral periods of time? A.2 Exact differential equation General solution to a differential Learning Targets: Define appropriate quantities for equation - Construct antiderivatives using the purpose of descriptive Growth constant the Fundamental Theorem of modeling. First-order differential equation Calculus First-order linear differential - Solve initial value problems in CCSS.MATH.CONTENT.HSG.M equation dy the form = f(x), yo = f(xo). G.A.3 Graphical solution of a differential dx - Construct slope fields using equation technology and interpret slope Apply geometric methods to solve Half-life design problems (e.g., designing Heaviside method fields as visualizations of an object or structure to satisfy Indefinite integral different equations physical constraints or minimize Initial condition - Use Euler’s Method for cost; working with typographic Initial value problem graphing a solution to an initial grid systems based on ratios).* Integral sign value problem Integrand - Compute indefinite and definite Integration by parts integrals by the method of Law of Exponential Change substitution Leibniz notation for integrals - Use integration by parts to Logistic differential equation evaluate indefinite and definite Logistic growth model integrals Logistic growth model - Use tabular integration or the Logistic regression method of solving for the Newton’s Law of Cooling unknown integral i order to Numerical method evaluate integrals that require Numerical solution of a differential repeated use of integration by equation parts Order of a differential equation - Use integration by parts to Partial fraction decomposition integrate inverse trigonometric Particular solution and logarithmic functions Proper rational function - Solve problems involving Properties of indefinite integrals exponential growth and decay Radioactive in a variety of applications Radioactive decay - Solve problems involving Resistance proportional to exponential or logistic velocity population growth Second-order differential equation Separable differential equations Separation of variables Slope field Solution of a differential equation Substitution in definite integrals Tabular integration Variable of integration

Big Ideas: - Predicting future positions from the present position and known velocity - Deduce what we need to know about a function from one of its known values and rate of change - Examine the analytic, graphical, and numerical techniques on which we create predictions

Unit Eight: Applications of Definite Integrals Timeline: 6 weeks

CCSS.MATH.CONTENT.HSG.G Concepts: Driving Questions: Summative: MD.A.1 Arc length - How can we use an integral to - Pottery Project Area between curves calculate net change and total - Quiz Give an informal argument for the Cavalieri’s theorems accumulation? formulas for the circumference of Center of mass - How can we calculate the area Formative: a circle, area of a circle, volume Constant-force formula in between curves? - Workshop Practice of a cylinder, pyramid, and cone. Cylindrical shells - How can we calculate the - Classwork/Homework Use dissection arguments, Displacement volume of a three dimensional Assignments Cavalieri's principle, and informal Fluid pressure solid? - Warm-Ups limit arguments. Foot-pound - How can we use definite Force constant integrals to calculate the length CCSS.MATH.CONTENT.HSG.G Gaussian curve of a smooth curve? MD.A.2 Hooke’s Law Inflation rate (+) Give an informal argument Joule Learning Targets: using Cavalieri's principle for the Length of a curve - Solve problems in which a rate formulas for the volume of a Mean is integrated to find the net sphere and other solid figures. Moment change over time in a variety Net change of applications CCSS.MATH.CONTENT.HSG.G Newton - Use integration to calculate MD.A.3 Normal curve areas of regions in a plane Use volume formulas for Normal pdf - Use integration by slices or cylinders, pyramids, cones, and Probability density function shells to calculate volumes of spheres to solve problems. Smooth curve solids Smooth function - Use integration to calculate CCSS.MATH.CONTENT.HSG.G Solid of revolution surface areas of solids of a MD.B.4 Standard deviation revolution Identify the shapes of Surface area - Use integration to calculate two-dimensional cross-sections of Total distance traveled lengths of curves in a plane three-dimensional objects, and Universal gravitational constant - Adapt their knowledge of identify three-dimensional objects Volume by cylindrical shells integral calculus to model generated by rotations of Volume by slicing problems involving rates of two-dimensional objects. Volume of a solid change in a variety of Weight-density applications work

Big Ideas: - Finding the limits of Riemann sums - Calculate the regular pieces using known formulas - Evaluate definite integrals with antiderivatives - Fit the proper integrable function to the situation at hand - Use programs like NINT to help fit antiderivatives to certain situations - Break down the irregular whole into regular parts and set up a function to be integrated

Calculus Maria Collier [email protected] [email protected]

Materials Needed Everyday: Spiral Notebook Writing Utensil Computer

Topics to be covered: Unit 1: Prerequisites for Calculus Unit 2: Limits and Continuity Unit 3: Derivatives Unit 4: More Derivatives Unit 5: Applications of Derivatives Unit 6: The Definite Integral Unit 7: Differential Equations and Mathematical Modeling Unit 8: Applications of Definite Integrals Unit 9: Sequences, L’Hopital’s Rule, and Improper Integrals

Assignment Headings When you turn in work electronically, I need you to put a heading on your assignments so that it is easier to keep track of the assignments along with the members of your group.

Last name: Assignment Title Collier: Order of Operations HW

Group Work Last name: Group members: Assignment Title Collier: Cook, Garton, Irwin: Order of Operation Project

Make-up Work: Every student has the ability to check his or her assignments from home as long as wifi is available. Make-up work will be taken care of on an individual basis, but students that aren’t in school will be expected to contact their groups to make sure that they are contributing as much as possible to help the group run smoothly to finish the projects. Absent students need to check the Agenda to see if there are any daily assignments that need to be accomplished before they come back to school. Assignments will only be accepted up to 5 school days late unless a plan has been created with the teacher.

100 – 93 A 92 – 85 B 84 – 77 C 76 – 70 D 69 – below F

We are looking forward to an exciting year where everyone is learning and growing together.

Sincerely,

Mrs. Collier

Collaboration Team Checklist High School

The Team Collaboration Checklist is intended to serve as a useful reminder on the important aspects of team dynamics. It is not a rubric for grading purposes, but rather a reminder for student and adult teams about the key conditions for good collaboration. Teams might regularly refer to the collaboration checklist throughout a project, revisit it in moments when their progress is stuck, or us it to reflect on successes and challenges.

We intend these to be two separate docs that serve different purposes. While the Collaboration rubric would feature regularly in project design, facilitation, and assessment, the checklist is more of a supplemental tool to be used as needed to boost team performance. Given the differences between individual and group behaviors it is best to think of these two resources as complimenting each other rather than being aligned to one another.

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New Tech Network Team Collaboration Checklist

Behavior Description

Equal Participation Each member is equally engaged in the work of team, as represented by the role each member plays in accomplishing the task and how well each voice is heard during discussion. Established roles allow for equal participation.

Project The team has collaboratively developed a context-specific plan for task completion that is regularly updated to reflect needed adjustments Management throughout the timeline.

Making Decisions The team uses a transparent process, or set of processes, for making decisions that impact the entire group.

Physical The team members exhibit physical cues that suggest active listening, engagement, and an openness to new ideas. In addition, team Disposition meetings are physically organized in ways that best support collaborative and cooperative work.

Creating/Using The team has established and is using a set of norms that guide the behavior of the team. The team regularly revisits the norms to assess Norms their effectiveness and to determine whether they are an accurate reflection of the team’s behavior.

Intellectual The team regularly engages in constructive intellectual discourse aimed at deepening the team’s understanding of key ideas and individual Discourse perspectives related to the task at hand.

Passionate The team exhibits shared and passionate ownership over the successful completion of the task. All group members are made to feel Ownership valuable, that their contributions are meaningful, and their accomplishments are celebrated.

Conflict Resolution The team anticipates that conflict may happen, and has a plan for addressing it directly. Group members engage constructively and reference both the plan and their norms when conflict occurs.

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Collaboration Rubric High School

Overview

In designing our collaboration rubric, we drew a distinction between individual and group behaviors. While both are important for successful collaboration, distinguishing between the two provides useful guidance for how to support and assess student progress.

The Individual Collaboration Rubric focuses on specific aspects of individual collaboration. The indicators are designed to be simple and accessible to students using the Peer Evaluation Tool as well as instructive to guide group conversations. The number of dimensions (rows) for this rubric makes it unlikely a teacher would use it in its entirety. A teacher might opt to focus on particular rows by project or a school might focus on particular indicators in particular grade levels. Schools may also find opportunities to bring additional collaboration and project management skills to extend this outcome as their students grow as collaborators and we encourage you to do so.

Individual Collaboration – High School Collaboration involves behaviors under the control of individual group members including effort they put into group tasks, their manner of interacting with others on group, and the quantity and quality of contributions they make to group discussions.

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Emerging ED Developing DP Proficient PA Advanced

Contribution and Ideas lack supporting Shares ideas, and explains Provides ideas or arguments with Acknowledges the strengths and Development of reasoning the reasons behind them convincing reasons limitations of their ideas Ideas Limited acknowledgement Acknowledges others’ Builds on the thinking of others Builds on the thinking of others and of others’ thinking thinking checks back for agreement

Equal Shares ideas without Allows for equal Encourages equal participation In addition to proficient, actively Participation listening or listens without participation by both by asking clarifying or probing invites others to participate sharing ideas sharing ideas and listening questions, paraphrasing ideas, equitably, promoting divergent and to the ideas of others and synthesizing group thinking creative perspectives

Group Norms Follows group norms and Understands and follows Understands and follows group In addition to proficient, initiates the processes but only with group created norms and created norms and processes and use of norms and group processes modeling and/or reminders processes helps others do the same in each meeting

Respectful Tone At times, words and tone Words and tone indicate Words and tone indicate respect In addition to proficient, provides and Style indicate respectful intent, but respectful intent, but and sensitivity to others gentle feedback about others’ not consistently might not be sensitive to words and tone to foster an others environment of respect

Positive Body Sporadically faces speaker, Faces speaker and is free When others are speaking, both When others are speaking, body Language/ Active or engages without distraction of distractions when body language and verbal language and verbal responses Listening some of the time others are speaking responses indicate engagement indicate positive, energetic engagement

Roles Knows role, and fulfills it only Accepts role and shows Knows the roles of self and In addition to proficient, uses some of the time understanding by fulfilling others, and uses the roles to group roles as opportunities to use it maximize group effectiveness strengths or address areas of weakness

Work Ethic Completes only some Completes all assigned Completes all assigned tasks by Models consistently high standards assigned tasks tasks by deadline deadline; work is quality, and for timeliness, quality, and advances the project ownership of work Comes to meetings without Comes to meetings partially evidence of preparation prepared Comes to meetings fully Preparation for meetings surpasses prepared expectations

Team Support Either doesn’t help, or Predictably helps when Always helps when asked, and Actively checks in to understand occasionally helps, but must asked by others, but only sometimes offers help to others how others are progressing and how be asked then they can be of help

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Curriculum Framework for

School: First State Military Academy Course: G eometry

Course Description: Students discover, explore and make conjectures about geometric concepts and relationships including parallelism, congruence, similarity, area, volume, trigonometry and coordinate geometry. Emphasis is placed on discovery of patterns, real life problem solving using technology, mathematical connections to other disciplines, critical thinking, reasoning, and communicating mathematics. Algebra skills are reviewed and strengthened throughout the course through the application of geometric concepts. 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: Basics of Geometry Timeline: About 5 weeks

CCSS.Math.Content.HSG-MG.A. Concepts: Driving Questions: Summative: 1 - Use geometric shapes, their Points - Why do we measure? - FSMA Blueprint Project measures, and their properties to Lines - Why are geometric figures and - Quiz describe objects (e.g., modeling a Planes terms used to represent and tree trunk or a human torso as a Rays describe real-world situations? Formative: cylinder). Line Segments How are geometric figures and - Workshop Practice Midpoint Formula terms used on - Classwork/Homework CCSS.Math.Content.HSG-GPE. Distance Formula maps/blueprints? Assignments B.7 - Use coordinates to compute Perimeter - Warm-Ups perimeters of polygons and areas Circumference Learning Targets: of triangles and rectangles, e.g., Area - To identify special angle pairs using the distance formula. Measuring Angles and use their relationships to Complementary Angles find angle measures CCSS.Math.Content.HSG-GPE. Supplementary Angles - To find and compare lengths of B.4 - Use coordinates to prove Adjacent Angles segments simple geometric theorems Vertical Angles - To find the midpoint of a algebraically. Linear Pair segment - To find the distance between CCSS.Math.Content.HSG-CO Big Ideas: two points in the coordinate .A.1 - Know precise - Create an awareness of the plane definitions of angle, circle, structure of a math system, - To find the perimeter of connecting definitions, circumference of basic shapes perpendicular line, parallel postulates, reasoning, and - To find the area of basic line, and line segment, based theorems shapes on the undefined notions of - Use construction to explore - To find and compare the point, line, distance along a attributes of geometric figures measure of angles line, and distance around a and to make conjectures about - To identify special angle pairs circular arc. geometric relationships and use their relationships to - Use 1D and 2D coordinate find angle measures systems to represent points, lines, rays, line segments, and figures - Find areas of regular polygons, circles, and composite figures

Unit Two: Parallel and Perpendicular Lines Timeline: About 3 weeks

CCSS.Math.Content.HSG-MG.A. Concepts: Driving Questions: Summative: 3 - Apply geometric methods to Parallel Lines - Why do we have undefined - Photography Project solve design problems (e.g., Skew Lines terms such as point and line? - Quiz designing an object or structure to Parallel Planes - How can we use undefined satisfy physical constraints or Transversal terms? Formative: minimize cost; working with Interior Angles - Why do architects, carpenters, - Workshop Practice typographic grid systems based Exterior Angles and engineers use parallel and - Classwork/Homework on ratios). Corresponding Angles perpendicular lines to design Assignments Alternate Interior Angles buildings, furniture, and - Warm-Ups CCSS.Math.Content.HSG-GPE. Alternate Exterior Angles machines? B.5 - Prove the slope criteria for Same-Side Interior Angles parallel and perpendicular lines Congruency Learning Targets: and use them to solve geometric Perpendicular Lines - To identify relationships problems (e.g., find the equation Slope between figures in space of a line parallel or perpendicular - To identify angles formed by to a given line that passes Big Ideas: two lines and a transversal through a given point). - Make conjectures about lines - To use properties of parallel and determine the validity of lines to find angle measures CCSS.Math.Content.HSG-CO.D. those conjectures - To relate parallel and 12 - Make formal geometric - Make conjectures about perpendicular lines constructions with a variety of angles and determine the tools and methods (compass and validity of those conjectures straightedge, string, reflective - Use slopes to investigate devices, paper folding, dynamic geometric relationships, geometric software, etc.). including parallel and Copying a segment; copying an perpendicular lines angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

CCSS.Math.Content.HSG-CO.C. 9 - Prove theorems about lines and angles.

CCSS.Math.Content.HSG-CO.A. 1 - Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Unit Three: Polygons and Quadrilaterals Timeline: About 6 weeks

CCSS.Math.Content.HSG-MG.A. Concepts: Driving Questions: Summative: 3 - Apply geometric methods to Polygon - Why do we name figures? - Quadrilateral Detective solve design problems (e.g., Triangle - How much do we need to Problem Set designing an object or structure to Quadrilateral know before we can start - Quiz satisfy physical constraints or Pentagon making assumptions? minimize cost; working with Hexagon Formative: typographic grid systems based n-gon Learning Targets: - Workshop Practice on ratios). Parallelogram - To find and use the sum of the - Classwork/Homework Square measures of the interior angles Assignments CCSS.Math.Content.HSG-MG.A. Rectangle of a polygon - Warm-Ups 1 - Use geometric shapes, their Rhombus - To find and use the sum of the measures, and their properties to Trapezoid exterior angles of a polygon describe objects (e.g., modeling a Kite - To recognize and apply tree trunk or a human torso as a properties of the sides and cylinder). Big Ideas: angles of parallelograms - Use patterns to make - To recognize and apply CCSS.Math.Content.HSG-GPE. generalizations about properties of the diagonals of B.4 - Use coordinates to prove geometric properties, including parallelograms simple geometric theorems properties of polygons - To determine whether a algebraically. - Formulate and test conjectures quadrilateral is a parallelogram about the properties and - To define and classify special CCSS.Math.Content.HSG-CO.C. attributes of polygons types of parallelograms 11 - Prove theorems about - Use formulas involving length, - To use properties of diagonals parallelograms. slope and midpoint to of rhombuses and rectangles determine the type of - To verify and use properties of quadrilateral trapezoids and kites - Formulate and test conjectures about the properties and attributes of polygons Unit Four: Congruent Triangles Timeline: About 4 weeks

CCSS.Math.Content.HSG-SRT. Concepts: Driving Questions: Summative: B.5 - Use congruence and Acute Triangle - How can you compare two - Joanna’s Cafe Project similarity criteria for triangles to Equiangular Triangle objects? - Quiz solve problems and to prove Obtuse Triangle - How can you tell if two objects relationships in geometric figures. Right Triangle are congruent? Formative: Scalene Triangle - How can you tell if two - Workshop Practice CCSS.Math.Content.HSG-CO.D. Isosceles Triangle triangles are congruent? - Classwork/Homework 12 - Make formal geometric Equilateral Triangle - What is the importance of Assignments constructions with a variety of Congruent manufacturing an item the - Warm-Ups tools and methods (compass and Congruent Polygons same way every time it is straightedge, string, reflective Corresponding Parts made? devices, paper folding, dynamic Congruent Triangles geometric software, etc.). Congruency Statement Learning Targets: Copying a segment; copying an Side-Side-Side Congruence - To identify and classify angle; bisecting a segment; Side-Angle-Side Congruence triangles by and and side bisecting an angle; constructing Angle-Side-Angle Congruence measures perpendicular lines, including the Included Side - To apply the Triangle perpendicular bisector of a line Angle-Angle-Side Congruence Angle-Sum Theorem segment; and constructing a line Hypotenuse-Leg Congruence and the Exterior Angle parallel to a given line through a Hypotenuse Theorem point not on the line. - Name and use corresponding Big Ideas: parts of congruent polygons CCSS.Math.Content.HSG-GPE. - Use patterns to make - Prove triangles congruent B.4 - Use coordinates to prove generalizations about using the definition of simple geometric theorems geometric properties congruence algebraically. - Use logical reasoning to prove - Use the SSS and SAS statements are true Postulates to test for triangle CCSS.Math.Content.HSG-CO.C. congruence 10 - Prove theorems about - To prove two triangles triangles. congruent using the ASA Congruence Postulate and the CCSS.Math.Content.HSG-CO.B. AAS, and HL Congruence 8 - Explain how the criteria for Theorems triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

CCSS.Math.Content.HSG-CO.B. 7 - Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Unit Five: Relationships Within Triangles Timeline: About 3 weeks

CCSS.Math.Content.HSG-SRT. Concepts: Driving Questions: Summative: B.5 - Use congruence and Triangle Midsegment - What makes a triangle a - Card Design Project (want to similarity criteria for triangles to Perpendicular Bisector triangle? change this project next year) solve problems and to prove Angle Bisector - How are the sides and angles - Quiz relationships in geometric figures. Bisectors in Triangles of a triangle related? Medians Formative: CCSS.Math.Content.HSG-CO.D. Altitudes Learning Targets: - Workshop Practice 12 - Make formal geometric Inequalities in One Triangle - To use midsegments of - Classwork/Homework constructions with a variety of Inequalities in Two Triangles triangles in the coordinate Assignments tools and methods (compass and plane - Warm-Ups straightedge, string, reflective Big Ideas: - To use the Triangle devices, paper folding, dynamic - Use slope and equations of Midsegment Theorem to find geometric software, etc.). lines to investigate geometric Distances Copying a segment; copying an relationships, including special - To use properties of angle; bisecting a segment; segments of triangles perpendicular bisectors and bisecting an angle; constructing - Analyze geometric angle bisectors perpendicular lines, including the relationships in order to verify - To identify properties of perpendicular bisector of a line conjectures perpendicular bisectors and segment; and constructing a line angle bisectors parallel to a given line through a - To identify properties of point not on the line. medians and altitudes in CCSS.Math.Content.HSG-CO.C. triangles 9 - Prove theorems about lines - To recognize and apply and angles. properties of inequalities to the relationships between the CCSS.Math.Content.HSG-CO.C. angles and sides of a triangle 10 - Prove theorems about - To apply inequalities in two triangles. triangles

CCSS.Math.Content.HSG-C.A.3 - Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Unit Six: Right Triangles and Trigonometry Timeline: About 5 weeks

CCSS.Math.Content.HSG-SRT. Concepts: Driving Questions: Summative: D.10 - (+) Prove the Laws of The Pythagorean Theorem - Why do we use mathematics - Video Game Project Sines and Cosines and use them 45°-45°-90° Triangles to model real-world situations? - Quiz to solve problems. 30°-60°-90° Triangles - Where can mathematics be Trigonometry found in video game Formative: CCSS.Math.Content.HSG-SRT. Ratio programming? - Workshop Practice C.8 - Use trigonometric ratios and Sine - Classwork/Homework the Pythagorean Theorem to Cosine Learning Targets: Assignments solve right triangles in applied Tangent - To use the Pythagorean - Warm-Ups problems. Angles of Elevation Theorem and its converse Angles of Depression - To use the properties of CCSS.Math.Content.HSG-SRT. The Law of Sines 45°-45°-90° and 30°-60°-90° C.7 - Explain and use the The Law of Cosines triangles relationship between the sine and - To use sine, cosine, and cosine of complementary angles. Big Ideas: tangent ratios to determine - Justify conjectures about side lengths and angle CCSS.Math.Content.HSG-SRT. geometric figures measures in right triangles C.6 - Understand that by - Extend and use the - To solve problems involving similarity, side ratios in right Pythagorean Theorem angles of elevation and triangles are properties of the - Identify and apply patterns depression angles in the triangle, leading to from right triangles to solve - To use angles of elevation and definitions of trigonometric ratios meaningful problems, including depression to find the distance for acute angles. special right triangles between two objects (45°-45°-90° and 30°-60°-90°) - To use the Law of Sines to CCSS.Math.Content.HSG-MG.A. and triangles with sides that solve triangles 3 - Apply geometric methods to are Pythagorean triples - To use the Law of Cosines to solve design problems (e.g., - Develop, apply, and justify solve triangles designing an object or structure to triangle similarity relationships, satisfy physical constraints or such as trigonometric ratios minimize cost; working with using a variety of methods typographic grid systems based on ratios).

CCSS.Math.Content.HSG-CO.C. 10 - Prove theorems about triangles.

Unit Seven: Proportions and Similarity Timeline: About 5 weeks

CCSS.Math.Content.HSG-MG.A. Concepts: Driving Questions: Summative: 3 - Apply geometric methods to Ratio - How can two objects be - Mini Golf Madness Project solve design problems (e.g., Proportion similar? - Quiz designing an object or structure to Cross Product - How does similarity in satisfy physical constraints or Similar Polygons mathematics compare to Formative: minimize cost; working with Scale Factor similarity in everyday life? - Workshop Practice typographic grid systems based Similar Triangles - Classwork/Homework on ratios). Triangle Similarity Learning Targets: Assignments Angle-Angle Similarity - To write ratios - Warm-Ups CCSS.Math.Content.HSG-SRT. Side-Side-Side Similarity - To write and solve proportions A.2 - Given two figures, use the Side-Angle-Side Similarity - To use proportions to identify definition of similarity in terms of Right Triangle Similarity similar polygons similarity transformations to Proportions in Triangles - To solve problems using the decide if they are similar; explain properties of similar polygons using similarity transformations Big Ideas: - To identify similar triangles the meaning of similarity for - Use ratios to solve problems using the AA Similarity triangles as the equality of all involving similar figures Postulate and the SSS and corresponding pairs of angles and - Create and test conjectures SAS Similarity Theorems the proportionality of all about the properties and - To use similar triangles to corresponding pairs of sides. attributes of polygons and their solve problems corresponding parts based on - To find and use relationships CCSS.Math.Content.HSG-SRT. explorations and concrete in similar right triangles B.4 - Prove theorems about models - To recognize and use triangles. proportional relationships of corresponding angle bisectors, CCSS.Math.Content.HSG-SRT. altitudes, and medians of B.5 - Use congruence and similar triangles similarity criteria for triangles to - To use the Triangle Bisector solve problems and to prove Theorem relationships in geometric figures.

Unit Eight: Transformations Timeline: About 5 weeks

CCSS.Math.Content.HSG-CO.A. Concepts: Driving Questions: Summative: 4 - Develop definitions of Reflection - Where can transformations be - MC Escher Art Project rotations, reflections, and Translation found? - Quiz translations in terms of angles, Rotation - Why is symmetry desirable? circles, perpendicular lines, Center of Rotation Formative: parallel lines, and line segments. Angle of Rotation Learning Targets: - Workshop Practice Transformation - To draw reflections - Classwork/Homework CCSS.Math.Content.HSG-CO.A. Glide Reflection - To draw reflections in the Assignments 5 - Given a geometric figure and a Symmetry coordinate plane - Warm-Ups rotation, reflection, or translation, Line of Symmetry - To draw translations draw the transformed figure Axis of Symmetry - To draw translations in the using, e.g., graph paper, tracing Rotational Symmetry coordinate plane paper, or geometry software. Dilation - To draw rotations Specify a sequence of - To draw rotations in the transformations that will carry a Big Ideas: coordinate plane given figure onto another. - Use congruence - To draw glide reflections and transformations to make other compositions of CCSS.Math.Content.HSG-GMD. conjectures and justify isometries in the coordinate B.4 - Identify the shapes of properties of geometric figures plane two-dimensional cross-sections of - To draw compositions of three-dimensional objects, and reflections in parallel and identify three-dimensional objects intersecting lines generated by rotations of - To identify line and rotational two-dimensional objects. symmetries in 2D figures - To identify plane and axis CCSS.Math.Content.HSG-CO.A. symmetries in 3D figures 2 - Represent transformations in - To draw dilations the plane using, e.g., - To draw dilations in the transparencies and geometry coordinate plane software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

CCSS.Math.Content.HSG-CO.A. 3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

CCSS.Math.Content.HSG-SRT. A.1a - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

CCSS.Math.Content.HSG-SRT. A.1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Unit Nine: Surface Area and Volume Timeline: About 4 weeks

CCSS.Math.Content.HSG-GMD. Concepts: Driving Questions: Summative: B.4 - Identify the shapes of Cross Section - How are 2D and 3D figures - Marketing Mania (Product two-dimensional cross-sections of Lateral Faces related? Packaging) Project three-dimensional objects, and Lateral Edges - Quiz identify three-dimensional objects Altitude Learning Targets: generated by rotations of Height - To find the surface area of a Formative: two-dimensional objects. Base Edges prism and a cylinder - Workshop Practice Lateral Area - To find the surface area of a - Classwork/Homework CCSS.Math.Content.HSG-GMD. Composite Solid pyramid and a cone Assignments A.3 - Use volume formulas for Regular Pyramid - To find the volume of a prism - Warm-Ups cylinders, pyramids, cones, and Slant Height and a cylinder spheres to solve problems. Right Cone - To find the volume of a Oblique Cone pyramid and a cone CCSS.Math.Content.HSG-GMD. Prism - To find the surface area and A.1 - Give an informal argument Cylinder and the volume of a sphere for the formulas for the Basic Area Formulas circumference of a circle, area of Sphere a circle, volume of a cylinder, pyramid, and cone. Big Ideas: - Find surface areas and CCSS.Math.Content.HSG-MG.A. volumes of prisms, pyramids, 3 - Apply geometric methods to spheres, cones, cylinders, and solve design problems (e.g., composites of these figures designing an object or structure to - Describe the effect on area satisfy physical constraints or and volume when one or more minimize cost; working with dimensions of a figure are typographic grid systems based changed on ratios).

CCSS.Math.Content.HSG-MG.A. 1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

CCSS.Math.Content.HSG-MG.A. 2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Unit Ten: Probability Timeline: About 3 weeks

CCSS.Math.Content.HSS-CP.9 - Concepts: Driving Questions: Summative: (+) Use permutations and Event - How can probability be used to - Create a Game Project combinations to compute Experiment predict the likelihood of - Quiz probabilities of compound Sample Space different outcomes of the events and solve problems. Tree Diagram games that we play? Formative: Two-Stage Experiment - Workshop Practice CCSS.Math.Content.HSS-MD.7 - Multistage Experiment Learning Targets: - Classwork/Homework (+) Analyze decisions and Fundamental Counting Principle - To use lists, tables, and tree Assignments strategies using probability Intersection diagrams to represent sample - Warm-Ups concepts (e.g., product testing, Complement spaces Permutation - To use the Fundamental medical testing, pulling a hockey Factorial Counting Principle to count goalie at the end of a game). Circular Permutation outcomes

Combination - To describe events as subsets CCSS.Math.Content.HSG-MG.3 Geometric Probability of sample spaces by using - Apply geometric methods to Compound Event intersections and unions solve design problems (e.g., Independent Events - To find probabilities of designing an object or structure Dependent Events complements to satisfy physical constraints or Mutually Exclusive - To use permutations with minimize cost; working with Conditional Probability probability typographic grid systems based Two-Way Frequency Table - To use combinations with on ratios). Marginal Frequencies probability Joint Frequencies - To find probabilities by using CCSS.Math.Content.HSS-MD.6 - Relative Frequency lengths (+) Use probabilities to make - To find probabilities by using fair decisions (e.g., drawing by Big Ideas: area lots, using a random number - Understand sample spaces - To apply the multiplication rule generator). and design simulations to situations involving - Compute probabilities for independent events CCSS.Math.Content.HSS-CP.2 - independent, dependent, - To apply the multiplication rule Understand that two events A mutually exclusive, not to situations involving and B are independent if the mutually exclusive, and dependent events probability of A and B occurring conditional events - To apply the addition rule to together is the product of their - Calculate geometric situations involving mutually probabilities exclusive events probabilities, and use this - To apply the addition rule to characterization to determine if situations involving events that they are independent. are not mutually exclusive - To find the probability of CCSS.Math.Content.HSS-CP.3 - events given the occurrence of Understand the conditional other events probability of A given B as P(A - To explain conditional and B)/P(B), and interpret probability and independence independence of A and B as of everyday events saying that the conditional - To decide whether events are probability of A given B is the independent by using two-way same as the probability of A, frequency tables and the conditional probability - To approximate conditional of B given A is the same as the probabilities by using two-way probability of B. frequency tables - CCSS.Math.Content.HSS-CP.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

CCSS.Math.Content.HSS-CP.6 - Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

CCSS.Math.Content.HSS-CP.1 - 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 ("or," "and," "not").

CCSS.Math.Content.HSS-CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

NTN Agency Rubric, High School

Develop Growth Mindset: I can grow my intelligence and skills through effort, practice, and challenge. The brain grows bigger with use, like a muscle.

EMERGING E/D DEVELOPING D/P PROFICIENT P/A ADVANCED

Use Effort ● Does not connect effort or ● Superficially connects effort ● Understands how effort and ● Understands that effort and and Practice practice to getting better at a and practice to getting better practice relate to getting better at practice improve skills, work to Grow skill, improved work quality, or at a skill, improved work skills, improved work quality, or quality, and performance and performance quality, or performance performance that the process takes patience and time

Seek ● Rarely takes on academic ● With encouragement, ● Seeks academic challenges and ● Strategically and independently Challenge challenges and risks to pursue sometimes takes on takes risks to pursue learning seeks academic challenges and learning academic challenges and takes risks to pursue learning risks to pursue learning

● Struggles to identify the ● Superficially describes ● Analyzes personal barriers ● Analyzes and overcomes personal barriers (mindset, personal barriers (mindset, (mindset, beliefs, circumstances) personal barriers (mindset, beliefs, circumstances) that beliefs, circumstances) that that inhibit taking risks beliefs, circumstances) that inhibit taking risks inhibit taking risks could inhibit taking risks

Grow from ● Identifies challenges, failures, ● Identifies challenges, failures, ● Identifies challenges, failures, or ● Reflects on personal or Setbacks or setbacks, but does not or setbacks and describes setbacks and reflects on how academic growth from describe reactions to them reactions to them (e.g. giving reactions to them (e.g. giving up challenges, failures, or (e.g. giving up or trying up or trying harder) or trying harder) affect process, setbacks as well as why and harder) product, or learning how reactions (e.g. giving up or trying harder) affect the process, product, and learning

Build ● Struggles to identify academic ● Identifies an academic ● Builds confidence in success (on ● Consistently confident that Confidence strengths, previous strength, previous success, a new task, project, or class) by success is possible (on a new successes, or endurance or endurance gained through knowing and using academic task, project, or class) by gained from personal struggle personal struggle, but does strengths, previous success, or knowing and using academic to build confidence in not use these skills to build endurance gained through strengths, previous successes, academic success for a new confidence in success for a personal struggle or endurance gained through task, project, or class new task, project, or class personal struggle

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Find ● Rarely, and with significant ● With support, sometimes ● Often finds personal relevance in ● Independently seeks and finds Personal support, finds personal finds personal relevance in the work by connecting it to personal relevance in the work Relevance relevance in the work by the work by connecting it to interests or goals, reflecting on by connecting it to interests or connecting it to interests or interests or goals, reflecting progress towards mastery, or goals, reflecting on progress goals, reflecting on progress on progress towards identifying autonomous choices towards mastery, or identifying towards mastery, or identifying mastery, or identifying autonomous choices autonomous choices autonomous choices

Take Ownership Over One’s Learning: I can learn how to learn and monitor progress to be successful on tasks, school, and life.

EMERGING E/D DEVELOPING D/P PROFICIENT P/A ADVANCED

Meet ● Completes few benchmarks ● Completes some ● Usually completes polished ● Achieves personal best work on Benchmarks and class assignments and benchmarks and class benchmarks and class almost all benchmarks and may resist or struggle to use assignments; and, only when assignments by using resources class assignments by setting resources and supports forced to, or at the last and supports when necessary goals, monitoring progress, and (e.g. study groups, teacher minute, uses resources and (e.g. study groups, teacher using resources and supports support, workshops, supports (e.g. study groups, support, workshops, tutorials) (e.g. study groups, teacher tutorials) teacher support, workshops, support, workshops, tutorials) tutorials)

Seek ● Rejects feedback and/or ● Sometimes shows evidence ● Consistently shows evidence of ● Consistently shows evidence of Feedback does not revise work of accepting feedback to accepting and using feedback to actively seeking, identifying, revise work, but at times may revise work to high quality and using feedback to revise resist when it’s difficult work to high quality

Tackle and ● For a task or project, ● For a task or project, ● For a task or project identifies ● For a task or project, identifies Monitor superficially identifies what identifies what is known, what is known, what needs to be what is known, what needs to is known, what needs to be what needs to be learned, learned, and how hard it will be; be learned, and how hard it will Learning learned, and how hard it will and how hard it will be; but uses a strategy and steps to be; selects an appropriate be may not use a strategy to tackle the task; and monitors strategy and takes steps to tackle the task or does not how well the approach and effort tackle the task; and monitors monitor how well the strategy are working and adjusts based on how well is working the approach and effort are working

Actively ● Stays focused for part of the ● Mostly stays focused on the ● Actively participates in the ● Actively participates and takes Participate activity/discussion, team activity/discussion, team activity/discussion, team initiative on the meeting, or independent meeting, or independent time meeting, or independent time activity/discussion, team time but often cannot resist and knows when and why and has strategies for staying meeting, or independent time distraction or does not disengagement or distraction focused and resisting most and has personal strategies for notice when or why a loss of happens distraction staying focused focus happens

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Build ● Does not build relationships ● Does not initiate building ● Builds and uses relationships ● Actively builds trusting Relationships with trusted adults or peers relationships, but has a few with trusted adults and peers to relationships with adults and to get back on track as trusted adults or peers to get get back on track as needed and peers to pursue goals, enhance needed or to enhance back on track as needed or to enhance learning learning, and get back on track learning to enhance learning as needed

Impact Self & ● Identifies the ups and ● Has limited understanding of ● Analyzes individual role in the ● Monitors and adjusts individual Community downs of the classroom and individual role in the ups and ups and downs of the classroom role to positively influence the home community downs of the classroom and and home community ups and downs of the home community classroom and home community

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Oral Communication Rubric, High School

Overview

Interpersonal Communication Section - Focuses on the listening and speaking skills exhibited by individual students in a wide variety of informal conversations (e.g. student and teacher, student and student and expert). While there is some unavoidable overlap with the Collaboration Rubric, the Collaboration rubric emphasizes how teammates should talk to one another while collaborating.

Presentation Section - Focuses on the elements of a strong presentation. This section of the rubric could be used in its entirety to describe a complete presentation - though it’s often good to focus on a few dimensions (rows), or indicators (bullets). Useful for providing a group grade on a presentation.

Delivery Section - Focuses on the individual aspects of a presentation and can be used to provide individualized grades for a student in a presentation, even in the case of a group presentation.

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Interpersonal Communication The ability to communicate knowledge and thinking through effective informal, pair, and small group conversations.

EMERGING E/D DEVELOPING D/P PROFICIENT P/A ADVANCED College Ready College Level

Listening and After listening, shows recall of some After listening, shows recall After listening, can After listening, can synthesize main Comprehension key details but limited understanding of some key details and synthesize main points points, reference key details, and of main points main points and reference key details evaluate the strength or value of the ideas

Clear Presentation Communicates ideas in an unclear Communicates ideas clearly Communicates ideas Communicates ideas clearly, of Ideas way; ideas are difficult to follow most of the time, clearly adjusting as needed to enhance occasionally ideas are clarity for audience difficult to follow

Asking Questions Asks questions that repeat stated Ask questions that help Asks thoughtful questions Asks thoughtful questions that details or main points clarify a topic or a line of that develop or challenge develop or challenge a line of reasoning a topic or line of reasoning reasoning and explore connections to a larger theme or idea

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PRESENTATION The ability to communicate knowledge and thinking orally.

EMERGING E/D DEVELOPING D/P PROFICIENT P/A ADVANCED College Ready College Level

Clarity Central message is unclear or unstated Central message can be Presents a clear central Presents a central message deduced but may not be explicit message that is clear and original Does not include alternate perspectives when appropriate Includes alternate perspectives Addresses alternative or Addresses alternative or when appropriate opposing perspectives when opposing perspectives in a appropriate way that sharpens one's own perspective

Evidence Draws on facts, experience, or research in Draws on facts, experience, Draws on facts, experiences Facts, experience and a minimal way and/or research inconsistently and research to support a research are synthesized to central message support a central message Demonstrates limited understanding of the Demonstrates an incomplete or topic uneven understanding of the topic Demonstrates an emonstrate an in-depth understanding of the topic understanding of the topic

Organization ·A lack of organization and/or transitions Inconsistencies in organization Organization and transitions Organization and transitions makes it difficult to follow the presenter’s and limited use of transitions reveal the line of reasoning supports the line of reasoning ideas and line of reasoning detract from audience understanding of line of reasoning

Use of Digital Digital media or visual displays are Digital media or visual displays Digital media or visual displays Digital media or visual displays Media / Visual confusing, extraneous, or distracting are informative and relevant are informative and support are polished, informative, and displays audience engagement and support audience engagement understanding and understanding

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DELIVERY The ability to communicate knowledge and thinking orally.

EMERGING E/D DEVELOPING D/P PROFICIENT P/A ADVANCED College Ready College Level

Language Uses language and style that is unsuited to Uses language and style that is at Uses appropriate language Uses sophisticated and varied Use the purpose, audience, and task times unsuited to the purpose, and style that is suited to the language that is suited to the audience, and task purpose, audience, and task purpose, audience, and task Stumbles over words, interfering with audience understanding Speaking is fluid with minor Speaking is fluid and easy to Speaking is consistently fluid lapses of awkward or incorrect follow and easy to follow language use that detracts from audience understanding

Presentation Makes minimal use of presentation skills: Demonstrates a command of Demonstrates a command Demonstrates consistent Skills lacks control of body posture; does not some aspects of presentation of presentation skills, command of presentation skills, make eye contact; voice is unclear and/or skills, including control of body including control of body including control of body posture inaudible; and pace of presentation is too posture and gestures, language posture and gestures, eye and gestures, eye contact, clear slow or too rushed fluency, eye contact, clear and contact, clear and audible and audible voice, and audible voice, and appropriate voice, and appropriate appropriate pacing in a way that Presenter's energy and affect are pacing pacing keeps the audience engaged unsuitable for the audience and purpose of the presentation Presenter's energy, and/or affect Presenter's energy and affect Presenter maintains a presence are usually appropriate for the are appropriate for the and a captivating energy that is audience and purpose of the audience and support appropriate to the audience and presentation, with minor lapses engagement purpose of the presentation

Interaction Provides a vague response to questions Provides an indirect or partial Provides a direct and Provides a precise and with response to questions; complete response to persuasive response to Audience Demonstrates a minimal command of the questions questions facts or understanding of the topic Demonstrates a partial command of the facts or understanding of Demonstrates an adequate Demonstrates an in-depth the topic command of the facts and understanding of the facts and understanding of the topic topic

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Curriculum Framework for

School: First State Military Academy Course: P recalculus

Course Description: This course provides algebraic and graphical explorations of polynomial, rational, exponential, logarithmic, and inverse functions with real life applications. In addition, trigonometric functions are studied as circular functions with applications to triangle problems. Topics include trigonometric identities, inverse trigonometric functions and oblique triangle trigonometry. Limits and sequences and series will be introduced if time permits. Extensive use of the graphing calculator will assist the student in a balanced approach to solving problems.

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: Functions from a Calculus Perspective Timeline: About 4 weeks

CCSS.Math.Content.F.BF.1 - Concepts: Driving Questions: Summative: Build a function that models a Set-builder notation - How are functions used - Project relationship between two Interval notation throughout the business - Quiz quantities Implied domain world? c. (+) compose functions Placewise-defined function - How are functions used to Formative: Relevant domain analyze costs, predict sales, - Workshop Practice CCSS.Math.Content.F.BF.4.b - Zeros calculate profit, forecast future - Classwork/Homework (+) Verify by composition that one Roots costs and revenue, estimate Assignments function is the inverse of another. Line symmetry depreciation, and determine - Warm-Ups Point symmetry the proper labor force? CCSS.Math.Content.F.BF.4.c - Event function (+) Read values of an inverse Odd function Learning Targets: function from a graph or a table, Continuous - To describe subsets of real given that the function has an Limit numbers inverse. Discontinuous - To identify and evaluate Infinite functions and state their CCSS.Math.Content.F.BF.4.d - Jump domains (+) Produce an invertible from a Point - To use graphs of functions to non-invertible function by Removable estimate function values restricting the domain Nonremovale - To identify even and odd Discontinuities functions End behavior - To use limits to determine the Increasing continuity of a function Decreasing - To use limits to describe the Constant end behavior of functions Maximum - To find intervals on which Minimum functions are increasing, Extrema constant, or decreasing Average rate of change - To identify, graph, and Secant line describe parent functions Transformation - To identify and graph Translation transformations of functions Reflection - To perform operations with Dilation functions Parent square root - To find compositions of Quadratic cubic functions Reciprocal absolue value step - To use the horizontal line test Greatest integer functions to determine whether a Composition function has an inverse Inverse relation function Inverse function - To find inverse functions One-to-one algebraically and graphically

Big Ideas: - Identify functions and determine their domains, ranges, y-intercepts, and zeros - Evaluate the continuity, end behavior, limits, and extrema of a function - Calculate rate of change of nonlinear functions - Identify parent functions and transformations - Perform operations with functions, identify composite functions, and calculate inverse functions

Unit Two: Power, Polynomial, and Rational Functions Timeline: About 3 weeks

CCSS.Math.Content.F.IF.7 - Concepts: Driving Questions: Summative: Graph functions expressed Power function - How are polynomial functions - Project symbolically and show key Monomial function used when designing and - Quiz features of the graph, by hand in Radical function building new structures? simple cases and using Extraneous solutions - How do architects use Formative: technology for more complicated Polynomial function functions to determine the - Workshop Practice cases. ★ Leading coefficient weight and strength of the - Classwork/Homework d. Graph rational functions, Leading-term test materials, analyze the costs, Assignments identifying zeros and asymptotes Turning point estimate deterioration of - Warm-Ups when suitable factorizations are Quadratic form materials, and determine the available, and showing end Repeated zero proper labor force? behavior. Multiplicity Synthetic division Learning Targets: Depressed polynomial - To graph and analyze power Synthetic substitution functions Rational Zero Theorem - To graph and analyze radical Descartes’ Rule of Signs functions and solve radical Fundamental Theorem of Algebra equations Linear Factorization Theorem - To graph polynomial functions Complex conjugates - To model real-world data with Rational function polynomial functions Asymptote - To divide polynomials using Vertical asymptote long division and synthetic Horizontal asymptote division Oblique asymptote - To use the Remainder and Holes Factor Theorems Polynomial inequality - To find real zeros of Sign chart polynomial functions Rational inequality - To find complex zeros and polynomial functions Big Ideas: - To analyze and graph rational - Graph and analyze power, functions radical, polynomial, and - To solve rational equations rational functions - To solve polynomial - Divide polynomials using long inequalities division and synthetic division - To solve rational inequalities - Use the Remainder and Factor Theorems - Find all zeros of polynomial functions - Solve radical and rational equations - Solve polynomial and rational inequalities

Unit Three: Exponential and Logarithmic Functions Timeline: About 4 weeks

CCSS.Math.Content.F.BF.5 - (+) Concepts: Driving Questions: Summative: Understand the inverse Algebraic function - How are exponential functions - Project relationship between exponents Transcendental function used to model the growth and - Quiz and logarithms and use this Exponential function decline of populations of relationship to solve problems Natural base endangered species? Formative: involving logarithms and Continuous compound interest - Workshop Practice exponents Logarithmic function with base b Learning Targets: - Classwork/Homework Logarithm - To evaluate, analyze, and Assignments Common logarithm graph exponential functions - Warm-Ups Natural logarithm - To solve problems involving Logistic growth function exponential growth and decay Linearize - To evaluate expressions involving logarithms Big Ideas: - To sketch and analyze graphs - Identify the mathematical of logarithmic functions domains, ranges, and end - To apply properties of behaviors of exponential and logarithms logarithmic functions - To apply the Change of Base - Use the properties of Formula exponents and logarithms to - To apply the One-to-One solve exponential and Property of Exponential logarithmic equations Functions to solve equations - Collect and organize data, - Apply the One-to-One Property make and interpret scatter of Logarithmic Functions to plots, fit the graph of a function solve equations to the data, and interpret the - To model data using results exponential, logarithmic, and - Use function models to predict logistic functions and make decisions and - To Linearize and analyze date critical judgements - Use nonlinear regression

Unit Four: Trigonometric Functions Timeline: About 3 weeks

CCSS.Math.Content.F.TF.3 - (+) Concepts: Driving Questions: Summative: Use special triangles to determine Trigonometric functions - How is trigonometry used in - Project geometrically the values of sine, Reciprocal function satellite navigation? - Quiz cosine, tangent for /3, /4, and Inverse trigonometric function - How are the techniques used /6, and use the unit circle to Angles of elevation and in satellite navigation also Formative: express the values of sine, depression used when navigating cars, - Workshop Practice cosine, and tangent for - x, + Vertex planes, ships, and spacecraft? - Unit circle coffee filter activity x, and 2 - x in terms of their Initial side - Classwork/Homework values for x, where x is any real Terminal side Learning Targets: Assignments number Standard position - To find values of trigonometric - Warm-Ups Radian functions for acute angles of CCSS.Math.Content.F.TF.4 - (+) Coterminal angles right triangles Use the unit circle to explain Linear speed - To solve right triangles symmetry (odd and even) and Angular speed - To convert degree measures periodicity of trigonometric Sector of angles to radian measures functions. Quadrantal angle and vice versa Reference angle - Use angle measures to solve CCSS.Math.Content.F.TF.6 - (+) Unit circle real-world problems Understand that restricting a Circular function - To find values of trigonometric trigonometric function to a domain Periodic function functions for any angle on which it is always increasing or Period - To find values of trigonometric always decreasing allows its Sinusoid functions using the unit circle inverse to be constructed Amplitude - To graph transformations of Frequency the sine and cosine functions CCSS.Math.Content.F.TF.7 - (+) Phase shift - To use sinusoidal functions to Use inverse functions to solve Vertical shift solve problems trigonometric equations that arise Midline - To graph tangent and -1 in modeling contexts; evaluate the Sin function reciprocal trigonometric -1 solutions using technology, and Cos function functions -1 interpret them in terms of the Tan function - To graph damped context. ★ Oblique triangles trigonometric functions Law of Sines - To evaluate and graph inverse Ambiguous case trigonometric functions CCSS.Math.Content.F.BF.1 - Law of Cosines - To find compositions of Build a function that models a Heron’s Formula trigonometric functions relationship between two - To solve oblique triangles by quantities Big Ideas: using the Law of Sines or Law c. (+) compose functions - Solve right triangles using of Cosines trigonometric and inverse - To find areas of oblique CCSS.Math.Content.F.BF.4.b - trigonmoetric functions triangles (+) Verify by composition that one - Convert between degrees and function is the inverse of another. radians - Solve real-world problems CCSS.Math.Content.F.BF.4.c - using trigonometric functions (+) Read values of an inverse - Graph trigonometric functions function from a graph or a table, and their inverses given that the function has an - Solve oblique triangles and inverse. find their area using various laws and formulas CCSS.Math.Content.F.BF.4.d - (+) Produce an invertible from a non-invertible function by restricting the domain

Unit Five: Trigonometric Identities and Equations Timeline: About 4 weeks

CCSS.Math.Content.F.TF.9 - (+) Concepts: Driving Questions: Summative: Prove the addition and Identity - What makes a triangle a - Project subtraction formulas for sine, Trigonometric identity triangle? - Quiz cosine, and tangent and use them Cofunction - How are the sides and angles to solve problems. Odd-even identities of a triangle related? Formative: Verify an identity - Workshop Practice Reduction identity Learning Targets: - Classwork/Homework - To identify and use basic Assignments Big Ideas: trigonometric identities to find - Warm-Ups - Identify and use trigonometric trigonometric values identities to find trigonometric - To use basic trigonometric values identities to simplify and - Use trigonometric identities to rewrite trigonometric simplify and rewrite expressions trigonometric expressions - To verify trigonometric - Verify trigonometric identities identities - Solve trigonometric equations - To determine whether - Use sum and difference equations are identities identities to evaluate - To solve trigonometric trigonometric functions equations using algebraic - Use double-angle, techniques power-reducing, half-angle, - To solve trigonometric and product-to-sum identities equations using basic to evaluate trigonometric identities expressions and solve - To use sum and distance trigonometric equations identities to evaluate trigonometric functions - To use sum and difference identities to solve trigonometric equations - To use double-angle, power-reducing, half-angle and product-to-sum identities to evaluate trigonometric expressions and solve trigonometric equations

Unit Six: Systems of Equations and Matrices Timeline: About 3 weeks

CCSS.Math.Content.N.VM.6 - Concepts: Driving Questions: Summative: (+) Use matrices to represent and Multivariable linear system, - Why has linear programming - Project manipulate data, e.g., to Row-echelon form become a standard tool for - Quiz represent payoffs or incidence Gaussian elimination many businesses, like relationships in a network Augmented matrix farming? Formative: Coefficient matrix - What are constraints farmers - Workshop Practice CCSS.Math.Content.N.VM.7 - Reduced row-echelon form must take into account to - Classwork/Homework (+) Multiply matrices by scalars to Gauss-Jordan elimination maximize profits? Assignments produce new matrices, e.g., as Identity matrix - Warm-Ups when all of the payoffs in a game Inverse matrix Learning Targets: are doubled Inverse - To solve systems of linear Invertible equations using matrices and CCSS.Math.Content.N.VM.8 - Singular matrix Gaussian elimination (+) Add, subtract, and multiply Determinant - To solve systems of linear matrices of appropriate Square system equations using matrices and dimensions Cramer’s Rule Gauss-Jordan elimination Partial fraction - To multiply matrices CCSS.Math.Content.N.VM.9 - Partial fraction decomposition - To find determinants and (+) Understand that, unlike Optimization inverses of 2x2 and 3x3 multiplication of numbers, matrix Linear programming matrices multiplication for square matrices Objective function - To solve systems of linear is not a commutative operation, Constraints equations using inverse but still satisfies the associative Feasible solutions matrices and distributive properties Multiple optimal solutions - To solve systems of linear Unbounded equations using Cramer’s Rule CCSS.Math.Content.N.VM.10 - - To write partial fraction (+) Understand that the zero and Big Ideas: decompositions of rational identity matrices play a role in - Solve systems of linear expressions with linear factors matrix addition and multiplication equations using matrices and in the denominator similar to the role of 0 and 1 in the Gaussian or Gauss-Jordan - Write partial fraction real numbers. The determinant of elimination decompositions of rational a square matrix is nonzero if and - Multiply matrices expressions with prime only if the matrix has a - Find determinants and quadratic factors in the multiplicative inverse inverses of 2x2 and 3x3 denominator matrices - To use linear programming to CCSS.Math.Content.A.REI.8 - - Solve systems of linear solve applications (+) Represent a system of linear equations using inverse - To recognize situations in equations as a single matrix matrices and Cramer’s Rule which there are multiple points equation in a vector variable - Write partial fraction at which a function is decompositions of rational optimized CCSS.Math.Content.A.REI.9 - expressions with linear and (+) Find the inverse of a matrix if it irreducible quadratic factors exists and use it to solve systems - Use linear programming to of linear equations (using solve applications technology for matrices for - Recognize situations in which dimension 3x3 or greater). there are no solutions or more than one solutions of a linear programming application

Unit Seven: Conic Sections and Parametric Equations Timeline: About 5 weeks

CCSS.Math.Content.G.GPE.3 - Concepts: Driving Questions: Summative: (+) Derive the equations of the Conic section - When a ball is hit or thrown, - Project ellipses and hyperbolas given the Degenerate conic like a baseball, why can the - Quiz foci, using the fact that the sum or Locus bath of the ball be represented difference of distances from the Parabola and traced by parametric Formative: foci is constant. Focus equations? - Workshop Practice Directrix - Classwork/Homework CCSS.Math.Content.G.GMD.2 - Axis of symmetry Learning Targets: Assignments (+) Give an informal argument Vertex - To analyze and graph - Warm-Ups using Cavalieri’s principle for the Latus rectum equations of parabolas formulas for the volume of a Ellipse - To write equations of sphere and other solid figures Foci parabolas Major axis - To analyze and graph Center equations of ellipses and Minor axis circles Vertices - To use equations to identify Co-vertices ellipses and circles Eccentricity - Analyze and graph equations Hyperbola of hyperbolas Transverse axis - To use equations to identify Conjugate axis types of conic sections Parametric equation - To find rotation of axes to write Parameter equations of rotated conic Orientation sections Parametric curve - To graph rotated conic sections - To graph parametric equations Big Ideas: - To solve problems related to - Analyze, write, and graph the motion of projectiles equations of parabolas, ellipses, circles, and hyperbolas - Use equations to identify types of conic sections - Use rotation of axes to write equations of rotated conic sections - Graph rotated conic sections - Graph parametric equations - Solve problems related to the motion of projectiles

Unit Eight: Vectors Timeline: About 3 weeks

CCSS.Math.Content.N.VM.1 - Concepts: Driving Questions: Summative: (+) Recognize vector quantities as Vector - How are vectors used to model - Project having both magnitude and Initial point changes in direction due to - Quiz direction. Represent vector Terminal point water and air currents? quantities by directed line Standard position Formative: segments, and use appropriate Direction Learning Targets: - Workshop Practice symbols for vectors and their Magnitude - To represent and operate with - Classwork/Homework magnitudes (e.g., v, |v|, ||v||, v). Quadrant bearing vectors geometrically Assignments True bearing - To solve vector problems and - Warm-Ups CCSS.Math.Content.N.VM.2 - Parallel vectors resolve vectors into their (+) Find the components of a Opposite vectors rectangular components vector by subtracting the Resultant - To represent and operate with coordinated of an initial point from Zero vector vectors in the coordinate plane the coordinates of a terminal point Components - To write vector as a linear Component form combination of unit vectors CCSS.Math.Content.N.VM.3 - Unit vector - To find the dot product of two (+) Solve problems involving Linear combination vectors and use the dot velocity and other quantities that Dot product product to find the angle can be represented by vectors Orthogonal between them Vector projection - To find the projection of one CCSS.Math.Content.N.VM.4.a - Work vector onto another Add vectors end-to-end, 3D coordinate system - To plot points and vectors in component-wise, and by the Z-axis the 3D coordinate system parallelogram rule. Understand Octant - To express algebraically and that the magnitude of a sum of Ordered triple operate with vectors in space two vectors is typically not the Cross product - To find dot products of and sum of the magnitude Torque angles between vectors in Triple scalar product space CCSS.Math.Content.N.VM.4.b - - To find cross products of Given two vectors in magnitude Big Ideas: vectors in space and use cross and direction form, determine the - Represent and operate with products to find area and magnitude and direction of their vectors both geometrically and volume sum algebraically - Resolve vectors into their CCSS.Math.Content.N.VM.4.c - rectangular components Understand vector subtraction v - - Write a vector as the linear w as v + (-w), where -w is the combination of unit vectors additive inverse of w, with the - Find the dot product of two same magnitude as w and vectors and use the dot pointing in the opposite direction. product to find the angle REpresent vector subtraction between them graphically by connecting the tips - Find the projection of one in the appropriate order, and vector onto another perform vector subtraction - Graph and operate with component-wise. vectors in space - Find the dot and cross product CCSS.Math.Content.N.VM.5.a - of and angles between vectors Represent scalar multiplication in space graphically by scaling vectors and - Find areas of parallelograms possibly reversing their direction; and volumes of parallelepipeds perform scalar multiplication in space component-wise, e.g. as c(vx, vy) = (cvx, cvy)

CCSS.Math.Content.N.VM.5.b - Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0)

Unit Nine: Polar Coordinates and Complex Numbers Timeline: About 3 weeks

CCSS.Math.Content.N.CN.3 - (+) Concepts: Driving Questions: Summative: Find the conjugate of a complex Polar coordinate system - How can polar equations be - Project number; use conjugates to find Polar axis used to model sound patterns - Quiz moduli and quotients of complex Polar coordinate to help determine state numbers Polar equation arrangement, speaker and Formative: Polar graph microphone placement, and - Workshop Practice CCSS.Math.Content.N.CN.4 - Limaçon volume and recording levels? - Classwork/Homework Represent complex numbers and Cardioid - How can they also be used Assignments their operations on the complex Rose with lightning and camera - Warm-Ups plane. (+) Represent complex Lemniscate angles when concerts are numbers on the complex plane in Spiral of Archimedes filmed? rectangular and polar form Complex plane (including real and imaginary Real axis Learning Targets: numbers), and explain why the Imaginary axis - To graph points with polar rectangular and polar forms of a Argand plane coordinates given complex number represent Absolute value of a complex - To graph simple polar the same number number equations Polar form - To graph polar equations CCSS.Math.Content.N.CN.5 - (+) Trigonometric form - To identify and graph classical Represent addition, subtraction, Modulus curves multiplication, and conjugation of Argument - To convert between polar and complex numbers geometrically pth roots of unity rectangular coordinates on the complex plane; use - To convert between polar and properties of this representation Big Ideas: rectangular equations for computation - Graph points with polar - To identify polar equations of coordinates conics CCSS.Math.Content.N.CN.6 - (+) - Graph polar equations - To write and graph the polar Calculate the distance between - Identify and graph classic polar equation of a conic given its numbers in the complex plane as curves eccentricity and the equation the modulus of the difference, and - Convert between polar and of its directrix the midpoint of a segment as the rectangular coordinates - To convert complex numbers average of the numbers and its - Convert between polar and from rectangular to polar form points rectangular equations and vice versa - Identify polar equations of - To find products quotients, conics powers, and roots of complex - Write and graph the polar numbers in polar form equation of a conic given its eccentricity and the equation of its directrix - Convert complex numbers from rectangular to polar form and vice versa - Find products, quotients, and roots of complex numbers in polar form

Unit Ten: Sequences and Series Timeline: About 4 weeks

Concepts: Driving Questions: Summative: Sequence - How are sequences and series - Project Term used to predict patterns? - Quiz Finite sequence Infinite sequence Learning Targets: Formative: Recursive sequence - To investigate several different - Workshop Practice Explicit sequence types of sequences - Classwork/Homework Fibonacci sequence - To use sigma notation to Assignments Converge represent and calculate sums - Warm-Ups Diverge of series Series - To find nth terms and Finite series arithmetic means of arithmetic nth partial sum sequences Infinite series - To find sums of n terms of Sigma notation arithmetic series Arithmetic sequence - To find nth terms of geometric Common difference means of geometric Arithmetic means sequences First difference - To find sums of n terms of Second difference geometric series and the sums Arithmetic series of infinite geometric series Geometric sequence - To use mathematical induction Common ratio to prove summation formulas Geometric means and properties of divisibility Geometric series involving a positive integer n Principle of mathematical - To extend mathematical induction induction Anchor step - To use Pascal’s Triangle to Inductive hypothesis write binomial expansions Inductive step - To use the Binomial Theorem Extended principle of to write and find the mathematical induction coefficients of specified terms Binomial coefficients in binomial expansions Pascal’s triangle - To use a power series to Binomial Theorem represent a rational function Power series - To use power series Exponential series representation to approximate Euler’s Formula value of transcendental functions Big Ideas: - Use sigma notation to represent and calculate sums of series - Find nth terms of arithmetic sequences and arithmetic series - Find nth terms of geometric sequences and geometric series. Find sums of infinite geometric series. - Use mathematical induction to prove summation formulas and properties of divisibility involving a positive integer n - Use Pascal’s Triangle or the Binomial Theorem to write binomial expansions - Use a power series to represent a rational function - Use power series representations to approximate values of transcendental functions

COURSE OVERVIEW: The Introduction to Applied Math course will prepare students to enter the work force or to attend college with an understanding of the mathematics in the real world. The course will help students develop quantitative literacy as a habit of mind and an approach to problems that employs and enhances both statistics and mathematics. The main goal of the course is for students to see that mathematics is a powerful tool for living,as they develop confidence with mathematics, habits of inquiry and logical thinking, and the ability to use mathematics to make decisions in everyday life. Topics address the math used to run our country’s households, businesses, and governments, such as the mathematics of consumption, inflation, depreciation, borrowing, saving, and taxation, as well as the mathematics of logic, likelihood, statistics, and sports.

EXPECTED OUTCOMES Students are expected to perform at a proficient level on a variety of tasks and assessments addressing the Common Core Standards for Mathematical Practice and selected high school Common Core State Standards for Math. Levels of proficiency are defined near the end of this course outline under Performance Criteria.

Common Core State Standards for Mathematical Practice (SMP)

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.

INSTRUCTIONAL METHOD AND/OR STRATEGIES: A variety of instructional strategies will be utilized to accommodate all learning styles. Universal Design for Learning strategies and guidelines will be utilized to provide choices to address the learning needs of students with disabilities, English Language Learners and students of low or high abilities in each lesson and unit.

PERFORMANCE CRITERIA: Students will be assessed on knowledge and content as well as agency, oral communication, and written communication. The New Tech Network High School rubrics will be utilized. The students will self-assess using the rubrics as well as the teacher.

Common Core Mathematical Standards

Reasoning with Equations & Inequalities Reason quantitatively and use units to solve problems. CCSS.MATH.CONTENT.HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.

CCSS.MATH.CONTENT.HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Linear, Quadratic, & Exponential Model

Construct and compare linear, quadratic, and exponential models and solve problems.

CCSS.MATH.CONTENT.HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. CCSS.MATH.CONTENT.HSF.LE.A.1.B Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. CCSS.MATH.CONTENT.HSF.LE.A.1.BC Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. CCSS.MATH.CONTENT.HSF.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Statistics and Probability Interpreting Categorical and Quantitative Data CCSS.MATH.CONTENT.HSS.ID.A Summarize, represent, and interpret data on a single count or measurement variable. CCSS.MATH.CONTENT.HSS-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.MATH.CONTENT.HSS-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme date points (outliers).

Make inferences and justify conclusions from sample surveys, experiments, and observational studies CCSS.MATH.CONTENT.HSS.IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. CCSS.MATH.CONTENT.HSS.IC.B.6 Evaluate reports based on data.

Conditional Probability and the Rules of Probability CCSS.MATH.CONTENT.HSS-CP.A Understand independence and conditional probability and use them to interpret data.

CCSS.MATH.CONTENT.HSS-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

Using Probability to Make Decisions CCSS.MATH.CONTENT.HSS-MD.A Calculate expected values and use them to solve problems. CCSS.MATH.CONTENT.HSS-MD.B Use probability to evaluate outcomes of decisions. CCSS.MATH.CONTENT.HSS-MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game.)

COURSE CONTENT AND SUGGESTED TIME ALLOTMENT: Content sequencing, activities, and time allocations are only suggestions and may be adjusted to suit school site curriculum plans, available materials, and student needs.

Unit 1: The Mathematics of Calculation

Duration: 16 days

Description: Students use computational skills to make sense of and solve problems in real-world contexts. First, students use the order of operations to evaluate expressions including formulas. Next, they use technology to solve problems, analyzing the results in terms of the context to determine if solutions are reasonable. Then, students solve a variety of real-world problems involving percent. Finally, they use units as a way to understand problems and to guide the solution of multi-step problems.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSN.Q.A.1 CCSS.MATH.CONTENT.HSN.Q.A.2 CCSS.MATH.CONTENT.HSN.Q.A.3

Unit 2: The Mathematics of Consumption

Duration: 15 days

Description: In this unit, students study the mathematics involved in making purchases and budgeting. Students will analyze and compare unit prices in making purchases. They will find markup and discounts, including finding final prices after multiple discounts. Students will find sales tax, excise tax, and value-added tax on items. Finally, students will learn how to create, balance and analyze a monthly budget, write checks and balance a checkbook.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8

Unit 3: The Mathematics of Logic and the Media

Duration: 17 days

Description: In this unit, students study the mathematics involved in logic and the media. Students use set and set diagrams to describe unions, intersections and complements of sets. Students will study statements and negations, deductive an inductive reasoning, and recognize fallacies in logic.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSS.IC.B.3 CCSS.MATH.CONTENT.HSS.IC.B.6

Unit 4: The Mathematics of Inflation and Depreciation

Duration: 16 days

Description: In this unit, students study the mathematics involved in inflation and depreciation. Students will study exponential growth and decay, inflation and the consumer price index, and depreciation.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSF.LE.A.1 CCSS.MATH.CONTENT.HSF.LE.A.1.B CCSS.MATH.CONTENT.HSF.LE.A.1.C CCSS.MATH.CONTENT.HSF.LE.A.3

Unit 5: The Mathematics of Taxation

Duration: 15 days

Description: In this unit, students study the mathematics involved in taxation. Students will study flat tax and political philosophy, graduated income tax, property tax, social security and payroll taxes.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8

Unit 6: The Mathematics of Borrowing and Saving

Duration: 16 days

Description: In this unit, students study the mathematics involved in borrowing and saving. Students will be introduced to lending, including promissory notes and loans. They will create an amortization table and analyze the cost of buying on credit. Students will compare rates and terms for home mortgages, and compare the costs of buying and renting. Finally, students will analyze savings and retirement plans.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8

Unit 7: The Mathematics of Patterns and Nature

Duration: 15 days

Description: In this unit, students study the mathematics involved in patterns and nature. Students will recognize and describe linear, exponential, quadratic, and other patterns in nature, art, and science.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSF.LE.A.1 CCSS.MATH.CONTENT.HSF.LE.A.1.B CCSS.MATH.CONTENT.HSF.LE.A.1.C CCSS.MATH.CONTENT.HSF.LE.A.3

Unit 8: The Mathematics of Likelihood

Duration: 15 days

Description: In this unit, students study the mathematics of likelihood. Students will use probability to describe the likelihood of an event, analyze likelihood of a risk, and describe actuarial data. They will find theoretical and experimental probability, and find expected values for events.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSS-CP.A CCSS.MATH.CONTENT.HSS-MD.A CCSS.MATH.CONTENT.HSS-MD.B

Unit 9: The Mathematics of Description

Duration: 15 days

Description: In this unit, students study the mathematics of description. Students will read, interpret and create stacked area graphs and radar graphs. Students will use mean, median and mode to describe average value of a data set, and understand the effect of outliers on averages. They will read and understand box-and-whisker plots and histograms. Students will use standard deviation to describe dispersion of a data set, and compare different types of distributions. Finally, students will study various sampling methods.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8 CCSS.MATH.CONTENT.HSS.ID.A CCSS.MATH.CONTENT.HSS.ID.A.2 CCSS.MATH.CONTENT.HSS.ID.A.3

Unit 10: The Mathematics of Fitness and Sports

Duration: 16 days

Description: In this unit, students study the mathematics involved in fitness and sports. Students will study various statistics related to a person’s fitness and health, and also statistics used in a variety of sports activities.

Standards Addressed: Common Core Standards for Mathematical Practice 1-8

Universal Design for Learning Guidelines

I. Provide Multiple Means of II. Provide Multiple Means of III. Provide Multiple Means of Representation Action and Expression Engagement

1: Provide options for perception 4: Provide options for physical action 7: Provide options for recruiting interest

1.1 Offer ways of customizing the display of information 4.1 Vary the methods for response and navigation 7.1 Optimize individual choice and autonomy

1.2 Offer alternatives for auditory information 4.2 Optimize access to tools and assistive technologies 7.2 Optimize relevance, value, and authenticity

1.3 Offer alternatives for visual information 7.3 Minimize threats and distractions

2: Provide options for language, mathematical 5: Provide options for expression and communication 8: Provide options for sustaining effort and persistence expressions, and symbols 5.1 Use multiple media for communication 8.1 Heighten salience of goals and objectives 2.1 Clarify vocabulary and symbols 5.2 Use multiple tools for construction and composition 8.2 Vary demands and resources to optimize challenge 2.2 Clarify syntax and structure 5.3 Build uencies with graduated levels of support for 8.3 Foster collaboration and community 2.3 Support decoding of text, mathematical notation, practice and performance 8.4 Increase mastery-oriented feedback and symbols

2.4 Promote understanding across languages

2.5 Illustrate through multiple media

3: Provide options for comprehension 6: Provide options for executive functions 9: Provide options for self-regulation

3.1 Activate or supply background knowledge 6.1 Guide appropriate goal-setting 9.1 Promote expectations and beliefs that optimize motivation 3.2. Highlight patterns, critical features, big ideas, and 6.2 Support planning and strategy development relationships 9.2 Facilitate personal coping skills and strategies 6.3 Facilitate managing information and resources 3.3 Guide information processing, visualization, and 9.3 Develop self-assessment and re ection manipulation 6.4 Enhance capacity for monitoring progress

3.4 Maximize transfer and generalization

Resourceful, knowledgeable learners Strategic, goal-directed learners Purposeful, motivated learners

© 2011 by CAST. All rights reserved. www.cast.org, www.udlcenter.org APA Citation: CAST (2011). Universal design for learning guidelines version 2.0. Wake eld, MA: Author. NTN Written Communication Rubric, Grade 10 The ability to effectively communicate knowledge and thinking through writing by organizing and structuring ideas and using discipline appropriate language and conventions.

EMERGING E/ DEVELOPING D/ PROFICIENT P/ ADVANCED D P A 12 Grade Proficient

DEVELOPMENT • Does not explain background • Provides a cursory or partial • Addresses appropriate • Explains appropriate What is the or context of topic/issue explanation of background and background and context of background and context of evidence that • Controlling idea* is unclear or context of topic/issue topic/issue topic/issue the student can not evident throughout the • Controlling idea* is present but • Controlling idea* is presented • Controlling idea* is develop ideas? writing unevenly addressed throughout clearly throughout the writing consistently maintained • Ideas and evidence are the writing • Ideas and evidence are throughout the writing underdeveloped • Ideas and evidence are somewhat developed • Ideas and evidence are developed developed

ORGANIZATION • Ideas and evidence are • Ideas and evidence are loosely • Ideas and evidence are • Ideas and evidence are What is the disorganized, making sequenced or organization may be sequenced to show logically sequenced to evidence that relationships unclear formulaic relationships show clear relationships the student can • No transitions are used, or are • Transitions connect ideas with • Transitions connect ideas • Transitions are varied and organize and used ineffectively some lapses; may be repetitive or • Conclusion, when appropriate, connect ideas, showing structure ideas • Conclusion, when appropriate, is formulaic follows from and supports the clear relationships for effective absent or restates the • Conclusion, when appropriate, controlling idea • Conclusion, when communication? introduction or prompt follows from the controlling idea appropriate, is logical and raises important implications

LANGUAGE AND • Language, style, and tone are • Language, style, and tone are • Language, style, and tone are • Language, style, and tone CONVENTIONS inappropriate to the purpose, mostly appropriate to the purpose, appropriate to the purpose, are appropriate to the What is the task, and audience. task, and audience with minor task, and audience with minor purpose, task, and audience evidence that • Uses norms and conventions of lapses lapses • Follows the norms and the student can writing that are inappropriate to • Attempts to follow the norms and • Attempts to follow the norms conventions of writing in the use language the discipline/genre** conventions of writing in the and conventions of writing in discipline/genre with minor skillfully to • Has an accumulation of errors discipline/genre** with major errors the discipline/genre** with errors** communicate in grammar, usage, and • Has some minor errors in some errors • Is free of distracting errors in ideas? mechanics that distract or grammar, usage, and mechanics • Is generally free of distracting grammar, usage, and interfere with meaning that partially distract or interfere errors in grammar, usage, and mechanics • Textual citation is missing or with meaning mechanics • Cites textual evidence incorrect, when appropriate • Cites textual evidence with partially • Cites textual evidence with consistently and or using an incorrect format, some minor errors, when accurately, when when appropriate appropriate appropriate

*Controlling idea may refer to a thesis, argument, topic, or main idea, depending on the type of writing **E.g. accurate use of scientific/technical terms, quantitative data, and visual representations in science; use of multiple representations in math

Created with support from Stanford Center for Assessment, Learning, and Equity (SCALE and based on similar rubrics from Envision Schools. The Attribution-NonCommercial-ShareAlike 3.0 Unported license means that people can use our materials, must give appropriate credit, and indicate if any changes have been made. They may not use the material for any commercial purpose. And they must re-share any adaptations under the same kind of license.

NTN Written Communication Rubric, Grade 12 The ability to effectively communicate knowledge and thinking through writing by organizing and structuring ideas and using discipline appropriate language and conventions.

EMERGING E/ DEVELOPING D/ PROFICIENT P/ ADVANCED D P College Ready A College Level

DEVELOPMENT • Does not explain background • Provides a cursory or partial • Explains appropriate • Thoroughly explains What is the or context of topic/issue explanation of background and background and context of appropriate background and evidence that • Controlling idea* is unclear or context of topic/issue topic/issue context of topic/issue the student can not evident throughout the • Controlling idea* is evident but • Controlling idea* is • Controlling idea* is clearly develop ideas? writing unevenly addressed throughout consistently maintained and consistently • Ideas and evidence are the writing throughout the writing communicated throughout underdeveloped • Ideas and evidence are somewhat • Ideas and evidence are the writing developed developed • Ideas and evidence are thoroughly developed and elaborated

ORGANIZATION • Ideas and evidence are • Ideas and evidence are somewhat • Ideas and evidence are • Ideas are logically sequenced What is the disorganized or loosely organized but not always logically logically sequenced to show to present a coherent whole evidence that sequenced; relationships are sequenced to show relationships clear relationships • Transitions are varied and the student can unclear • Transitions connect ideas with • Transitions are varied and clearly orient the reader in organize and • No transitions are used, or are minor lapses, or may be repetitive connect ideas, showing clear the development and structure ideas used ineffectively or formulaic relationships reasoning of the for effective • Conclusion, when appropriate, is • Conclusion, when appropriate, • Conclusion, when appropriate, controlling idea communication? absent or restates the follows from the controlling idea follows from and supports the • Conclusion, when introduction or prompt controlling idea appropriate, is logical and raises important implications

LANGUAGE AND • Language, style, and tone are • Language, style, and tone are • Language, style, and tone are • Language, style, and tone CONVENTIONS inappropriate to the purpose, appropriate to the purpose, task, appropriate to the purpose, are tailored to the purpose, What is the task, and audience and audience with minor lapses task, and audience task, and audience evidence that • Attempts to follow the norms • Follows the norms and conventions • Follows the norms and • Consistently follows the the student can and conventions of writing in the of writing in the discipline/genre with conventions of writing in the norms and conventions of use language discipline/genre with major, consistent errors discipline/genre** with minor writing in the discipline/genre skillfully to consistent errors • Has some minor errors in errors • Is free of distracting errors in communicate • Has an accumulation of errors grammar, usage, and mechanics • Is generally free of distracting grammar, usage, and ideas? in grammar, usage, and that partially distract or interfere errors in grammar, usage, and mechanics mechanics that distract or with meaning mechanics • Cites textual evidence interfere with meaning • Cites textual evidence with some • Cites textual evidence consistently and • Textual citation is missing or minor errors, when appropriate consistently and accurately, accurately, when incorrect, when appropriate when appropriate appropriate