Algebra II JMG. Module 2 Lesson 2 The Height & Coheight. PBL Community Blood Drive Final Planning

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1 Lesson Plans Lesson Plan WEEK 32 April 17-April 21 Subject to change Mrs. Whitman 1 st 2 nd Period 3 rd Period 4 th Period 5 th Period 6 th Period H S Period Prep Geometry Math Extensions Algebra II JMG Geometry Monday 4/17/17 Lesson 11 Perimeters & Areas of Polygonal Regions Defined by Systems of Inequalities triangle or given a description by inequalities area of a triangle or given a description by inequalities by Green s theorem Exercises 1, 2 Module 2 Lesson 2 The Height & Coheight of a Ferris Wheel Students model & graph 2 functions given by the location of a passenger car on a Ferris Wheel as it is rotated by a number of degrees about the origin from an initial reference position Exploratory Challenge continued PBL Community Blood Drive Final Planning Lesson 9 Perimeter & Area of Triangles in the Cartesian Plane triangle in the using the distance formula Students sate & apply the formula for the ares of a triangle with vertices (0,0), Problem Set th Period Algebra IB Module 3 Lesson 20 Four Interesting Transformations of Students apply their understanding of transformations of functions & their graphs to piecewise functions Exploratory Challenge 1, 2 8 th Period Algebra II Module 2 Lesson 2 The Height & Coheight of a Ferris Wheel Students model & graph 2 functions given by the location of a passenger car on a Ferris Wheel as it is rotated by a number of degrees about the origin from an initial reference position Exploratory Challenge continued Tuesday 4/18/17 Lesson 12 Dividing Segments Proportionately Students find midpoints of segments & the points that divide segments into 3, 4, or more proportional equal Moon, Sun & Stars Motivating Students explore the historical context of of celestial bodies in a Badger Buddies Lesson 10 Perimeter & Area of Polygonal Region in the Cartesian Plane Students fin the Module 3 Lesson 20 Four Interesting Transformations of Students apply their understanding of transformations of functions & their graphs to piecewise functions Moon, Sun & Stars Motivating Students explore the historical context of of celestial bodies in a presumed circular arc

2 Wednesday 4/19/17 parts Exercises 1-3 Problem Set 2, 3, 4 Lesson 13 Analytic Proofs of Theorems Previously Proved by Synthetic Means Using coordinates students prove that the intersections of the medians of a triangle meet at a point that is 2/3 of the way along each median from the intersected vertex Using coordinates students prove that the diagonals of a parallelogram bisect one another & meet at the intersection of the segments joining the midpoints of opposite sides Problem Set 1-8 presumed circular arc Students describe the position of an object along a line of sight in the context of circular Students understand the naming of the is deemed the positive direction of rotation in mathematics Moon, Sun & Stars Motivating Students explore the historical context of of celestial bodies in a presumed circular arc Students describe the position of an object along a line of sight in the context of circular Students understand the naming of the is deemed the positive direction of rotation in mathematics Problem Set 1-4 PBL Community Blood Drive Implementation edges area of a edges by employing Green s Theorem Exercises 1 a-d, 4, 5, 6 Lesson 10 Perimeter & Area of Polygonal Region in the Cartesian Plane Students fin the edges area of a edges by employing Green s Theorem Exercises 1e, 2, 3 Problem Set 1, 2, 5 Problem Set 1-4 Module 3 Lesson 21 Comparing Linear & Exponential Models Again Students create models & understand the differences between linear & exponential models that are represented in different ways Opening Exercise Problem Set 1-3 Students describe the position of an object along a line of sight in the context of circular Students understand the naming of the is deemed the positive direction of rotation in mathematics Moon, Sun & Stars Motivating Students explore the historical context of of celestial bodies in a presumed circular arc Students describe the position of an object along a line of sight in the context of circular Students understand the naming of the is deemed the positive direction of rotation in mathematics Problem Set 1-4 Thursday Lesson Module 2 Team Building Module 3 Lesson 21 Module 2 Lesson

3 4/20/17 15 The Distance from a point to a Line Students are able to derive a distance formula & apply it Problem Set 1-4 Lesson 4 From Circle-ometry to Students define Sine & Cosine as functions for degrees of rotation of the ray formed by the positive x- axis up to 1 full turn determine the values of Sine & Cosine for 30, 45, 60 & 90 Exercises 1-5 Problem Set 1, 2 Exercise Lesson 11 Perimeters & Areas of Polygonal Regions Defined by Systems of Inequalities triangle or given a description by inequalities area of a triangle or given a description by inequalities by Green s theorem Exercises 1, 2 Comparing Linear & Exponential Models Again Students create models & understand the differences between linear & exponential models that are represented in different ways Problem Set From Circleometry to Students define Sine & Cosine as functions for degrees of rotation of the ray formed by the positive x-axis up to 1 full turn determine the values of Sine & Cosine for 30, 45, 60 & 90 Exercises 1-5 Problem Set 1, 2 Friday 4/21/17 Lessons 9-15 Assessment Module 2 Lesson 4 From Circle-ometry to Students define Sine & Cosine as functions for degrees of rotation of the ray formed by the positive x- axis up to 1 full turn determine the values of Sine & Cosine for 30, 45, 60 & 90 Time Management Lesson Lesson 12 Dividing Segments Proportionately Students find midpoints of segments & the points that divide segments into 3, 4, or more proportional equal parts Exercises 1-3 Problem Set 2, 3, 4 Module 3 Lesson 23 Newton s Law of Cooling Students apply knowledge of exponential functions & transformations of functions in a contextual situation Opening Exercise Mathematical Modeling Exercise 1-3 Problem Set 1, 2 Module 2 Lesson 4 From Circleometry to Students define Sine & Cosine as functions for degrees of rotation of the ray formed by the positive x-axis up to 1 full turn determine the values of Sine & Cosine for 30, 45, 60 & 90 Problem Set 3-10

4 Problem Set 3-10 G-CO.A.1 Know precise definitions of angle, circle, perpendicular & parallel line, line segment based on the undefined notions of point, line, distance along a line, distance along a curve G- CO.A.2 Represent transformations in a plane using transparencies & geometry software, describe transformations as functions that take points in the plane as input & give other points as output. Compare transformations that preserve distance & angles to those that do not (e.g. translations vs horizontal stretch) G-CO.A.3 given a rectangles, parallelogram, trapezoid or regular polygon describe the rotations & reflections that carry it onto itself G-CO.A.4 develop definitions of rotations, reflections & translations in terms of angles, circles, perpendicular & parallel lines & line segments G-CO.A.5 Given a geometric figure & the Isometric (rigid) transformation draw the transformed figure using graph or tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another G-CO.B.6 use geometric descriptions of rigid s, to transform figures & to predict the effect of a given rigid on a given figure; Given 2 figures use the definition of congruence in terms of rigid to determine if they are G-CO.B.7 Use the definition of congruence in terms of rigid to show that 2 triangles are If & only if corresponding pairs of sides &/or angles are G-CO.B.8 Explain how the A.SSE.2 Seeing Structure In Expressions Interpret The Structure Of Expressions 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). A-APR.B.2 Know & apply the Remainder Theorem: For a polynomial p(x) & a number a, the remainder on division by x-a is p(a), so p(a) = 0 if & only if (x-a) is a factor of p(x) A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available & use the zeros to construct a rough graph of the function defined by the polynomial. N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling A-APR.D.6 Rewrite simple rational expressions in different forms: write a(x)/b(x)in the form q(x)+r(x)/b(x), where a(x), b(x), q(x) & r(x) are polynomials with the degree of r(x) less than b(x), using inspection, long division or for the more complicated examples, a computer algebra system F-IF.C.7 Graph expressions expressed symbolically & show key features of the graph by hand in simple cases & using technology for more complicated cases c. Graph polynomial functions, identifying zeros when suitable factorizations are available & showing end behavior A-REI.A.1 Explain each G-CO.A.1 Know precise definitions of angle, circle, perpendicular & parallel line, line segment based on the undefined notions of point, line, distance along a line, distance along a curve G- CO.A.2 Represent transformations in a plane using transparencies & geometry software, describe transformations as functions that take points in the plane as input & give other points as output. Compare transformations that preserve distance & angles to those that do not (e.g. translations vs horizontal stretch) G-CO.A.3 given a rectangles, parallelogram, trapezoid or regular polygon describe the rotations & reflections that carry it onto itself G-CO.A.4 develop definitions of rotations, reflections & translations in terms of angles, circles, perpendicular & parallel lines & line segments G-CO.A.5 Given a geometric figure & the Isometric (rigid) transformation draw the transformed figure using graph or tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another G-CO.B.6 use geometric descriptions of rigid s, to transform figures & to predict the effect of a given rigid on a given figure; Given 2 figures use the definition of congruence in terms of rigid to determine if they are G-CO.B.7 Use the F-IF.A.1 Understand that a function from 1 set (called the domain) to another set (called the range) assigns to each element in the domain exactly 1 element in the range. If f is a function & x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. the graph of f is the graph of the equation y = f(x) F-IF.A.2 Use function notation, evaluate functions for inputs in their domain & interpret statements that use function notation in terms of a context F-IF.A.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 F-IF.B.4 for a function that models a relationship between 2 quantities interpret key features of graphs & table sin terms of the quantities & sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts, intervals where the function is increasing, decreasing, positive or negative; relative maximums & minimums; symmetries; end behavior & periodicity F-IF.B.5 Relate the domain of a function to its graph & where applicable to the quantitative relationship it describes. For example if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function F-IF.B.6 Calculate & interpret the average rate of change of a function (presented A.SSE.2 Seeing Structure In Expressions Interpret The Structure Of Expressions 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). A-APR.B.2 Know & apply the Remainder Theorem: For a polynomial p(x) & a number a, the remainder on division by x-a is p(a), so p(a) = 0 if & only if (x-a) is a factor of p(x) A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available & use the zeros to construct a rough graph of the function defined by the polynomial. N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling A-APR.D.6 Rewrite simple rational expressions in different forms: write a(x)/b(x)in the form q(x)+r(x)/b(x), where a(x), b(x), q(x) & r(x) are polynomials with the degree of r(x) less than b(x), using inspection, long division or for the more complicated examples, a computer algebra system F-IF.C.7 Graph expressions expressed symbolically & show key features of the graph by hand in simple cases & using technology for more complicated cases c. Graph polynomial functions, identifying zeros when suitable factorizations are available & showing end behavior A-REI.A.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

5 criteria for triangle congruence ( ASA,SAS,& SSS) follow from the definition of congruence in terms of rigid G-CO.C.9 Prove theorems about lines & angles. Theorems include: vertical angles are ; when a transversal crosses parallel lines, alternate interior angles are & corresponding angles are ; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints G-CO.C.10 Prove theorems about triangles: Theorems include: measures of the interior angles of a triangle sum to 180 ;base angles of isosceles triangles are ; the segment joining the midpoints of the a triangle is parallel to the 3 rd side & half the length; the medians of a triangle meet at a point G-CO.C.11 Prove theorems about parallelograms: Theorems include: opposite sides are ; opposite angles are ; the diagonals of a parallelogram bisect each other; & conversely, rectangles are parallelograms with diagonals G-CO.D.12 Make formal geometric constructions with a variety of tools & methods (compass & straightedge, string, reflective devices, paper-folding, dynamic geometric software) Copying: a segment & angle, Bisecting a segment & angle, Constructing perpendicular lines & parallel lines through a given point not on the line G-CO.D.13 Construct an equilateral triangle, a square, & a regular hexagon inscribed in a circle G-SRT.A.1 Verify experimentally the properties of dilations given by a center & a scale factor: a) A dilation takes a line not passing through the center of the dilation to a parallel 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. A-REI.A.2 Solve simple rational & radical equations in 1 variable & give examples showing how extraneous solutions may arise. definition of congruence in terms of rigid to show that 2 triangles are If & only if corresponding pairs of sides &/or angles are G-CO.B.8 Explain how the criteria for triangle congruence ( ASA,SAS,& SSS) follow from the definition of congruence in terms of rigid G-CO.C.9 Prove theorems about lines & angles. Theorems include: vertical angles are ; when a transversal crosses parallel lines, alternate interior angles are & corresponding angles are ; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints G-CO.C.10 Prove theorems about triangles: Theorems include: measures of the interior angles of a triangle sum to 180 ;base angles of isosceles triangles are ; the segment joining the midpoints of the a triangle is parallel to the 3 rd side & half the length; the medians of a triangle meet at a point G-CO.C.11 Prove theorems about parallelograms: Theorems include: opposite sides are ; opposite angles are ; the diagonals of a parallelogram bisect each other; & conversely, rectangles are parallelograms with diagonals G-CO.D.12 Make formal geometric constructions with a variety of tools & methods (compass & straightedge, string, reflective devices, paperfolding, dynamic geometric software) Copying: a segment & angle, Bisecting a symbolically or as a table) over a specified interval. Estimate the rate of change from a graph F-IF.C.7a Graph functions Determine an explicit expression, a recursive process or steps for calculation from a context F-LE.A.1 Distinguish between situations that can be modeled with linear functions & with exponential functions a) Prove that linear functions grow by equal differences over equal intervals & that exponential functions grow by equal factors over equal intervals b) Recognize situations in which 1 quantity changes at a constant rate per unit interval relative to another c) Recognize situations in which a quantity grows or decays by a constant percent per unit interval relative to another F-LE.A.2 Construct linear & exponential functions including arithmetic & geometric sequences, given a graph, a description of a relationship or 2 input-output pairs (include reading these from a table) F-LE.A.3 Observe using graphs & tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically or (more generally) as a polynomial function expressed symbolically & show key features of the graph by hand in simple cases & use technology for more complicated cases a) graph linear & quadratic functions & show intercepts, maxima, & minima F-BF.A.1 Write a function that describes the relationship between 2 quantities a) method. A-REI.A.2 Solve simple rational & radical equations in 1 variable & give examples showing how extraneous solutions may arise.

6 line & leaves a line passing through the center unchanged b) The dilation of a line segment is longer or shorter in the ratio given by the scale factor G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other 2 proportionally & conversely; the Pythagorean Theorem proved using triangle similarity segment & angle, Constructing perpendicular lines & parallel lines through a given point not on the line G-CO.D.13 Construct an equilateral triangle, a square, & a regular hexagon inscribed in a circle G-SRT.A.1 Verify experimentally the properties of dilations given by a center & a scale factor: a) A dilation takes a line not passing through the center of the dilation to a parallel line & leaves a line passing through the center unchanged b) The dilation of a line segment is longer or shorter in the ratio given by the scale factor G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other 2 proportionally & conversely; the Pythagorean Theorem proved using triangle similarity