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Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 1 – Basics of Geometry G.GCO.1* G.GCO.11* G.GGPE.6 G.GGPE.7* Define angle, perpendicular line, line segment, ray, circle, and skew in terms of the undefined notions of point, line, and plane. Use geometric figures to represent and describe real-world objects. Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships. Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. Use the distance and midpoint formulas to determine distance and midpoint in a coordinate plane, as well as areas of triangles and rectangles, when given coordinates. Unit 1 – Basics of Geometry Concepts/Essential Knowledge Resources/Activities (G.GCO.1) Terminology Students should be able to define: ● point ● line ● plane ● intersection ● rays ● segments ● vertex, angle ● acute ● obtuse ● right ● postulate (if, then) ● theorem (if and only if) ● biconditional ● congruence ● parallel ● perpendicular ● ● ● Anderson School District Five Exploring Points and Planes Basic Terms Activities Points, Lines Planes Lesson Plan Page 1 Textbook Reference # of Blocks (90 min) 1.2 1.3 1.4 2.2 2.3 0.5 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 1 – Basics of Geometry Concepts/Essential Knowledge (G.GCO.11) Construct: ● Perpendicular bisector ● Angle bisector ● Congruent segments ● Congruent angles (G.GGPE.6) Midpoint formula Addition postulates ● midpoint formula ● segment bisector ● angle addition ● segment addition (G.GGPE.7) Distance formula Resources/Activities ● ● ● ● Basic Constructions Patty Paper Constructions Hands on Geometry Constructions Construction Worksheets ● http://jwilson.coe.uga.edu/EMAT6680Fa08/Kuzle/Instructional%20unit/Co nstructions.html (history of construction & ideas) http://www.mathsisfun.com/geometry/constructions.html (step by step on constructions) ● ● ● ● ● ● ● ● Midpoint of Segment Angle Additions Segment Addition Segment Addition String Activity Deriving Midpoint and Distance Formula Stuck in the Middle Whitebeard’s Treasure ● http://alex.state.al.us/lesson_view.php?id=26361 (midpoint of a segment) ● ● Deriving Midpoint and Distance Formula Lake Geometria Activity (Distance and Midpoint Formulas Activity) ● http://www.regentsprep.org/Regents/math/geometry/GCG3/Tdistance.htm (Distance Formula Game) http://www.mathwarehouse.com/algebra/distance_formula/interactivedistance-formula.php (Interactive Distance Formula) ● Review and Unit Test Anderson School District Five Page 2 Textbook Reference # of Blocks (90 min) 1.6 0.5 1.7 1.0 1.7 1.0 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 2 Angles and Lines G.GCO.8* G.GCO.8a G.GCO.8b G.GCO.8c G.GCO.8d G.GCO.11* G.GGPE.5* Prove and apply in mathematical and real-world contexts, theorems about lines and angles, including the following: vertical angles are congruents; when a transversal crosses parallel lines, alternate interior angles are interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary; any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment; perpendicular lines form four right angles. Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships. Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither. Write the equation of a line passing through a given point that is parallel or perpendicular to a given line. Solve geometric and real-world problems involving lines and slopes. Unit 2 Angles and Lines Essential Tasks/Key Concepts (G.GCO.8, G.GCO.8a, G.GCO.8b, G.GCO.8c, G.GCO.8d) Students should know properties of: ● Vertical angles ● Transversals ● Corresponding angles ● Angles Bisectors ● Alternate interior and exterior angles ● Perpendicular bisectors Resources/Activities ● ● ● ● ● ● ● ● Parallel Lines Practice and Answers Vertical Angles Angle Bisectors Teaching Ideas for Angles Discovering Angles Discovery Lesson on Angles Angle and Perpendicular Bisector Discovery Worksheet on Angle Bisectors and Perpendicular Bisectors ● http://163.150.89.242/yhs/Faculty/AB/bagg/Geometry/images/Geometry %20text%20PDFs/2.4.pdf (vertical angles Worksheet) http://www.superteacherideas.com/math5-geometry-angles.html (vertical angles with macaroni & popcorn) http://lessonplanspage.com/mathanglerelationshipsandparallellinespaperfo ldingactivity810-htm/ (paper folding activity for angles) http://mathforum.org/sanders/exploringandwritinggeometry/proof.htm ● ● ● Anderson School District Five Page 3 Textbook Reference # of Blocks (90 min) 1.5 3.1 3.2 3.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 2 Angles and Lines Essential Tasks/Key Concepts Textbook Reference Resources/Activities ● ● Island Conquer Game Geoboard Area & Perimeter ● ● http://alex.state.al.us/lesson_view.php?id=24037 (Geometry City) https://sites.google.com/site/salamancamath/MathClasses/graphing/geom etry-projects/garden-project (Creating a Garden Project) (G.GGPE.5) ● Application problems of parallel and perpendicular lines ● ● ● City Project Common Core Activities for Parallel and Perpendicular Worksheet on Parallel and Perpendicular Equations 3.4 (G.GCO.11) ● Construct parallel and perpendicular lines using geometry tools ● Construct perpendicular bisectors and circumcenters in triangles ● Construct angle bisectors and incenters in triangles ● ● ● ● ● ● ● ● ● Concurrency with Patty paper Points of Concurrency worksheet Concurrency Word Search PowerPoint on Constructing Parallel and Perpendicular Worksheet on Constructing Parallels and Perpendiculars Paper Folding Activity for points of Concurrency Archeology and Points of Concurrency The Search for Pythagoras’ Treasure Points of Concurrency 3.6 5.2 (G.GGPE.5) ● Slopes of parallel and perpendicular lines ● Equations of parallel and perpendicular lines Review and Unit Test Anderson School District Five Page 4 3.3 3.4 3.7 3.8 # of Blocks (90 min) 2.0 0.5 1.5 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 3 – Relationships in Triangles and Logic G.GCO.9* G.GCO.9c G.GCO.9d G.CO.10 G.GSRT.3* G.GSRT.4* G.GSRT.4a G.GSRT.4b Prove, and apply in mathematical and real-world contexts, theorems about the relationship within and among triangles, including the following: the segment joining midpoints of two sides of a triangle is parallel to the third side of half the length; the medians of a triangle meet at a point. Prove that two triangles are similar suing the Angle-Angle criterion and apply the proportionality of corresponding sides to solve problems and justify results. Prove, and apply in mathematical and real-world contexts, theorems involving similarity about triangles, including the following: A line drawn parallel to one side of a triangle divides the other two sides into parts of equal proportion. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Unit 3 - Relationships in Triangles and Logic Essential Tasks/Key Concepts (G.GCO.9) ● Two Column Proofs ● Law of Syllogism ● Paragraph Proof (G.GCO.9, G.GCO.9c, G.GCO.9d, G.GSRT.4, G.GSRT.4a, G.GSRT.4b) ● Side Splitter Theorem ● Geometric Mean ● Midsegements Resources/Activities ● Different Methods of Proof ● ● http://www.mathsteacher.com.au/year7/ch09_polygons/02_anglesum/su m.htm (Sum of Triangles) http://www.regentsprep.org/Regents/math/geometry/GP5/TRTri.htm (Discover Triangle Sum) http://illuminations.nctm.org/ActivityDetail.aspx?ID=9 (Triangle Sums) ● ● ● Midsegments Worksheet Geometric Mean Activity Constructing Midsegments Worksheet ● http://handsonmathinhighschool.blogspot.com/2012/07/made4mathgeometry-proofs.html (fill in proofs) http://www.thinkfun.com/smartplayblog/?p=186 (Chocolate Lab for Proofs) http://www.regentsprep.org/Regents/math/geometry/GP10/MidLineR.htm (Discovering Midsegments) ● ● ● Anderson School District Five Page 5 Textbook Reference # of Blocks (90min) 2.4 3.5 4.5 2.0 2.5 2.6 5.1 7.4 7.5 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 3 - Relationships in Triangles and Logic Essential Tasks/Key Concepts Resources/Activities (G.GSRT.3) ● AA ● ● ● How Tall is the Wall Activity Worksheet on Proving Triangles Similar Similar Triangles Project Test Day and Review Anderson School District Five Textbook Reference # of Blocks (90min) 7.3 1.0 2.0 Page 6 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 4 – Triangle Congruency G.GCO.7* G.GCO.9a G.GCO.9b G.GSRT.5* Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions. measures of interior angles or a triangle sum to 180°; base angles of isosceles triangles are congruent; Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Unit 4 – Triangle Congruency Essential Tasks/Key Concepts (G.GCO.7, G.GCO.9a, G.GCO.9b) ● ASA, SAS, SSS ● Sum of angles in a triangle is 180° ● Base angles of Isosceles triangles are congruent ● ● ● ● ● ● ● ● Congruent Triangle Patty Congruent Triangle Project Triangle Congruency Practice Triangle Congruency Quiz 1 and Quiz 2 Lesson on Congruent Triangles Discovering Congruent Triangles Lab Worksheet on Congruent Triangles Why not SSA ● http://www.youtube.com/watch?v=TPL12Tk7L6U (video on lesson to teach triangle congruence) http://mste.illinois.edu/courses/ci303fa01/students/kethoms1/unitplan/day 4.html (Fetticini and Congruent Triangles) http://www.k12.hi.us/~mathappl/im12tri.htm (idea for teaching congruent triangles) https://sites.google.com/site/salamancamath/MathClasses/graphing/geom etry-projects/ch4-tri-tri-again-project (Build a Bridge) ● ● ● Anderson School District Five Textbook Reference Resources/Activities Page 7 # of Blocks (90 min) 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 4 – Triangle Congruency Essential Tasks/Key Concepts (G.SRT.2) ● CPCTC ● AA Textbook Reference Resources/Activities ● ● ● ● ● ● Building Congruent Triangles Discovering Congruent Triangles Lesson on Discovering Triangle Congruence Similar Triangles and Heights Investigating Similar Triangles Investigating Similar Right Triangles ● http://illuminations.nctm.org/ActivityDetail.aspx?ID=4 (Activities for CPCTC) https://sites.google.com/site/salamancamath/ch8-measure-for-measure (Star Gazing) ● Review and Unit Test Anderson School District Five Page 8 # of Blocks (90 min) 2.0 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 5 – Right Triangles G.GSRT.4c G.GSRT.6* G.GSRT.7 G.GSRT.8* The square of the hypotenuse of a right triangle is equal to the sum of squares of the other two sides. Understand how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle. Explain and use the relationship between the sine and cosine of complementary angles. Solve right triangles in applied problems using trigonometric ratios and the Pythagorean Theorem. Unit 5 – Right Triangles Essential Tasks/Key Concepts (G.GSRT.4c) ● Pythagorean Theorem and its converse (G.GSRT.6, G.GSRT.7, G.GSRT.8) ● Sine, Cosine, Tangent ● Special Right Triangles Anderson School District Five Textbook Reference Resources/Activities ● ● ● ● ● ● ● ● ● Pythagorean Theorem Pythagorean Theorem and Converse Pythagorean Theorem with Algebra Pythagorean Spiral Project and Rubric Developing the Pythagorean Theorem Pythagorean Theorem Activities Pythagorean Theorem Game http://www.nbclearn.com/nfl/cuecard/51220 (Geometry & the NFL) http://www.math-play.com/Pythagorean-Theorem-Jeopardy/PythagoreanTheorem-Jeopardy.html (Jeopardy) ● ● ● ● ● ● ● ● ● ● Is the Handicap Ramp Legal? A Day at the Park Measuring Height with Trigonometry Water Balloon Launch Project Trigonometry Word Problems Investigating Trigonometry Ratios Trigonometry Activities Building Bridges Task Building Bridges Lesson Trigonometry Project ● http://blogs.warwick.ac.uk/emmacooke/entry/discovering_the_trig/ (discovering trig ratios) Page 9 # of Blocks (90 min) 1.5 8.1 8.2 8.3 8.4 3.5 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 5 – Right Triangles Essential Tasks/Key Concepts ● ● CONTINUED FROM PREVIOUS PAGE ● ● ● ● ● ● ● Law of Sines and Cosines (Extension: This is not a standard, but if time allows, please cover.) Textbook Reference Resources/Activities ● ● ● ● ● http://www.curriculumsupport.education.nsw.gov.au/secondary/mathemat ics/years7_10/teaching/trig.htm (Same shape lesson to explore trig ratios) http://illuminations.nctm.org/LessonDetail.aspx?id=L785 (Discover relationships of trig functions) http://illuminations.nctm.org/LessonDetail.aspx?ID=L383 (trig ratios) http://www.teachengineering.org/view_activity.php?url=http://www.teach engineering.org/collection/cub_/activities/cub_navigation/cub_navigation_l esson03_activity2.xml (Trig River Activity) http://illuminations.nctm.org/LessonDetail.aspx?ID=L703 (Develop law of sines) http://illuminations.nctm.org/LessonDetail.aspx?ID=L704 (Develop law of cosines) http://www.regentsprep.org/Regents/math/algtrig/ATT12/derivelawofsines .htm (develop both) http://www.algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigLa wSines.xml (Sines) https://www.teachingchannel.org/videos/laws-of-sines-cosines-lesson (applying laws of sine and cosine) http://hilbertshotel.wordpress.com/2013/01/27/a-better-law-ofsinescosines-project/ (Project) http://www.regentsprep.org/Regents/math/algtrig/ATT12/rescuelab.htm (Rescue Team Project) http://www.foresthills.edu/userfiles/161/Classes/5071/6.16.2%20Applications%20Worksheet.pdf (Wksht) http://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/U9L5T rigonometricApplications.pdf (Worksheet with applications) Review and Unit Test Anderson School District Five Page 10 # of Blocks (90 min) CONTINUED FROM PREVIOUS PAGE 8.5 8.6 1.0 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 BEGIN UNIT 6 BEFORE MIDTERM MIDTERM EXAM Anderson School District Five Page 11 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 6 - Quadrilaterals G.GCO.10* G.GCO.10a G.GCO.10b G.GCO.10c G.GCO.10d G.GCO.10e G.GGPE.4* Prove, and apply in mathematical and real-world contexts, theorems about parallelograms, including the following: opposite sides of a parallelogram are congruent; opposite angles of a parallelogram are congruent; diagonals of a parallelogram bisect each other; rectangles are parallelograms with congruent diagonals; a parallelogram is a rhombus if and only if the diagonals are perpendicular. Use coordinates to prove simple geometric theorems algebraically. Unit 6 - Quadrilaterals Essential Tasks/Key Concepts (G.GCO.10, G.GCO.10a, G.GCO.10b, G.GCO.10c, G.GCO.10d, G.GCO.10e) ● Understand and prove properties of parallelograms Resources/Activities ● ● ● ● ● ● ● ● Introduction to Polygons Property Check List Fill in Properties of Quadrilaterals Parallelogram Worksheet Parallelogram Jigsaw Activity Shape Tree Diagram Trapezoid and Kite Worksheet Sidewalk Chalk Shapes ● http://www.nsa.gov/academia/_files/collected_learning/high_school/geom etry/quadrilaterals1.pdf (Lessons on parallelograms with discovery) http://illuminations.nctm.org/LessonDetail.aspx?id=L350 (discover properties) http://havefunteaching.com/songs/shape-songs/parallelogram-song/ (parallelogram song) http://www.learner.org/channel/schedule/printmat.phtml?printmat_id=97 (teaching activities) http://www.successlink.org/gti/lesson_unit-viewer.asp?lid=3385 (Investigating parallelograms) http://alex.state.al.us/lesson_view.php?id=3009 (parallelogram mystery) http://hiregloriagranum.weebly.com/uploads/8/0/1/0/8010192/mathemati cs_module_assignment_8.pdf (lesson on parallelograms) https://sites.google.com/site/salamancamath/MathClasses/graphing/geom etry-projects/chapter-5-go-fly-a-kite (Making a Kite) ● ● ● ● ● ● ● Anderson School District Five Page 12 Textbook Reference # of Blocks (90 min) 6.1 6.2 6.3 6.4 6.5 6.6 3.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 6 - Quadrilaterals Essential Tasks/Key Concepts Resources/Activities (G.GGPE.4) ● Prove most precise quadrilateral using coordinates using distance formula and slope ● Determine the most precise quadrilateral formed by equations of lines ● ● ● http://www.regentsprep.org/Regents/math/geometry/GCG4/Coordinateres ource.htm (coordinate challenge) http://www.regentsprep.org/Regents/math/geometry/GCG4/CoordinatepR ACTICE.htm (practice proofs) http://www.atlanta.k12.ga.us/cms/lib/GA01000924/Centricity/Domain/262 /Math_1_APS_Teacher_Edition_Unit_6.v5.pdf (several activities) Review and Unit Test Anderson School District Five Page 13 Textbook Reference # of Blocks (90 min) 6.7 6.8 6.9 2.0 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 7 - Transformations G.GCO.2* G.GCO.3* G.GCO.4* G.GCO.5* G.GCO.6* G.GSRT.1 G.GSRT.2* Represent translations, reflections, rotations, and dilations of objects in the plane by using paper folding, sketches, coordinates, function notation, and dynamic geometry software, and use various representations to help understand the effects of simple transformations and their compositions. Describe rotations and reflections that carry a regular polygon onto itself and identify types of symmetry of polygons, including line, point, rotational, and self-congruence, and use symmetry to analyze mathematical situations. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Predict and describe the results of transformations on a given figure using geometric terminology from the definitions of the transformations, and describe a sequence of transformations that maps a figure onto its image. Demonstrate that triangles and quadrilaterals are congruent by identifying a combination of translations, rotations, and reflections in various representations that move one figure onto the other. Understand 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. Verify experimentally the properties of dilations given by a center and a scale factor. Understand the dilation of a line segment is longer or shorter in the ratio given by the scale factor. Use the definition of similarity to decide if figures are similar and justify decision. Demonstrate that two figures are similar by identifying a combination of translations, rotations, reflections, and dilations in various representations that move one figure onto the other. Unit 7 - Transformations Essential Tasks/Key Concepts (G.GCO.2, G.GCO.4) ● Preserving distance and angle measures when performing transformations. ● Transformations in terms of functions. (G.GCO.2) ● Perform and determine transformations applied to rectangles, parallelograms, trapezoids, and regular polygons. Resources/Activities ● ● ● ● ● ● ● Making a Tessellation with Patty Paper Penrose Tiles with Answers Wind Chime Project Exploring Geometric Transformations Transformation and Translation Lesson Flips and Turns Activities on Symmetry and Transformations ● http://www.mathsisfun.com/geometry/transformations.html (shows translations and transformations) http://www.regentsprep.org/Regents/math/geometry/GT2/indexGT2.htm (Translations) http://www.projectmaths.ie/students/cdstrand1and2/docs4/spongebob.html (Symmetry of Sponge Bob) http://www.kidsmathgamesonline.com/geometry.html (Transformation Games) http://staff.argyll.epsb.ca/jreed/math9/strand3/transformations.htm (interactive on computer) ● ● (G.GCO.4) ● General properties of transformations such as equal distance from between points in both preimage and post image. Anderson School District Five ● ● Page 14 Textbook Reference # of Blocks (90 min) 9.1 9.2 9.3 9.4 2.5 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 7 - Transformations Essential Tasks/Key Concepts Resources/Activities (G.GCO.2) ● Construction of transformations (rotations). (G.GCO.3, G.GCO.5, G.GCO.6) ● Determine if two shapes are congruent, then determine the composition of transformations used. (G.GSRT.1, G.GSRT.2) ● Use scale factors to perform dilations on lines, triangles, and polygons. ● Define/discover characteristics of dilations (picture on pg. 587) ● Geometry Rotation and Dilation ● http://www.superteacherworksheets.com/geometry/translation-rotationreflection-1_TZQTQ.pdf (Worksheet) http://www.superteacherworksheets.com/geometry/translation-rotationreflection-2_TZQTM.pdf (Worksheet) http://www.jmap.org/JMAP/RegentsExamsandQuestions/PDF/Worksheets ByPITopic/Geometry/Transformational_Geometry/G.G.60.IdentifyingTransform ations.pdf (identify transformations) ● ● ● ● ● ● Dilation and Scale Factor Worksheet Scale Models Dilation Project Almagamation Art (Uses dilations, transformations, and translations) ● http://www.lemars.k12.ia.us/webfiles/mboyd/PreAlgebra%20Textbook%20(e-edition)/Source/J9D13GAD.pdf (Dilations) http://tellier.edublogs.org/2011/10/24/super-size-me-project-3/ (supersize me project) # of Blocks (90 min) 9.1 9.2 9.3 9.4 0.5 9.5 1.0 9.6 ● (G.GSRT.2) ● Determine if two shapes are similar, then determine the composition of transformations used. 1.0 9.7 Review and Unit Test Anderson School District Five Textbook Reference Page 15 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 8 - Area G.GGPE.7* G.GM.1* Use the distance and midpoint formulas to determine distance and midpoint in a coordinate plane, as well as areas of triangles and rectangles, when given coordinates. Use geometric shapes, their measures, and their properties to describe real-world objects. Unit 8 - Area Essential Tasks/Key Concepts Resources/Activities (G.GM.1) ● Application of areas of geometric shapes (G.GGPE.7. G.GM.1) ● Find the area of: o Parallelograms o Triangles o Trapezoids o Rhombi o Kites ● Use distance formula for computing area and perimeter of shapes. (G.GGPE.7, G.GM.1) ● Determine area of regular polygons using: o Properties of Special Right Triangles o Trigonometry (G.GGPE.7) ● Use A = ½ ab sin(C) to find area of irregular triangles given SAS ● ● Island Conquer Game Geoboard Area & Perimeter ● ● http://alex.state.al.us/lesson_view.php?id=24037 (Geometry City) https://sites.google.com/site/salamancamath/MathClasses/graphing/geom etry-projects/garden-project (Creating a Garden Project) ● Circle Folding Activity ● ● http://nrich.maths.org/public/leg.php?code=97 (Various Activities) http://www.mathopenref.com/constinhexagon.html (Video to inscribe a hexagon) http://alex.state.al.us/lesson_view.php?id=32262 (Constructions using GeoGebra) ● ● ● http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 (deriving area) http://www.regentsprep.org/Regents/math/algtrig/ATT13/areatriglesson.h tm (How to derive) Review and Unit Test Anderson School District Five Page 16 Textbook Reference # of Blocks (90 min) Most of Chapter 10 Throughout Unit 10.1 10.2 2.0 10.3 10.4 2.0 10.5 0.5 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 9 – 3-Dimensional Figures G.GGMD.1* G.GGMD.2 G.GGMD.3* G.GGMD.4* G.GM.1* G.GM.2 Explain the derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone. Apply these formulas to solve mathematical and real-world problems. Explain the derivation of the formulas for the volume of a sphere and other solid figures using Cavalieri’s principle. Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and justify results. Include problems that involve algebraic expressions, composite figures, geometric probability, and real-world applications. Describe the shapes of two-dimensional cross-sections of three-dimensional objects and use those cross-sections to solve mathematical and realworld problems. Use geometric shapes, their measures, and their properties to describe real-world objects. Use geometry concepts and methods to model real-world situations and solve problems using a model. Unit 9 – 3-Dimensional Figures Essential Tasks/Key Concepts (G.GGMD.4) ● Identify cross sections of 3D figures ● Identify that a cone is a rotation of a triangle, a sphere is a rotation of a circle, and a cylinder is a rotation of a rectangle. (G.GMD.1, G.GMD.3, G.GM.1, G.GM2) ● Applications of geometric shapes such as objects in the classroom or a tree trunk. ● Surface Area Anderson School District Five Textbook Reference Resources/Activities ● ● ● ● ● ● ● ● ● ● Making Nets of 3 Dimensional Figures 3D Review (1st 2 Stages) and Key Review Surface Area Review Surface Area and Volume Household Item Project Exploring 3D Geometry Notes on Making 3D Shapes from Rotations Rotate to Form Solids Geometric Shape Project Geometry Treats ● http://www.ehow.com/info_7891957_ideas-teaching-cross-sections.html (lots of ideas for presenting) http://ispeakmath.org/2012/05/28/volume-of-3d-shapes-with-play-doh (play doh ideas) ● Page 17 # of Blocks (90 min) 11.1 3.0 11.2 11.3 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 9 – 3-Dimensional Figures Essential Tasks/Key Concepts (G.GMD.3, G.GM.1, G.GM2) ● Formulas: ➢ Circumference of a circle ➢ Area of a circle ➢ Volume of a cylinder, pyramid, and cone ● ● ● ● ● ● ● ● ● ● ● ● (G.GGMD.2) ● Informal argument of Cavalieri’s principle (G.GGMD.2, G.GMD.3, G.GM.1, G.GM2) ● Application of volume formulas Textbook Reference # of Blocks (90 min) Student Formula Sheet Review Volume Inquiry Lesson on Circumference Parachutes and Circles Big Ideas Math – Circles and Circumference http://illuminations.nctm.org/LessonDetail.aspx?ID=L573 (ratio of circumference to diameter) http://alex.state.al.us/lesson_view.php?id=26202 (discovery lesson for circumference) http://www.youtube.com/watch?v=YokKp3pwVFc (derive the formula for Area) http://www.educationworld.com/a_tsl/archives/00-2/lesson0011.shtml (derive area of circle) http://www.youtube.com/watch?v=SYJsrUby6Zg (target practice application) http://illuminations.nctm.org/ActivityDetail.aspx?ID=116 (investigation) http://www.cut-the-knot.org/Curriculum/Calculus/Cavalieri.shtml (Cavalieri Principle) http://books.google.com/books?id=B4HPFu_uaIC&pg=PA107&lpg=PA107&dq=activities+to+teach+cavalieri's+principl e&source=bl&ots=YkhyrfJRcT&sig=1I_VPuV6EAv96Fb-Ui4GvqcKnU&hl=en&sa=X&ei=JV7sUbj2E6rj4APmhIDABg&ved=0CDkQ6AEwAg#v =onepage&q=activities%20to%20teach%20cavalieri's%20principle&f=fals e (Activity for Cavalieri Prin) 11.4 3.0 Crush and Run http://www.learner.org/interactives/geometry/area_surface.html (surface area and volume) http://www.scholastic.com/teachers/article/hands-ways-teach-area-andvolume (teaching ideas) 11.4 11.5 11.6 1.0 Resources/Activities ● ● ● ● Review and Unit Test Anderson School District Five Page 18 2.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 10 - Circles G.GCI.1 G.GCI.2* G.GCI.3 G.GCI.4 G.GCI.5* G.GGPE.1* Prove that all circles are similar. Identify and describe relationships among inscribed angles, radii, and chords; among inscribed angles, central angles, and circumscribed angles; and between radii and tangents to circles. Use those relationships to solve mathematical and real-world problems. Construct the inscribed and circumscribed circles of a triangle using a variety of tools, including a compass, a straightedge, and dynamic geometry software, and prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line to a circle through a point on the circle, and construct a tangent line from a point outside a given circle to the circle; justify the process used for each construction. Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world problems. Understand that the standard equation of a circle is derived from the definition of a circle and the distance formula. Unit 10 - Circles Textbook Reference Essential Tasks/Key Concepts Resources/Activities (G.GCI.1) ● Prove circles are similar ● Ratios of circumference and area are similar ● ● ● ● Worksheet on Circles and Similarity Similarities in Circles and Arcs Sectors of Pizza Circles (G.GCI.2, G.GCI.5) ● Central angles and arc length are proportional ● Area of a sector ● ● ● http://middleschoolatsage.weebly.com/uploads/5/2/5/8/5258770/g.c.1_g. c.5_copy.pdf (Activities) http://www.geom.uiuc.edu/~dwiggins/conj44.html (Arcs) http://alex.state.al.us/lesson_view.php?id=26412 (Sector Area) ● ● ● ● ● ● ● ● Circle Intro ; Printable Circle Intro ; Circle Intro Answer Goat Farmer Pizza Problem Broken Pottery Activity Circle Worksheet Circle Conjectures Geometry Construction Project Tangent and Chord Properties ● http://freemotionquilting.blogspot.com/2010/01/day-123-angles-andcircles.html (Quilt Project) (G.GCI.2, G.GCI.4) ● Identify and determine the relationships in the following: ➢ Central angle ➢ Inscribed angles ➢ Circumscribed angles ➢ Diameters ➢ Radii ➢ Chords ➢ Tangents Anderson School District Five Page 19 # of Blocks (90 min) 10.6 1.0 10.6 10.7 12.1 12.2 12.4 3.0 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 10 - Circles Essential Tasks/Key Concepts (G.GCI.5, G.GCI.3) ● Arc Addition Postulate ● Properties of angles for quadrilateral inscribed in a circle ● Opposite angles of inscribed quadrilateral are supplementary ● Inscribed, circumscribed, angle bisector, perpendicular bisector (G.GCI.1. G.GGPE.1) ● Determine the equation of a circle using: ➢ Radius and point ➢ Two points ➢ Completing the square ➢ Inscribed in an equilateral triangle Review and Unit Test Anderson School District Five Resources/Activities ● ● ● Discovering the Properties of an Inscribed Quadrilateral Points of Concurrency Constructions including Bisectors ● http://www.ck12.org/geometry/Inscribed-Quadrilaterals-in-Circles/ (videos and other things) ● ● Equation of a Circle Lab Inscribed Right Triangles ● ● http://www.youtube.com/watch?v=pZVufpgozCw (video to derive from Pythagorean Theorem) http://www.regentsprep.org/Regents/math/algtrig/ATE12/completesqlesso n.htm (How to complete the square) http://alex.state.al.us/lesson_view.php?id=6690 (Circles) ● ● Circle Review Circle Review 2 ● Textbook Reference # of Blocks (90 min) 12.3 2.0 12.5 2.0 2.0 Page 20 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 11 – Statistics G.SPID.1* G.SPID.2* G.SPID.3* Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers. Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers. Summarize and represent data from a single data set. Interpret differences in shape, center, and spread in the context of the data set, accounting for possible effects of extreme data points (outliers). Unit 11 - Statistics Essential Tasks/Key Concepts (G.SPID.1) ● Make dot plots, histograms, and box and whisker plots with appropriate sets of data (G.SPID.2) ● Calculate measures of spread (variance, standard deviation, range, and quartiles) (G.SPID.2, G.SPID.3) ● Compare multiple sets of data using the same type of display (such as one box plot to another box plot) ● Compare center and spread between two or more data sets Anderson School District Five Resources/Activities Textbook Reference # of Blocks (90 min) N/A 1.5 ● ● ● Fruit Loops Activity for Boxplots Worksheet Frequency Tables & Histogram worksheet Histogram Lesson Worksheet ● ● http://illuminations.nctm.org/LessonDetail.aspx?ID=L737 (NBA Data) http://www.scholastic.com/browse/lessonplan.jsp?id=459 (Lesson to use histogram about flood damage) ● ● Deriving Standard Deviation Worksheet Hair Measuring Activity Worksheet N/A 1.5 ● http://www.educationworld.com/a_lesson/03/lp293-02.shtml (Using candy colors to find mean, median, mode) http://www.proteacher.org/c/336_Mean,_Median,_and_Mode.html (Has several ideas) http://pinterest.com/carolann1956/mean-median-mode-and-range/ (Many ideas from pinterest) N/A 1.0 ● ● Page 21 2015-2016 Geometry Honors – Curriculum Pacing Guide – 2015-2016 Unit 11 - Statistics Essential Tasks/Key Concepts (G.SPID.3) ● Calculate outliers using the interquartile range ● Determine if a data value is an outlier based on the standard deviation Resources/Activities ● Effects of outliers worksheet ● http://illuminations.nctm.org/LessonDetail.aspx?ID=L455 (effects) Review and Test Textbook Reference # of Blocks (90 min) N/A 1.0 2.0 END OF COURSE EXAM Anderson School District Five Page 22 2015-2016