Cassia County School District #151. Expected Performance Assessment Students will: Instructional Strategies. Performance Standards

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1 Unit 1 Congruence, Proof, and Constructions Doain: Congruence (CO) Essential Question: How do properties of congruence help define and prove geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Analyze geoetric theores through transforation, construction, and proof. G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segent, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Construction Activity: Construct various geoetric figures based on properties and descriptions G.CO.1: Students ay use geoetry software and/or anipulatives to odel and copare transforations. G-CO(**) Experient with transforations in the plane G.CO.2: Represent transforations in the plane using, e.g., transparencies and geoetry software; describe transforations as functions that take points in the plane as inputs and give other points as outputs. Copare transforations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.3: Given a rectangle, parallelogra, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Transforations Worksheet: Construct shapes on a coordinate plane then transforation the based on based on given instructions. Transforation Exit Check: Describe the transforation of a figure based on a given diagra or process. G.CO.2: Students ay use geoetry software and/or anipulatives to odel and copare transforations. G.CO.3: Students ay use geoetry software and/or anipulatives to odel transforations. Vocabulary: angle, bisector, circle, diagonals, line segent, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

2 Unit 1 Congruence, Proof, and Constructions Doain: Congruence (CO) Essential Question: How do properties of congruence help define and prove geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Analyze geoetric theores through transforation, construction, and proof. G-CO(**) Experient with transforations in the plane G-CO(**) Understand congruence in ters of rigid otions. G.CO.4: Develop definitions of rotations, reflections, and translations in ters of angles, circles, perpendicular lines, parallel lines, and line segents. G.CO.5: Given a geoetric figure and a rotation, reflection, or translation, draw the transfored figure using, e.g., graph paper, tracing paper, or geoetry software. Specify a sequence of transforations that will carry a given figure onto another. G.CO.6: Use geoetric descriptions of rigid otions to transfor figures and to predict the effect of a given rigid otion on a given figure; given two figures, use the definition of congruence in ters of rigid otions to decide if they are congruent. Moveent Group Work: Evaluate the anner in which an object was oved on a coordinate plane and identify the correct odel for the otion. Justify the odel based on the properties of the shape. Translation Exit Check: Analyze a figure and deterine the sequence of transforations needed to ove the figure to a new location. Discovery of Congruence Activity: Deterine congruence of shapes based on apping and aligning one to another through rigid otion. G.CO.4: Students ay use geoetry software and/or anipulatives to odel transforations. Students ay observe patterns and develop definitions of rotations, reflections, and translations. G.CO.5: Students ay use geoetry software and/or anipulatives to odel transforations and deonstrate a sequence of transforations that will carry a given figure onto another. G.CO.6: A rigid otion is a transforation of points in space consisting of a sequence of one or ore translations, reflections, and/or rotations. Rigid otions are assued to preserve distances and angle easures. Vocabulary: angle, bisector, circle, diagonals, line segent, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

3 Unit 1 Congruence, Proof, and Constructions Doain: Congruence (CO) Essential Question: How do properties of congruence help define and prove geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Analyze geoetric theores through transforation, construction, and proof. G-CO(**) Understand congruence in ters of rigid otions. G-CO(**) Prove geoetric theores G.CO.7: Use the definition of congruence in ters of rigid otions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow fro the definition of congruence in ters of rigid otion. G.CO.9: Prove theores about lines and angles. Theores include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segent are exactly those equidistant fro the segent s endpoints. We Do Worksheet: Unit Lessons\We Do Task Geoetry Unit 1 G.CO.7.doc Lines and Angles Exit Check: Verify congruent relationships of angles fored by lines using transforations. G.CO.7: A rigid otion is a transforation of points in space consisting of a sequence of one or ore translations, reflections, and/or rotations. Two triangles are said to be congruent if one can be exactly superiposed on the other by a rigid otion. The congruence theores specify the conditions under which this can occur. G.CO.8: Students ay use geoetric siulations (coputer software or graphing calculator) to explore theores about lines and angles. G.CO.9: Students ay use geoetric siulations (coputer software or graphing calculator) to explore theores about triangles. Vocabulary: angle, bisector, circle, diagonals, line segent, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

4 Unit 1 Congruence, Proof, and Constructions Doain: Congruence (CO) Essential Question: How do properties of congruence help define and prove geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Analyze geoetric theores through transforation, construction, and proof. G-CO(**) Prove geoetric theores G.CO.10: Prove theores about triangles. Theores include: easures of interior angles of a triangle su to 180 ; base angles of isosceles triangles are congruent; the segent joining idpoints of two sides of a triangle is parallel to the third side and half the length; the edians of a triangle eet at a point. G.CO.11: Prove theores about parallelogras. Theores include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogra bisect each other, and conversely, rectangles are parallelogras with congruent diagonals. Properties of Triangles Activity: Construct triangles, easure the interior angles and construct idsegents to evaluate the relationship between segents, sides and angles of a triangle. Properties of Parallelogras Worksheet: Evaluate the properties of a parallelogra based on understanding of congruent triangles. G.CO.10: Students ay use geoetric siulations (coputer software or graphing calculator) to explore theores about triangles. G.CO.11: Students ay use geoetric siulations (coputer software or graphing calculator) to explore theores about parallelogras. Vocabulary: angle, bisector, circle, diagonals, line segent, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

5 Unit 1 Congruence, Proof, and Constructions Doain: Congruence (CO) Essential Question: How do properties of congruence help define and prove geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Analyze geoetric theores through transforation, construction, and proof. G-CO(*) Make geoetric constructions G.CO.12: Make foral geoetric constructions with a variety of tools and ethods (copass and straightedge, string, reflective devices, paper folding, dynaic geoetric software, etc.). Copying a segent; copying an angle; bisecting a segent; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segent; and constructing a line parallel to a given line through a point not on the line. Match Me Activity: Construct a copy of a series of shapes using ultiple ethods when given figures or descriptions of figures What s Inside? Worksheet: Inscribe regular polygons inside a circle through construction. G.C O.12: Students ay use geoetric software to ake geoetric constructions. Exaples: Construct a triangle given the lengths of two sides and the easure of the angle between the two sides. Construct the circucenter of a given triangle. G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. G.CO.13: Students ay use geoetric software to ake geoetric constructions. Vocabulary: angle, bisector, circle, diagonals, line segent, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

6 Unit 2 Siilarity, Proof and Trigonoetry Doain: Siilarity, Right Triangles, and Trigonoetry (SRT) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Develop and apply triangle relationships using geoetric properties and laws. G-SRT(**) Understand siilarity in ters of siilarity transforations G.SRT.1: Verify experientally the properties of dilations given by a center and a scale factor: a. 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. b. The dilation of a line segent is longer or shorter in the ratio given by the scale factor. G.SRT.2: Given two figures, use the definition of siilarity in ters of siilarity transforations to decide if they are siilar; explain using siilarity transforations the eaning of siilarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.3: Use the properties of siilarity transforations to establish the AA criterion for two triangles to be siilar. Dilation Experient: Perfor a dilation given a scale factor and a shape. What s the Scale? Activity: Verify siilarity through dilation and confiration of corresponding congruent angles and proportional sides given two shapes that appear siilar. G.SRT.1: A dilation is a transforation that oves each point along the ray through the point eanating fro a fixed center, and ultiplies distances fro the center by a coon scale factor. Students ay use geoetric siulation software to odel transforations. Students ay observe patterns and verify experientally the properties of dilations. G.SRT.2: A siilarity transforation is a rigid otion followed by dilation. Students ay use geoetric siulation software to odel transforations and deonstrate a sequence of transforations to show congruence or siilarity of figures. Vocabulary: ASA, auxiliary line, congruence, corresponding sides, dilation, Laws of Sines and Cosines, Pythagorean Theore, right triangles, siilarity, SAS, SSS, trigonoetric ratios, typographic grid systes.

7 Unit 2 Siilarity, Proof and Trigonoetry Doain: Siilarity, Right Triangles, and Trigonoetry (SRT) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Develop and apply triangle relationships using geoetric properties and laws. G-SRT(**) Understand siilarity in ters of siilarity transforations G.SRT.4: Prove theores about triangles. Theores include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theore proved using triangle siilarity. Prove It! Activity: Evaluate properties of triangles based on transforations and congruent relationships. G.SRT.4: Students ay use geoetric siulation software to odel transforations and deonstrate a sequence of transforations to show congruence or siilarity of figures. G.SRT.5: Use congruence and siilarity criteria for triangles to solve probles and to prove relationships in geoetric figures. Siilarity Exit Check: Analyze the siilarity between two triangles to deterine the postulate deonstrated. G.SRT.5: Siilarity postulates include SSS, SAS, and AA. Congruence postulates include SSS, SAS, ASA, AAS, and H-L. Students ay use geoetric siulation software to odel transforations and deonstrate a sequence of transforations to show congruence or siilarity of figures. Vocabulary: ASA, auxiliary line, congruence, corresponding sides, dilation, Laws of Sines and Cosines, Pythagorean Theore, right triangles, siilarity, SAS, SSS, trigonoetric ratios, typographic grid systes.

8 Unit 2 Siilarity, Proof and Trigonoetry Doain: Siilarity, Right Triangles, and Trigonoetry (SRT) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Develop and apply triangle relationships using geoetric properties and laws. G-SRT(**) Define trigonoetric ratios and solve probles involving right triangles G.SRT.6: Understand that by siilarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonoetric ratios for acute angles. G.SRT.7: Explain and use the relationship between the sine and cosine of copleentary angles. G.SRT.8: Use trigonoetric ratios and the Pythagorean Theore to solve right triangles in applied probles. What s My Sine? Worksheet: Copare sine and cosine values in acute angles right triangles to deterine the relationship between the sides and angles. Acute Angles Exit Check: Copare acute angles and their trigonoetric ratios in right triangles. Measure that! Activity: Apply trigonoetric ratios to indirect easureent of large scale objects. G.SRT.6: See Unit Addendu G.SRT.7: Geoetric the relationship between sine and siulation software, applets, and graphing calculators can be used to explore cosine. G.SRT.8: See Unit Addendu Vocabulary: ASA, auxiliary line, congruence, corresponding sides, dilation, Laws of Sines and Cosines, Pythagorean Theore, right triangles, siilarity, SAS, SSS, trigonoetric ratios, typographic grid systes.

9 Unit 2 Siilarity, Proof and Trigonoetry Doain: Siilarity, Right Triangles, and Trigonoetry (SRT) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Develop and apply triangle relationships using geoetric properties and laws. G-SRT(+) Apply trigonoetry to general triangles. G.SRT.9: Derive the forula 1 A ab sin C for the area of a triangle by 2 drawing an auxiliary line fro a vertex perpendicular to the opposite side. G.SRT.10: Prove the Laws of Sines and Cosines and use the to solve probles. G.SRT.11: Understand and apply the Law of Sines and the Law of Cosines to find unknown easureents in right and non-right triangles (e.g., surveying probles, resultant forces) Exploration of Laws Activity: Develop the law of Sines and the Law of Cosines through construction and easureent of non-right triangles. Laws Applications Worksheet: Evaluate unknown easureents in right and non-right triangles that odel situations using the Law of Sines and the law of Cosines. G.SRT.11: Exaple: Tara wants to fix the location of a ountain by taking easureents fro two positions 3 iles apart. Fro the first position, the angle between the ountain and the second position is 78 o. Fro the second position, the angle between the ountain and the first position is 53 o. How can Tara deterine the distance of the ountain fro each position, and what is the distance fro each position? Vocabulary: ASA, auxiliary line, congruence, corresponding sides, dilation, Laws of Sines and Cosines, Pythagorean Theore, right triangles, siilarity, SAS, SSS, trigonoetric ratios, typographic grid systes.

10 Unit 2 Siilarity, Proof and Trigonoetry Doain: Modeling with Geoetry (MG) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Develop and apply triangle relationships using geoetric properties and laws. G-MG(***) Apply geoetric concepts in odeling situations G.MG.1: Use geoetric shapes, their easures, and their properties to describe objects (e.g., odeling a tree trunk or a huan torso as a cylinder). G.MG.2: Apply concepts of density based on area and volue in odeling situations (e.g., persons per square ile, BTUs per cubic foot). G.MG.3: Apply geoetric ethods to solve design probles (e.g., designing an object or structure to satisfy physical constraints or iniize cost; working with typographic grid systes based on ratios). Modeling Stations: Describe the properties of real world objects in ters of geoetric shapes; evaluate volue and area of real world scenarios; design an object to eet a set of geoetric standards. Modeling Exit Check: Describe a anner in which a specific scenario can be odeled. G.MG.1: Students ay use siulation software and odeling software to explore which odel best describes a set of data or situation. G.MG.2: Students ay use siulation software and odeling software to explore which odel best describes a set of data or situation. G.MG.3: Students ay use siulation software and odeling software to explore which odel best describes a set of data or situation. Vocabulary: ASA, auxiliary line, congruence, corresponding sides, dilation, Laws of Sines and Cosines, Pythagorean Theore, right triangles, siilarity, SAS, SSS, trigonoetric ratios, typographic grid systes.

11 Unit 3 Extending to Three Diensions Doain: Geoetric Measureent and Diension (GMD) Essential Question: How do two-diensional cross sections help describe three-diensional objects? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and analyze relationships between two and three diensional figures. G-GMD(*) Explain volue forulas and use the to solve probles G.GMD.1: Give an inforal arguent for the forulas for the circuference of a circle, area of a circle, volue of a cylinder, pyraid, and cone. Use dissection arguents, Cavalieri s principle, and inforal liit arguents. G.GMD.3: Use volue forulas for cylinders, pyraids, cones, and spheres to solve probles. Volue Discovery Activity: Copare and contrast volue of given shapes to establish a relationship between the shapes. Volue Scavenger Hunt: Evaluate the volue of real world objects based on easureent then ake conjectures about the changes to easureents if the volue is altered. G.GMD.1: Cavalieri s principle is if two solids have the sae height and the sae cross-sectional area at every level, then they have the sae volue. G.GMD.3: Missing easures can include but are not liited to slant height, altitude, height, diagonal of a pris, edge length, and radius. G-GMD(***) Visualize relationships between two-diensional and three diensional objects G.GMD.4: Identify the shapes of twodiensional cross-sections of threediensional objects, and identify threediensional objects generated by rotations of two-diensional objects. Cross Sections Worksheet: Identify and evaluate the shape of the cross section of three-diensional objects and the rotation of twodiensional objects. G.G MD.4: Students ay use geoetric siulation software to odel figures and create cross sectional views. Exaple: Identify the shape of the vertical, horizontal, and other cross sections of a cylinder. Vocabulary: Cavalieri s principle, circuference, cone, cylinder, liit, pyraid, three-diensions, sphere

12 Unit 3 Extending to Three Diensions Doain: Modeling with Geoetry (MG) Essential Question: How do properties of siilarity help define and prove right triangle relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and analyze relationships between two and three diensional figures. G-MG(***) Apply geoetric concepts in odeling situations G.MG.1: Use geoetric shapes, their easures, and their properties to describe objects (e.g., odeling a tree trunk or a huan torso as a cylinder). Get Creative Project: Design a odel of real world objects using geoetric shapes. G.MG.1: Students ay use siulation software and odeling software to explore which odel best describes a set of data or situation. Vocabulary: Cavalieri s principle, circuference, cone, cylinder, liit, pyraid, three-diensions, sphere

13 Unit 4 Connecting Algebra and Geoetry Through Coordinates Doain: Expressing Geoetric Properties with Equations (GPE) Essential Question: How does the coordinate syste help to verify geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Interpret geoetric relationships using algebraic reasoning. G-GPE(***) Use coordinates to prove siple geoetric theores algebraically G.GPE.4: Use coordinates to prove siple geoetric theores algebraically. Prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). G.GPE.5: Prove the slope criteria for parallel and perpendicular lines and use the to solve geoetric probles (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Are You Sure? Worksheet: Verify properties of figures using coordinate geoetry and algebra. What s My Line? Activity: Construct parallel and perpendicular lines and verify their relationship using slope and the equations of those lines. Is This Right? Exit Check: Verify properties of right triangles using coordinate geoetry and algebra. G.GPE.4: Students ay use geoetric siulation software to odel figures and prove siple geoetric theores. Exaple: Use slope and distance forula to verify the polygon fored by connecting the points (-3, -2), (5, 3), (9, 9), (1, 4) is a parallelogra. G.GPE.5: Lines can be horizontal, vertical, or neither. Students ay use a variety of different ethods to construct a parallel or perpendicular line to a given line and calculate the slopes to copare the relationships. Vocabulary: angle, bisector, circle, conic section, diagonals, directed line segent, directrix, focus, line segent, parabola, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

14 Unit 4 Connecting Algebra and Geoetry Through Coordinates Doain: Expressing Geoetric Properties with Equations (GPE) Essential Question: How does the coordinate syste help to verify geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Interpret geoetric relationships using algebraic reasoning. G-GPE(***) Use coordinates to prove siple geoetric theores algebraically G.GPE.6: Find the point on a directed line segent between two given points that partitions the segent in a given ratio. Proportional Reasoning Exit Check: Construct a proportionally divided line segent fro given inforation. G.GPE.6: Students ay use geoetric siulation software to odel figures or line segents. Exaple: Given A(3, 2) and B(6, 11), find the point that divides the line segent AB two-thirds of the way fro A to B. The point two-thirds of the way fro A to B has x-coordinate two-thirds of the way fro 3 to 6 and y coordinate two-thirds of the way fro 2 to 11. G.GPE.7: Use coordinates to copute perieters of polygons and areas of triangles and rectangles, e.g., using the distance forula. Coordinate Geoetry Worksheet: Evaluate area and perieter of shapes on a coordinate plane using forulas and algebra. So, (5, 8) is the point that is two-thirds fro point A to point B G.GPE.7: Students ay use geoetric siulation software to odel figures. Vocabulary: angle, bisector, circle, conic section, diagonals, directed line segent, directrix, focus, line segent, parabola, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

15 Unit 4 Connecting Algebra and Geoetry Through Coordinates Doain: Expressing Geoetric Properties with Equations (GPE) Essential Question: How does the coordinate syste help to verify geoetric relationships? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Interpret geoetric relationships using algebraic reasoning. G-GPE(***) Translate between the geoetric description and the equation for a conic section G.GPE.2: Derive the equation of a parabola given a focus and directrix. Parabola Practice Worksheet: Create the equations of a parabola based on given inforation and diagra. G.G PE.2: Students ay use geoetric siulation software to explore parabolas. Exaples: Write and graph an equation for a parabola with focus (2, 3) and directrix y = 1. Vocabulary: angle, bisector, circle, conic section, diagonals, directed line segent, directrix, focus, line segent, parabola, parallel line, perpendicular line, reflections, rigid otion, rotations, siilarity, transforations, translations

16 Unit 5 Circles with and without Coordinates Doain: Circles (C) Essential Question: How do geoetric relationships help to represent the properties of circles and conics? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and odel situations involving circles using geoetric theores and coordinate algebra. G-C(*) Understand and apply theores about circles G.C.1: Prove that all circles are siilar. G.C.2: Identify and describe relationships aong inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circuscribed angles; inscribed angles on a diaeter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Circles Are The Sae Exit Check: Copare and contrast the properties of siilar circles. Circle s Do Have Angles Worksheet: Classify and describe relationships between angles and lines in circles. G.C.1: Students ay use geoetric siulation software to odel transforations and deonstrate a sequence of transforations to show congruence or siilarity of figures. G.C.2: Exaples: Given the circle below with radius of 10 and chord length of 12, find the distance fro the chord to the center of the circle. Find the unknown length in the picture below. Vocabulary: arc, area of sector, central angle, circuscribed angle, diaeter, inscribed angle, inscribed chord, inscribed radius, radian easure

17 Unit 5 Circles with and without Coordinates Doain: Circles (C) Essential Question: How do geoetric relationships help to represent the properties of circles and conics? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and odel situations involving circles using geoetric theores and coordinate algebra. G.C.3: Construct the inscribed and circuscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Inscribe This Activity: Construct inscribed polygons and analyze the angle relationships that exist. G.C.3: Students ay use geoetric siulation software to ake geoetric constructions. G-C(*) Understand and apply theores about circles G.C.4: Construct a tangent line fro a point outside a given circle to the circle. Tangent Exit Check: Construct a tangent line fro a point to a given circle and analyze the segent and angle relationships that exist. G.C.4: Students ay use geoetric siulation software to ake geoetric constructions. G-C(**) Find arc lengths and areas of sectors of circles G.C.5: Derive using siilarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian easure of the angle as the constant of proportionality; derive the forula for the area of a sector. How Much Pizza? Worksheet: Evaluate the relationship between the central angle, radius and the area of a circle to develop the forula for the area of a sector. G.C.5: Students can use geoetric siulation software to explore angle and radian easures and derive the forula for the area of a sector. Vocabulary: arc, area of sector, central angle, circuscribed angle, diaeter, inscribed angle, inscribed chord, inscribed radius, radian easure

18 Unit 5 Circles with and without Coordinates Doain: Circles (C) Essential Question: How do geoetric relationships help to represent the properties of circles and conics? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and odel situations involving circles using geoetric theores and coordinate algebra. G-GPE(***) Translate between the geoetric description and the equation for a conic section G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theore; coplete the square to find the center and radius of a circle given by an equation. Circle Practice Worksheet: Derive the equation of a circle fro given inforation and diagras and construct a circle fro a given equation. G.G PE.1: Students ay use geoetric siulation software to explore the connection between circles and the Pythagorean Theore. Exaples: Write an equation for a circle with a radius of 2 units and center at (1, 3). Write an equation for a circle given that the endpoints of the diaeter are (-2, 7) and (4, -8). Find the center and radius of the circle 4x 2 + 4y 2-4x + 2y 1 = 0. Vocabulary: arc, area of sector, central angle, circuscribed angle, diaeter, inscribed angle, inscribed chord, inscribed radius, radian easure

19 Unit 5 Circles with and without Coordinates Doain: Modeling with Geoetric (MG) Essential Question: How do geoetric relationships help to represent the properties of circles and conics? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate and odel situations involving circles using geoetric theores and coordinate algebra. G-GPE(***) Use coordinates to prove siple geoetric theores algebraically G.GPE.4: Use coordinates to prove siple geoetric theores algebraically. For exaple, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). How Can You Be Sure? Activity: Verify shapes in a coordinate plane using slope and distance forula. G.GPE.4: Students ay use geoetric siulation software to odel figures and prove siple geoetric theores. Exaple: Use slope and distance forula to verify the polygon fored by connecting the points (-3, -2), (5, 3), (9, 9), (1, 4) is a parallelogra. G-MG(***) Apply geoetric concepts in odeling situations G.MG.1: Use geoetric shapes, their easures, and their properties to describe objects (e.g., odeling a tree trunk or a huan torso as a cylinder). Get Creative Project: Design a odel of real world objects using geoetric shapes and their properties. G.MG.1: Students ay use siulation software and odeling software to explore which odel best describes a set of data or situation. Vocabulary: arc, area of sector, central angle, circuscribed angle, diaeter, inscribed angle, inscribed chord, inscribed radius, radian easure

20 Unit 6 Applications of Probability Doain: Statistics Essential Question: How does probability help to develop infored decisions? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate probability odels using algebraic and geoetric reasoning. S-CP(*) Understand independence and conditional probability and use the to interpret data. S.CP.1: Describe events as subsets of a saple space (the set of outcoes) using characteristics (or categories) of the outcoes, or as unions, intersections, or copleents of other events. S.CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to deterine if they are independent. What s Coon? Worksheet: Copare shapes to deterine what is shared and not shared to establish the saple space, union and intersection of the shapes. Probability Rules Exit Check: Evaluate events and deterine if they are independent. S.CP.1: See Unit Addendu Vocabulary: cobinations, copleents, conditional probability, copleents, events, independent events, intersections, perutations, saple space, subsets, unions

21 Unit 6 Applications of Probability Doain: Statistics Essential Question: How does probability help to develop infored decisions? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate probability odels using algebraic and geoetric reasoning. S-CP(*) Understand independence and conditional probability and use the to interpret data. S.CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the sae as the probability of A, and the conditional probability of B given A is the sae as the probability of B. S.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 saple space to decide if events are independent and to approxiate conditional probabilities. For exaple, collect data fro a rando saple of students in your school on their favorite subject aong ath, science, and English. Estiate the probability that a randoly selected student fro your school will favor science given that the student is in tenth grade. Copare the results. Probability Models Stations: Evaluate conditional probability scenarios and odel the appropriately given the construct of the scenario. Conditional Probability Exit Check: Assess the probability of a specified event given a series of conditions. S.CP.4: Students ay use spreadsheets, graphing calculators, and siulations to create frequency tables and conduct analyses to deterine if events are independent or deterine approxiate conditional probabilities. Vocabulary: cobinations, copleents, conditional probability, copleents, events, independent events, intersections, perutations, saple space, subsets, unions

22 Unit 6 Applications of Probability Doain: Statistics Essential Question: How does probability help to develop infored decisions? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate probability odels using algebraic and geoetric reasoning. S-CP(*) Understand independence and conditional probability and use the to interpret data. S.CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For exaple, copare the chance of having lung cancer if you are a soker with the chance of being a soker if you have lung cancer. Conditional Probability Exit Check: Evaluate a conditional probability scenario to deterine the outcoes and establish independence of the events. S.CP.5: Exaples: What is the probability of drawing a heart fro a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced? Are these events independent or dependent? At Johnson Middle School, the probability that a student takes coputer science and French is The probability that a student takes coputer science is What is the probability that a student takes French given that the student is taking coputer science? Vocabulary: cobinations, copleents, conditional probability, copleents, events, independent events, intersections, perutations, saple space, subsets, unions

23 Unit 6 Applications of Probability Doain: Statistics Essential Question: How does probability help to develop infored decisions? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate probability odels using algebraic and geoetric reasoning. S-CP Use the rules of probability to copute probabilities of copound events in a unifor probability odel. S.CP.6: Find the conditional probability of A given B as the fraction of B s outcoes that also belong to A, and interpret the answer in ters of the odel. S.CP.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in ters of the odel. S.CP.8: Apply the general Multiplication Rule in a unifor probability odel, P(A and B) = P(A)P(B A) = P(B)P(A B), and interpret the answer in ters of the odel. Interpreting Probability Activity: Interpret the outcoe of probability scenarios in ters of the odel given using various representations. How Many Ways Worksheet: Evaluate the nuber of possible outcoes and cobinations to solve real world probles. S.CP.6: Students could use graphing calculators, siulations, or applets to odel probability experients and interpret the outcoes. S.CP.7: See Unit Addendu S.CP.8: Students could use graphing calculators, siulations, or applets to odel probability experients and interpret the outcoes. S.CP.9: Use perutations and cobinations to copute probabilities of copound events and solve probles. S.CP.9: See Unit Addendu Vocabulary: cobinations, copleents, conditional probability, copleents, events, independent events, intersections, perutations, saple space, subsets, unions

24 Unit 6 Applications of Probability Doain: Statistics Essential Question: How does probability help to develop infored decisions? Matheatical Practices: 1. Make sense of probles and persevere in solving the. 3. Construct viable arguents and critique the reasoning of others. 4. Model with Matheatics. Evaluate probability odels using algebraic and geoetric reasoning. S-MD Use probability to evaluate outcoes of decisions. S.MD.6: Use probabilities to ake fair decisions (e.g., drawing by lots, using a rando nuber generator). S.MD.7: Analyze decisions and strategies using probability concepts (e.g., product testing, edical testing, pulling a hockey goalie at the end of a gae). Model Real World Events Activity: Evaluate probability odels of real world probles and analyze results to ake decisions. Probability Analysis Worksheet: Analyze a real world scenario and deterine if the strategies utilized result in a fair decision. S.MD.6: Students ay use graphing calculators or progras, spreadsheets, or coputer algebra systes to odel and interpret paraeters in linear, quadratic or exponential functions. S.MD.7: Students ay use graphing calculators or progras, spreadsheets, or coputer algebra systes to odel and interpret paraeters in linear, quadratic or exponential functions. Vocabulary: cobinations, copleents, conditional probability, copleents, events, independent events, intersections, perutations, saple space, subsets, unions

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