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Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 1 Copyright July 1, 2013
Unit 1 – Basics of Geometry G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance
along a line, and distance around a circular arc.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★
Unit 1 – Basics of Geometry
Concepts/Essential Knowledge Resources/Activities Textbook Reference
# of Blocks (90 min)
(G.CO.1)
Terminology point
line
intersection
rays
segments
vertex, angle
acute
obtuse
right
straight
interior
exterior
postulate (if, then)
theorem (if and only if)
congruence
parallel
perpendicular
Exploring Points and Planes
Basic Terms Activities
Points, Lines Planes Lesson Plan
1.2
1.3 1.4
2.2
2.3
1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 2 Copyright July 1, 2013
Unit 1 – Basics of Geometry
Concepts/Essential Knowledge Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.CO.12) Construct:
Triangles
Perpendicular bisector
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)
1.6 1.0
(G.GPE.6)
Midpoint formula Addition postulates
midpoint formula
segment bisector
angle addition
segment addition
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)
1.7 0.5
(G.GPE.7)
Distance formula
Deriving Midpoint and Distance Formula
http://www.regentsprep.org/Regents/math/geometry/GCG3/Tdistance.htm
(Distance Formula Game)
http://www.mathwarehouse.com/algebra/distance_formula/interactive-
distance-formula.php (Interactive Distance Formula)
1.7 0.5
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 3 Copyright July 1, 2013
Unit 2 Angles and Lines G.CO.9 Prove theorems about lines and angles. Theorems 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 segment are exactly those equidistant from the segment’s endpoints.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working
with typographic grid systems based on ratios).★
Unit 2 Angles and Lines
Essential Tasks/Key Concepts Resources/Activities Textbook Reference
# of Blocks (90 min)
(G.CO.9)
Properties of: Vertical angles
Corresponding angles
Angles Bisectors
Alternate interior and exterior
Transversals
Perpendicular bisectors
Discovering Parallel Lines
Parallel Lines Practice
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
Worksheet on Medians and Altitudes
Different Methods of Proof
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
1.5
3.1 3.2
3.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 4 Copyright July 1, 2013
Unit 2 Angles and Lines
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.GPE.5)
Slopes of parallel and perpendicular lines
Equations of parallel and perpendicular
lines
Explore parallel and perpendicular lines
Island Conquer Game
Geoboard Area & Perimeter
http://pinterest.com/lleyden/math-area-perimeter/ (ideas)
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)
3.3 3.4
3.7 3.8
2.0
(G.MG.3) 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.CO.12)
Construct parallel and perpendicular lines
using geometry tools
Perpendicular bisectors and circumcenters in triangles
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
1.0
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 5 Copyright July 1, 2013
Unit 3 – Triangle Congruency G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity 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 similarity transformations to establish the AA criterion for two triangles to be similar.
Unit 3 – Triangle Congruency
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.CO.8) ASA, SAS, SSS
Congruent Triangle Patty
Congruent Triangle Project
Triangle Congruency Practice
Triangle Congruency Quiz and Quiz 2
Lesson on Congruent Triangles
Discovery Congruent Triangles Lab
Worksheet on Congruent Triangles
Why not SSA
Congruent Triangles Project
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)
4.1 4.2
4.3 4.4
4.6
4.7 7.3
2.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 First Nine Weeks
Anderson School District Five Page 6 Copyright July 1, 2013
Unit 3 – Triangle Congruency
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.SRT.2) CPCTC
AA
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)
2.0
(G.SRT.3)
AA
How Tall is the Wall Activity
Worksheet on Proving Triangles Similar
Similar Triangles Project
1.0
Review and Unit Test 1.5
End of First Nine Weeks 2.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 7 Copyright July 1, 2013
Unit 4 – Relationships within Triangles G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Unit 4 – Relationships within Triangles
Essential Tasks/Key Concepts Resources/Activities Textbook Reference
# of Blocks (90 min)
(G.SRT.4, G.SRT.5)
Side Splitter Theorem
Geometric Mean
Midsegements
Midsegement worksheet
Geometric Mean Activity
Constructing Midsegments Worksheet
http://handsonmathinhighschool.blogspot.com/2012/07/made4math-
geometry-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)
2.5
2.6 5.1
7.4
7.5
2.0
(G.CO.10)
SAS, ASA, SSS, HL, AAS
Two Column Proofs
CPCTC
Law of Syllogism
Paragraph Proof
Fill in the blank triangle proofs 1 and 2
Triangle Congruency Proofs
Triangle Congruency Proofs Quiz
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)
2.4
3.5 4.5
3.0
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 8 Copyright July 1, 2013
Unit 5 – Right Triangles G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios
for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Unit 5 – Right Triangles
Essential Tasks/Key Concepts Resources/Activities Textbook Reference
# of Blocks (90 min)
(G.SRT.8)
Pythagorean Theorem and its converse
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/Pythagorean-
Theorem-Jeopardy.html (Jeopardy)
8.1
8.2 8.3
8.4
1.0
(G.SRT.6)
Sine, Cosine, Tangent
Cosine, Secant, Cosecant
Special Right Triangles
Is the Handicap Ramp Legal?
A Day at the Park
Measuring Height with Trigonometry
Water Balloon Launch
Trigonometry Word Problems
Investigating Trigonometry Ratios
Trig Activities
Building Bridges Task
Building Bridges Lesson
Trig Project
http://www.curriculumsupport.education.nsw.gov.au/secondary/mathemat
ics/years7_10/teaching/trig.htm (Same shape lesson to explore trig ratios) http://blogs.warwick.ac.uk/emmacooke/entry/discovering_the_trig/
(discovering trig ratios)
3.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 9 Copyright July 1, 2013
Unit 5 – Right Triangles
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.SRT.7) 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)
0.5
(G.SRT.10, G.SRT.11)
Law of Sines and Cosines
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-of-
sinescosines-project/ (Project)
http://www.regentsprep.org/Regents/math/algtrig/ATT12/rescuelab.htm
(Rescue Team Project) http://www.foresthills.edu/userfiles/161/Classes/5071/6.1-
6.2%20Applications%20Worksheet.pdf (Wksht)
http://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/U9L5T
rigonometricApplications.pdf (Worksheet with applications)
8.5
8.6
1.0
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 10 Copyright July 1, 2013
Unit 6 - Quadrilaterals G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
Unit 6 - Quadrilaterals
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.CO.11)
Understand and prove properties of
parallelograms
Introduction to Polygons
Property Check List
Fill in Properties of Quadrilaterals
Parallelogram Worksheet Honors
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/mathematic
s_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)
6.1
6.2
6.3 6.4
6.5 6.6
3.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 11 Copyright July 1, 2013
Unit 6 - Quadrilaterals
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.GPE.4) Prove using coordinates using distance
formula and slope
Disprove isosceles right triangles
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)
6.7 6.8
6.9
2.0
Review and Unit Test 1.5
Review and Midterm Exam 2.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Second Nine Weeks
Anderson School District Five Page 12 Copyright July 1, 2013
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 13 Copyright July 1, 2013
Unit 7 - Area G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
G.SRT.9 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Unit 7 - Area
Essential Tasks/Key Concepts Resources/Activities Textbook Reference
# of Blocks (90 min)
(G.MG.1)
Application of areas of geometric shapes
Most of
Chapter 10
(G.GPE.7) Use distance formula for computing area
and perimeter of shapes.
Island Conquer Game
Geoboard Area & Perimeter
http://pinterest.com/lleyden/math-area-perimeter/ (ideas)
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)
10.1 10.2
1.5
(G.CO.13) Construct stated shapes in a circle using
interior angle measures.
Determine area of regular hexagon
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)
10.3 10.4
1.0
(G.SRT.9)
Use A = ½ ab sin(C) to find area of
irregular triangles
http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 (deriving area)
http://www.regentsprep.org/Regents/math/algtrig/ATT13/areatriglesson.h
tm (How to derive)
10.5 1.5
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 14 Copyright July 1, 2013
Unit 8 - Circles G.C.1 Prove that all circles are similar.
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.
G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a
circle given by an equation.
Unit 8 - Circles
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.C.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
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)
10.6 1.0
(G.C.5) Central angles and arc length are
proportional
Area of a sector
10.6 10.7
(G.C.2)
Identify and determine the relationships in
the following:
Central angle Inscribed angles
Circumscribed angles Diameters
Radii Chords
Tangents
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-and-
circles.html (Quilt Project)
12.1
12.2
12.4
2.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 15 Copyright July 1, 2013
Unit 8 - Circles
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.C.3, G.C.4) 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
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)
12.3 1.0
(G.GPE.1)
Determine the equation of a circle using:
Radius and point Two points
Completing the square
Inscribed in an equilateral triangle
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)
12.5 1.0
Review and Unit Test Circle Review
Circle Review 2 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 16 Copyright July 1, 2013
Unit 9 - Transformations G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points
in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch). G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two
figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions 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 from the definition of congruence in terms of rigid motions. G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
G.SRT.1a 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.
G.SRT.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity 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 similarity transformations to establish the AA criterion for two triangles to be similar.
Unit 9 - Transformations
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.CO.2) Preserving distance and angle measures
when performing transformations.
Transformations in terms of functions.
Making a Tessellation with Patty Paper
Penrose Tiles
Wind Chime Project
Exploring Geometric Transformations
Transformation and Translation Lesson
Flips and Turns
Activities on Symmetry and Transformations
Transformations using Tangrams
http://www.mathsisfun.com/geometry/transformations.html (shows
translations and transformations)
http://www.regentsprep.org/Regents/math/geometry/GT2/indexGT2.htm
(Translations)
9.1 9.2
9.3
9.4
3.0
(G.CO.3)
Perform and determine transformations
applied to rectangles, parallelograms, trapezoids, and regular polygons.
(G.CO.4)
General properties of transformations
such as equal distance from between points in both preimage and post image.
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 17 Copyright July 1, 2013
Unit 9 - Transformations
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
http://www.projectmaths.ie/students/cd-
strand1and2/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.CO.5)
Construction of transformations.
9.1
9.2 9.3
9.4
0.5
(G.CO.6) Determine if two shapes are congruent,
then based of congruence what was the
transformation used.
Geometry Rotation and Dilation
http://dhs.dist113.org/Faculty/StevensonA/Homework/Geometry/Chapter
%204/Homework%20Answers/4.7%20Congruence%20Transformations%
20Answers.pdf (examples to identify) http://www.superteacherworksheets.com/geometry/translation-rotation-
reflection-1_TZQTQ.pdf (Wksht)
http://www.superteacherworksheets.com/geometry/translation-rotation-
reflection-2_TZQTM.pdf (Wksht)
http://www.jmap.org/JMAP/RegentsExamsandQuestions/PDF/WorksheetsB
yPI-Topic/Geometry/Transformational_Geometry/G.G.60.IdentifyingTransform
ations.pdf (identify transformations)
9.5
(G.CO.7)
Prove that corresponding angles and
corresponding sides are congruent if and only if the figures are congruent.
(G.CO.8)
Prove that corresponding angles and
corresponding sides are congruent if and only if the figures are congruent using
abbreviated theorems (SAS, ASA, SSS).
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Third Nine Weeks
Anderson School District Five Page 18 Copyright July 1, 2013
Unit 9 - Transformations
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.SRT.1, G.SRT.1a, G.SRT.1b, G.SRT.2, G.SRT.3)
Use scale factors to perform dilations on
lines, triangles, and polygons. Define/discover characteristics of dilations
(picture on pg. 587)
Dilation and Scale Factor Worksheet
Scale Models
Dilation Project
Almagamation Art (Uses dilations, transformations, and translations)
http://www.lemars.k12.ia.us/webfiles/mboyd/Pre-
Algebra%20Textbook%20(e-edition)/Source/J9D13GAD.pdf (Dilations)
http://tellier.edublogs.org/2011/10/24/super-size-me-project-3/ (supersize
me project)
9.6 1.5
(G.SRT.2)
Determine if two figures are similar based
on congruent angles and proportional sides.
9.7
(G.SRT.3)
Explain how AA similarity is enough to
prove two triangles similar. Use and explain the Third Angle Theorem
Review and Unit Test Vocabulary Book/Word List for Vocabulary 1.5
End of Third Nine Weeks 2.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 19 Copyright July 1, 2013
Unit 10 – 3-Dimensional Figures G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use
dissection arguments, Cavalieri’s principle, and informal limit arguments. G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations
of two-dimensional objects.
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★
G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).★
Unit 10 – 3-Dimensional Figures
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.GMD.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.
Making Nets of 3 Dimensional
3D Review (1st 2 Stages)
Review Surface Area
Review Surface Area and Volume
Household Item Project
Exploring 3D Geometry
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)
Notes on making 3D shapes from rotations
Rotate to form solids
Geometric Shape Project
Geometry Treats
11.1 2.0
(G.MG.1) Applications of geometric shapes such as
objects in the classroom or a tree trunk.
Surface Area
11.2 11.3
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 20 Copyright July 1, 2013
Unit 10 – 3-Dimensional Figures
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.GMD.1) Formulas:
Circumference of a circle
Area of a circle Volume of a cylinder, pyramid, and
cone
Student Formula Sheet
Review Volume
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)
Inquiry Lesson on Circumference
Parachutes and Circles
http://www.youtube.com/watch?v=YokKp3pwVFc (derive the formula for
Area) http://www.bigideasmath.com/protected/content/ipe_cc/grade%206/06/g
6_06_01.pdf (circumference)
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+principle&source=bl&ots=YkhyrfJRcT&sig=1I_VPuV6EAv96Fb-Ui4Gvqc-
KnU&hl=en&sa=X&ei=JV7sUbj2E6rj4APmhIDABg&ved=0CDkQ6AEwAg (Activity for Cavalieri Prin)
11.4 2.0
(G.GMD.2) Informal argument of Cavalieri’s principle
(G.GMD.3) Application of volume formulas
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-and-
volume (teaching ideas)
11.4 11.5
11.6
1.0
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 21 Copyright July 1, 2013
Unit 10 – 3-Dimensional Figures
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.MG.2) Density based on area and volume
Application problems of density
http://learni.st/users/171/boards/2104-density-word-problems-
applications-common-core-standard-g-mg-2#/users/171/boards/2104-density-word-problems-applications-common-core-standard-g-mg-2
(density apps) http://www2.vims.edu/bridge/DATA.cfm?Bridge_Location=archive1207.ht
ml (buoyancy)
https://www.teachingchannel.org/videos/teaching-density (teaching
density)
11.7 1.0
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 22 Copyright July 1, 2013
Unit 11 – Conics
G.GPE.2 Derive the equation of a parabola given a focus and directrix.
G.GPE.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Unit 11 – Conics
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(G.GPE.2) Determine the equation of a parabola
given
Determine the focus, vertex, and directrix
If a point is part of a parabola
Worksheet – Parabola & Circle
Review – Parts of Conics
Conics
Angry Bird Parabola Project
http://www.youtube.com/watch?v=uA-PcAyIQ7g (video lesson)
http://www.classzone.com/eservices/home/pdf/student/LA210BAD.pdf
(lesson on parabola) http://www.intmath.com/plane-analytic-geometry/4-parabola.php
(parabola interactive)
http://www.youtube.com/watch?v=goYnB61nrjg (super math bros
parabola project) http://www.stlprioryschool.org/index.php?option=com_content&view=artic
le&id=1259:math-students-learn-through-parabola-
project&catid=13&Itemid=278 (Parabola Project) http://theparabolaproject.blogspot.com/ (Constructivist Lesson on
Parabolas)
2.0
(G.GPE.3)
**Before discussing ellipses, briefly review circle equations as conics.**
Write equation of ellipses and hyperbolas
given the foci
May need to complete the square to solve
problems
Worksheet – Ellipse
Worksheet – Hyperbola
Review – Circle, Hyperbola, Ellipse
Powerpoint on Conics
My Favorite Conic Section Project
Conics Art Project
http://www.classzone.com/eservices/home/pdf/student/LA210EAD.pdf
(Lesson on Hyperbolas)
http://www.classzone.com/eservices/home/pdf/student/LA210FBD.pdf
(Graph & Classify Conics) http://illuminations.nctm.org/LessonDetail.aspx?id=L792 (Cutting Conics)
3.0
Review and Unit Test 1.5
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 23 Copyright July 1, 2013
Unit 12 - Probability S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,” “and,” “not”).
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 determine if they are independent.
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 same as the probability of A, and the conditional probability of B given A is the same 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 sample space to decide if events are independent and to approximate conditional probabilities.
S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Unit 12 - Probability
Essential Tasks/Key Concepts Resources/Activities Textbook Reference
# of Blocks (90 min)
(S.CP.1)
Sample space, unions, intersections,
completments Formulate a Venn diagram using data
Sample Space Activity
Hands on Activities for sample space and Probability
Venn Diagram Worksheet
Reading a Venn Diagram
Using Venn Diagrams
Shade the intersection and union on a Venn Diagram
Name the shaded region on a Venn Diagram
Set Notation and Venn Diagrams
Probability Packet
Word Problems and Venn Diagrams
http://www.regentsprep.org/Regents/math/ALGEBRA/APR4/PracSamp.htm
(Sample space problems) http://www.regentsprep.org/Regents/math/ALGEBRA/APR4/PracTre.htm
(Tree Diagrams)
13.1
13.2 13.5
1.0
(S.CP.4)
Two-way frequency tables with two
categories
Determine probabilities from frequency
tables
(S.CP.5)
Conditional probability
Independent and Dependent situations
Situational word problems
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 24 Copyright July 1, 2013
Unit 12 - Probability
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
http://community.prometheanplanet.com/en/blog/b/blog/archive/2011/04/
01/venn-diagrams-fun-activities-for-the-maths-classroom.aspx (Venn diagrams activities)
http://www.regentsprep.org/Regents/math/ALGEBRA/APR3/Tconditional.ht
m (Conditional Probability) http://www.shodor.org/interactivate/lessons/ConditionalProb/ (Interactive
Conditional Probability)
http://www.shodor.org/interactivate/lessons/IdeasLeadProbability/ (Intro
to Probability)
http://www.math.wisc.edu/~skubak/132fall2012/Probability%20Games%2
0Article.pdf (Probability Games) http://www.proteacher.org/c/493_probability.html (Ideas to teach
probability)
https://sites.google.com/site/salamancamath/MathClasses/graphing/geom
etry-projects/geometry-probability (Geometric Probability Project)
(S.CP.7)
Apply the Addition Rule of Probability
http://www.math.ccsu.edu/mitchell/GameShow.pdf (Game Show
Probability)
http://www.mathgoodies.com/lessons/vol6/addition_rules.html (Addition
Rules) http://www.youtube.com/watch?v=N6Neycnv93k (multiplication rule)
http://www.ehow.com/how_10017536_explain-sum-product-rules-
probability.html (Probability Rules)
permutations and combinations activities
http://www.wikihow.com/Teach-Combinations-Using-Drink-Markers
(teaching combinations) http://www.warrick.k12.in.us/schools/castlesouth/docs/Math/Math7Book/
Math%207%2013.6%20pg%20667.pdf (teaching independent events)
13.4
(If time permits teach
13.3 first)
2.0
(S.CP.8)
Apply general Mulitplication Rule of
Probability
(S.CP.9) Permutations and Combinations
Factorials, Fundemental Counting Principle
(S.CP.2) Determining if two events are
independent from each other
13.6
(S.CP.3) Conditional Probability
Independent and Dependent
Conditional Probability and Independence Worksheet
Relative probability Worksheet
Conditional Probability Worksheet
http://www.shodor.org/interactivate1.9/lessons/pm4.html (Conditional
probability)
(S.CP.6)
Conditional Probability using
Formula on pg. 856
Geometry Honors – Curriculum Pacing Guide – 2013 – 2104 Fourth Nine Weeks
Anderson School District Five Page 25 Copyright July 1, 2013
Unit 12 - Probability
Essential Tasks/Key Concepts Resources/Activities Textbook
Reference
# of Blocks
(90 min)
(S.MD.6) Determine fairness and if a situation is
fair/unbias
Rock Paper Scissors and Fairness
Real Life Probabilities
Probability Activities
http://www.teachersdomain.org/resource/vtl07.math.data.pro.lpprobgame
/ (Probability & Fairness)
http://illuminations.nctm.org/LessonDetail.aspx?id=L290 (Explorations in
chance) http://www.teachforever.com/2009/08/three-fun-probability-games-
and.html (Games)
http://www.math.wichita.edu/history/activities/prob-act.html#rock
http://classroom.jc-schools.net/basic/math-prob.html
http://www.education.com/activity/probability-statistics/
http://www.scholastic.com/probabilitychallenge/
http://www.mathgoodies.com/worksheets/probability_wks.html
(worksheets)
http://illuminations.nctm.org/LessonDetail.aspx?id=L248 (Game)
http://www.transum.org/software/sw/starter_of_the_day/Similar.asp?ID_T
opic=30 (starters)
13.7
(S.MD.7)
Using probability to make decisions in real
world situations
Review and Unit Test 1.5
Review and End of Course Exam 2.0
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