Download Geometry Honors – Curriculum Pacing Guide – 2015

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
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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
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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)
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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)
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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
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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
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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
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Island Conquer Game
Geoboard Area & Perimeter
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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
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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
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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
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Different Methods of Proof
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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)
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Midsegments Worksheet
Geometric Mean Activity
Constructing Midsegments Worksheet
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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)
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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
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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
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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)
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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
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Building Congruent Triangles
Discovering Congruent Triangles
Lesson on Discovering Triangle Congruence
Similar Triangles and Heights
Investigating Similar Triangles
Investigating Similar Right Triangles
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http://illuminations.nctm.org/ActivityDetail.aspx?ID=4 (Activities for
CPCTC)
https://sites.google.com/site/salamancamath/ch8-measure-for-measure
(Star Gazing)
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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
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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)
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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
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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
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CONTINUED FROM PREVIOUS PAGE
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Law of Sines and Cosines (Extension:
This is not a standard, but if time allows,
please cover.)
Textbook
Reference
Resources/Activities
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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
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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)
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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
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●
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
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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)
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●
(G.GCO.4)
● General properties of transformations
such as equal distance from between
points in both preimage and post image.
Anderson School District Five
●
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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)
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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)
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Dilation and Scale Factor Worksheet
Scale Models
Dilation Project
Almagamation Art (Uses dilations, transformations, and translations)
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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
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●
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