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Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: Geometry Grade: 10 Quarter: 1st Essential Questions-Units-Chapters-Concepts UNIT 1 LANGUAGE OF GEOMETRY: How can the coordinate system, constructions, and precise language help us explore and justify geometric relationships? How can coordinates be used to describe attributes of geometric objects? (e.g. slope, midpoint, length, parallelism, and perpendicularity, and equations of lines) In what ways can two or more lines intersect? How can the relationship between the lines and the angle formed be represented and justified? What is the difference between inductive and deductive reasoning? What are the value and limitations of each type of reasoning? How are geometric constructions useful tools for representing and reasoning about geometric figures? UNIT 2 TRANSFORMATIONAL GEOMETRY: What impact does each type of transformation (reflection, rotation, translation, and dilation) have on the location, size, and orientation of geometric objects?) How does the value of the scale factor in a dilation influence the size of the image? How can geometric transformations be represented algebraically? Resources (include websites) Atlas Rubicon Oakland Schools (2015). https://oaklandk12public.rubiconatlas.org/Atlas/Browse/Vie w/Calendars Pearson Education(2015). www.pearsonsuccess.net (2012). Geometry Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.ht ml Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.p hp/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 1: G.CO.A.1, G.CO.D.12, G.CO.D.13, G.GPE.B.5, G.GPE.B.6, G.GPE.B.7 Unit 2: G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.D.12, G.SRT.A.1, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2 Vocabulary/Key Concepts Assessments/Projects Unit 1: Bisector, angle bisector, segment bisector, perpendicular Standard Based Assessment: Interpreting Data through charts, tables and graphs. bisector, conditional statements, if-then statements, inverse, (Pre/Post x 2) converse, contrapositive, constructions, coordinate geometry, counterexample, definition, distance between two points, Unit 1 Assessments (pre/post) hypothesis, conclusion, midpoint, perpendicular and parallel line relationships, reasoning, inductive, deductive, STEM Cross Curricular Projects Unit 2: Angle of rotation, center of dilations, center of rotations, composition/sequence of two or more transformations, M-STEP & SAT Prep congruence, dilation, geometric constructions, image, preimage, lines of dilation, reflection, rotation, scale factor, magnitude of dilation, similarity, similarity transformations, symmetry (rotational and reflectional), transformation, translation, triangle similarity Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: Geometry Grade: 10 Quarter: 2nd Essential Questions-Units-Chapters-Concepts UNIT 2 TRANSFORMATIONAL GEOMETRY: What impact does each type of transformation (reflection, rotation, translation, and dilation) have on the location, size, and orientation of geometric objects?) What impact does changing the center of dilation have on the location of the image? Which transformations preserve distance? Shape? Orientation? Angle? How might you investigate the composition of two or more transformations to determine which combinations are commutative? Resources (include websites) Atlas Rubicon Oakland Schools- https://oaklandk12public.rubiconatlas.org/Atlas/Browse/View/Calendars UNIT 3 TRIANGLES: What conditions must be met to show similarity or congruence of triangles? What are the properties of medians, altitudes, angle bisectors, and perpendicular bisectors of the sides of a triangle? What are the similarities and differences between similar and congruent triangles? Use a geometry software program or compass and straightedge to construct the medians, altitudes, perpendicular bisectors, and angle bisectors of a triangle. Make conjectures about their intersection points and any additional characteristics. Include the effect of changing the type of triangle from acute to obtuse. Pearson. (2012). Geometry UNIT 4 QUADRILATERALS: How are various quadrilaterals related and what are properties of their sides, angles, diagonals, and areas? How are properties of triangles used to justify properties of quadrilaterals (e.g., angle sums, diagonal lengths)? Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.html Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.php/page/lfsengaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 2: G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.D.12, G.SRT.A.1, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2 Unit 3: A.APR.C.4, G.CO.B.6, G.CO.B.7, G.CO.B.8, G.CO.B.10, G.SRT.A.2, G.SRT.A.3, G.SRT.B.4, G.SRT.B.5, G.C.A.3, G.GPE.B.4, G.GPE.B.7, G.MG.A.3 Unit 4:G.CO.C.11, G.MG.A.1, G.MG.A.3 Vocabulary/Key Concepts Unit 2: Angle of rotation, center of dilations, center of rotations, composition/sequence of two or more transformations, congruence, dilation, geometric constructions, image, pre-image, lines of dilation, reflection, rotation, scale factor, magnitude of dilation, similarity, similarity transformations, symmetry (rotational and reflectional), transformation, translation, triangle similarity Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 3: Altitude, angle bisectors, base angles, centroid, circumcenter, corresponding parts, hypotenuse, incenter, leg, medians, orthocenter, perpendicular bisectors, Pythagorean Theorem, Triangle congruence (SSS, SAS, AAS, ASA, HL), triangle similarity (SSS, SAS, AA), vertex angles, coordinate proofs M-STEP & SAT Prep Unit 4: Coordinate proofs, definitions of quadrilaterals, geometric modeling, measurement attributes of quadrilaterals (area, side length, angle measure, diagonal length, perimeter), necessary and sufficient conditions, properties of quadrilaterals (kite, parallelogram, rectangle, rhombus, square, trapezoid), Quadrilateral classification Unit 2 & 3 Assessments (pre/post) STEM Cross Curricular Projects Final Exam Semester 1 Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: Geometry Grade: 10 Quarter: 3rd Essential Questions-Units-Chapters-Concepts UNIT 4 QUADRILATERALS: How are various quadrilaterals related and what are properties of their sides, angles, diagonals, and areas? How can sufficient conditions for quadrilaterals be used to guide and/or justify their constructions? How do the properties of quadrilaterals help to make sense of and reason about real life objects? What are the sufficient and/or necessary conditions for trapezoids, isosceles trapezoids, parallelograms, rhombi, rectangles, squares and kites? How can coordinates, transformations, and properties of quadrilaterals be used in the process of classifying quadrilaterals? UNIT 5 RIGHT TRIANGLE TRIGONOMETRY: How can the unknown measures of the angles or sides of a triangle be found? How can trigonometry help find these missing parts in many real-world situations? What is the relationship between the side lengths of a right triangle and the sine, cosine, and tangent ratios? Why do trigonometric ratios yield the same values for different sizes of right triangles? What is the relationship between the sides in a 45-45-90 triangle? In a 30-60-90 triangle? When is it appropriate to use the Law of Sines to solve a problem? The Law of Cosines? Resources (include websites) Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/View /Calendars Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Pearson. (2012). Geometry Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.htm l Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.ph p/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 4: G.CO.B.6, G.CO.C.11, G.CO.C12, G.GPE.B.4, G.MG.A.1, G.GM.A.3 Unit 5: F.T.F.A.3, G.SRT.C.6, G.SRT.C.7, G.SRT.C.8, G.SRT.D.9, G.SRT.D.10, G.SRT.D.11 Vocabulary/Key Concepts Unit 4: Coordinate proofs, definitions of quadrilaterals, geometric modeling, measurement attributes of quadrilaterals (area, side length, angle measure, diagonal length, perimeter), necessary and sufficient conditions, properties of quadrilaterals (kite, parallelogram, rectangle, rhombus, square, trapezoid), Quadrilateral classification Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 4 & 5 Assessments (pre/post) STEM Cross Curricular Projects Unit 5: 30-60-90 triangles, 45-45-90 triangles, area of triangle using trig, cosine, Law of Cosines, Law of Sines, sine, tangent M-STEP & SAT Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: Geometry Grade: 10 Quarter: 4th Essential Questions-Units-Chapters-Concepts UNIT 6 CIRCLES: What are the properties and representations of special liens, segments, and angle as they relate to a circle and how can these properties be used to solve problems? How is pi related to the parts of a circle? Why is the measure of an inscribed angle half of the measure of a central angle inscribed in the same arc? What is the relationship of the area of a sector of a circle to the area of that circle? What is the relationship between the arc length on a circle and the circumference e of that circle? Give an example of an equation of a circle whose center is at the origin. How can you transform this equations to the size is the same, but the center is not at the origin? UNIT 7 MODELING WITH 3-DIMENSIONAL FIGURES: What are the connections between twodimensional and three-dimensional figures? How are pyramids like prims? How are they different? How are cones like cylinders? How are they different? What characteristics of a three dimensional object are necessary to draw a sketch of the object? Draw the object. Given a three-dimensional geometric object, how can you draw a two-dimensional net that represent this object? What are the possible cross sections of various polyhedral? Given a two-dimensional figure, sketch the result of rotating the figure about a line. What is the relationship between the volume of a prism and a pyramid with congruent baes and heights? What is the relationship between the volume of a cylinder and ac one with congruent bases and heights? Resources (include websites) Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/ View/Calendars Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.asp x Pearson. (2012). Geometry Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2. html Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index .php/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 6: F.TF.A.1, G.C.A.1, G.C.A.2, G.C.A.3, G.C.A.4, G.C.B.5, G.GPE.A.1 Unit 7: G.GMD.A.1, G.GMD.A.2, G.GMD.A.3, G.GMD.B.4, G.MG.A.1, G.MG.A.2, G.MG.A.3 Vocabulary/Key Concepts Unit 6: Radius, diameter, center, chord, central angle, inscribed angle, circumscribed angle, tangent, point of tangency, secant, equation of a circle, arc, arc length, locus, degree and radian measures and connections, circumference, area, sector, area of a sector Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 7: Altitude, appropriate use of units in area and volume calculations, cones, cross section, cylinders, faces, impact of scale factor on the surface area and volume of a figure, isometry, net, orthographic, planes of symmetry, polyhedron, prisms, pyramids, relationship between the volumes of prisms and pyramids; cylinders and cones, rotational symmetry of a 3-D figure, slant height, solids of revolution, spheres, surface area and volume of figures, vertex STEM Cross Curricular Projects Unit 6 & 7 Assessments (pre/post) Final Exam Semester 2