JMG. Algebra II. Resigning from a job. Working with Radian Measures & the Unit Circle Students. How to Effectively Write a Letter of Resignation

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1 Lesson Plans Lesson Plan WEEK 35 May 8-May 12 Subject to change Mrs. Whitman 1 st 2 nd Period 3 rd Period 4 th Period 5 th Period 6 th Period H S Mathematics Period Prep Geometry Math Extensions Algebra II JMG Geometry Monday 5/8/17 Tuesday 5/9/17 Module 4 Lessons 9-15 Mini-Assessment Tangram Activity Worksheet Packet Polygon Angle Sum that the sum of the exteriors of all polygons is always 360 that Radian Measures & the Unit Circle Students foundation of radian measures & use radians for measuring relationship between radians & degrees for measuring for Radian Measures & the Unit Circle Students foundation of radian measures & Resigning from a job How to Effectively Write a Letter of Resignation Teamwork & Problem Solving Activity Students practice Departmental Working Worksheet Packet Polygon Angle Sum that the sum of the exteriors of all polygons is always 360 Students understand that finding the individual angle measure of an interior in a regular polygon can be determined using the formula the different properties of parallelogram & utilize them to solve for missing measures Tangram Activity Students use tangrams to forms a variety of Worksheet Packet Polygon Angle Sum that the sum of the exteriors of all polygons is always 7 th Period Algebra IB Writing Linear Equations in Point-Slope Form Worksheet #3 Green worksheet writing linear equations from a graph Students utilize a given slope & the coordinates of a point to write an equation for a line using the distributive property of over addition & combining like terms Writing Linear Equations in Point-Slope Form Worksheet #1 Green worksheet writing linear equations from a 8 th Period Algebra II Radian Measures & the Unit Circle the foundation of radian measures & use radians for measuring relationship between radians & degrees for measuring for Radian Measures & the Unit Circle the foundation of radian measures & use radians for measuring

2 Wednesday 5/10/17 finding the individual angle measure of an interior in a regular polygon can be determined using the formula Students different properties of parallelogram & utilize them to solve for missing measures Tangram Activity Students use tangrams to forms a variety of Worksheet Packet Polygon Angle Sum that the sum of the exteriors of all polygons is always 360 that finding the individual angle measure of an interior in a regular polygon can be determined using the formula the different properties of parallelogram & utilize them to solve for missing measures Tangram Activity Students use tangrams to forms a variety of use radians for measuring relationship between radians & degrees for measuring for 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 tri to determine the values of Sine & Cosine for 30, 45, 60 & 90 Exercises 1-5 Problem Set 1, 2 Leaving a Job Scramble Unscramble words that are related to leaving a job 360 Students understand that finding the individual angle measure of an interior in a regular polygon can be determined using the formula the different properties of parallelogram & utilize them to solve for missing measures Tangram Activity Students use tangrams to forms a variety of Module 4 Lesson 15 The Distance from a point to a Line Students are able to derive a distance formula & apply it Problem Set 1-4 graph Students utilize a given slope & the coordinates of a point to write an equation for a line using the distributive property of over addition & combining like terms Module 4 Lesson 1 Multiplying & Factoring Polynomial Expressions Students use the distributive property to multiply a monomial by a polynomial & understand that factoring reverses the process Students use polynomial expressions as side lengths of polygons & find area by multiplying Students recognize patterns & formulate shortcuts for writing the expanded form of binomials whose expanded form is a perfect square or the difference of perfect squares Examples 1, 2, 3, 4 Exercises 1-9 relationship between radians & degrees for measuring for 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 tri to determine the values of Sine & Cosine for 30, 45, 60 & 90 Exercises 1-5 Problem Set 1, 2

3 Thursday 5/11/17 Friday 5/12/17 Module 5 Lesson 1 Thales Using observation from a pushing puzzle students explore the convers of Thales theorem: if ABC is a right triangle then A, B & C are 3 distinct points on a circle with a diameter AB Students prove the statement of Thales theorem: If A, B & C are 3 different points on a circle with diameter AB then < ABC is a right angle Exercises 1, 2 Problem Set 1-6 Module 5 Lesson 2 Circles, Chords, Diameters & Relationships Students identify the relationship between diameters of a circle & other chords of a circle Exercises 1-3 Problem Set 1-9 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 tri to determine the values of Sine & Cosine for 30, 45, 60 & 90 Problem Set 3-10 Lesson 5 Extending the Domain of Sine & Cosine to All Real Numbers Students define sine & cosine as functions for all real measured in degrees Students evaluate the sine & cosine functions at multiples of 30 &45 Exercises 1-10 Planning Elementary Fun Day Planning Elementary Fun Day Module 4 Lessons 9-15 Assessment Module 4 Lesson 1 Multiplying & Factoring Polynomial Expressions Students use the distributive property to multiply a monomial by a polynomial & understand that factoring reverses the process Students use polynomial expressions as side lengths of polygons & find area by multiplying Students recognize patterns & formulate shortcuts for writing the expanded form of binomials whose expanded form is a perfect square or the difference of perfect squares Problem Set 1-4 Module 4 Lesson 2 Multiplying & Factoring Polynomial Expressions that factoring reverses the process as they find the linear factors of basic factorable quadratic trinomials Examples 1-3 Exercises 1-10 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 tri to determine the values of Sine & Cosine for 30, 45, 60 & 90 Problem Set 3-10 Lesson 5 Extending the Domain of Sine & Cosine to All Real Numbers Students define sine & cosine as functions for all real measured in degrees Students evaluate the sine & cosine functions at multiples of 30 &45 Exercises 1-10

4 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 & to those that do not (e.g. translations vs horizontal stretch) G-CO.A.3 given a rect, 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, 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 motions, to transform figures & to predict the effect of a given rigid motion on a given figure; Given 2 figures use the definition of congruence in terms of rigid motion to determine if they are G-CO.B.7 Use the definition of congruence in terms of rigid motion to show that 2 tri are If & only if corresponding pairs of sides &/or 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 motion G-CO.C.9 Prove theorems about lines &. 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 : 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 asserted at the previous step, starting 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 & to those that do not (e.g. translations vs horizontal stretch) G-CO.A.3 given a rect, 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, 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 motions, to transform figures & to predict the effect of a given rigid motion on a given figure; Given 2 figures use the definition of congruence in terms of rigid motion to determine if they are G-CO.B.7 Use the definition of congruence in terms of rigid motion to show that 2 tri are If & only if corresponding pairs of 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 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 ; 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 symbolically or as a table) over a specified interval. Estimate the rate of change from a graph F-IF.C.7a Graph functions 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 : 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 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

5 s include: vertical are ; when a transversal crosses parallel lines, alternate interior are & corresponding 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 tri: s include: measures of the interior of a triangle sum to 180 ;base of isosceles tri 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: s include: opposite sides are ; opposite are ; the diagonals of a parallelogram bisect each other; & conversely, rect 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 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 tri. s 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. sides &/or 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 motion G-CO.C.9 Prove theorems about lines &. s include: vertical are ; when a transversal crosses parallel lines, alternate interior are & corresponding 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 tri: s include: measures of the interior of a triangle sum to 180 ;base of isosceles tri 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: s include: opposite sides are ; opposite are ; the diagonals of a parallelogram bisect each other; & conversely, rect 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 segment & angle, Constructing perpendicular lines & parallel lines through a given point not on the 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) solutions may arise.

6 include: a line parallel to one side of a triangle divides the other 2 proportionally & conversely; the Pythagorean proved using triangle similarity 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 tri. s include: a line parallel to one side of a triangle divides the other 2 proportionally & conversely; the Pythagorean proved using triangle similarity