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