LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
Course: Geometry A
Department: Math
Grade(s): 9-12
Unit 1:
Rigid Motion
and
Transformations
(10 days)
Constructions of
Geometric Parts
& Figures
Essential Questions:
What are fundamental parts of geometric figures and how can they be formally
constructed?
How does rigid motion or a transformation affect a geometric figure?
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□G.CO.A.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.A.2 Represent transformations in the plane
Figures in Rigid
Motion
Transformations
in a Coordinate
Plane
Congruence
Using
Coordinate
Formulas
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.A.3 Given a rectangle, parallelogram,
trapezoid, or regular polygon, describe the rotations and
reflections that carry it onto itself.
□G.CO.A.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.
□G.CO.A.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.B.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.
Core Content
(High School Standards)
Key Vocabulary: Points, Lines, Segments, Rays, Vertex, Angles, Adjacent, Linear Pair,
Parallel, Perpendicular, Vertical Angles, Supplementary Angles, Complementary Angles,,
Corresponding Parts, Distance, Midpoint, Perimeter, Area, Slope, Slope-Intercept Form, Polygon,
Circle, Radius, Center, Transformation, Translation, Reflection, Rotation, Rigid Motion,
Congruence, Perpendicular Bisector, Angle Bisector, Formal Constructions, Rotational
Symmetry, Reflectional Symmetry, Image, Pre-Image
Tier 3 Support
Assessment
Formal
Constructing angles, circles,
perpendicular and parallel lines,
bisectors, transformations of figures
using a variety of methods
including; a compass and straight
edge, string, paper folding, reflective
devices, and dynamic geometric
software applications.
Identify and name
basic parts of
geometric figures
appropriately.
Predict, compare, define, and
describe the effects of rigid
transformation when applied to a
figure in terms of angles, line
segments, and circles.
Identify basic
properties of circles
(radius, center)
Describe the rotations and
reflections necessary for a
symmetrical figure to be
transformed onto itself. Ex.
parallelograms, trapezoids, and
regular polygons
Justify that a rigid transformation
preserves congruence using
corresponding parts and the
definitions of congruence.
Define points, lines,
planes, angles, and
angle relationships.
Calculate the
distance and
midpoint between
two points.
Identify and name
polygons
appropriately.
Identify basic
properties of circles
(radius, center)
Pre Test
Quizzes
Unit Test
Informal
Checking for
Understanding
Questioning
Completion of
Project/Activity/
Assignments
Summarization
of Learning
Daily Exit Slip
Resources
Constructions
1. http://geogebrawiki.wikispaces.com/Comp
ass-and-Straightedge
2. http://illuminations.nctm.org/Activity.aspx
?id=4154
3. https://www.engageny.org/resource/geo
metry-module-1-topic-overview
4. https://www.illustrativemathematics.org/i
llustrations/508
Transformations/Symmetry/Rigid Motion
5. http://illuminations.nctm.org/Activity.aspx
?id=4154
6. https://www.engageny.org/resource/geo
metry-module-1-topic-c-overview
7. http://map.mathshell.org/materials/lesso
ns.php?taskid=524#task524
8. http://nlvm.usu.edu/en/nav/frames_asid_
294_g_4_t_3.html?open=activities&from=
topic_t_3.html
9. http://illuminations.nctm.org/Lesson.aspx
?id=1410
10. http://illuminations.nctm.org/Lesson.aspx
?id=1540
11. http://www.learner.org/teacherslab/math
/geometry/shape/quilts/index.html
12. http://robertkaplinsky.com/work/skytypers/
Geometric Properties of Shapes
13. http://illuminations.nctm.org/Lesson.aspx
?id=2788
14. http://www.learner.org/courses/learning
Updated: 2/9/2016
Course: Geometry A
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
G.CO.B.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.
Describe transformations on a
coordinate plane as functions
applied to coordinate points.
□G.CO.D.12 Make formal geometric constructions
Transform figures using dilations,
rotations, and reflections about
various points and lines in the
coordinate plane which may
include but are not limited to the
axis and origin.
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.B.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.GPE.B.7 Use coordinates to compute
perimeters of polygons and areas of triangles and rectangles,
e.g., using the distance formula.*verbal descriptions). For
example, given a graph of one quadratic function and an
algebraic expression for another, say which has the larger
maximum.
Mathematical Practices
MP.1-8
Use technology to transform
polygons.
Justify that a rigid transformation
preserves congruence using the
distance formula and properties of
parallel and perpendicular lines.
Prove the slope criteria for parallel
and perpendicular lines.
Determine and formulate the
equation of a line parallel or
perpendicular to a given line that
passes through a given point.
Solve problems using the criteria for
parallel and perpendicular lines in
geometric applications.
Define Congruence
and understand the
application of
corresponding parts
of congruent
figures.
Use and apply
formulas to
calculate perimeter
and area for
polygons.
Use and apply
formulas to write
equations of lines
on a coordinate
plane.
Write algebraic
expressions and
equations to
represent and solve
geometric
problems.
math/geometry/session3/part_b/game.ht
ml
15. http://illuminations.nctm.org/Activity.aspx
?id=3546
16. http://illuminations.nctm.org/Lesson.aspx
?id=2778
17. http://map.mathshell.org/materials/lesso
ns.php?taskid=214#task214
Distance/Midpoint Formulas
18. http://robertkaplinsky.com/work/bermudatriangle/
19. http://illuminations.nctm.org/Lesson.aspx?i
d=2688
20. http://education.ti.com/en/timathnspired/us/
detail?id=50D8F68B744F4327BFDCF02C
A613C503&sa=71A40A9FD9E84937B8C
6A8A4B4195B58&t=9D35ADD6DBEB4
B29B0005CAA54065AB6
Parallel and Perpendicular Lines
21. http://map.mathshell.org/materials/lessons.
php?taskid=226#task226
College Preparatory Mathematics
22. http://www.cpm.org/technology/geometry/
Discovery Geometry Website with mini-lessons
23. http://math.kendallhunt.com/x19812.html
Wolfram Player
24. http://demonstrations.wolfram.com/educati
on.html?edutag=High+School+Geometry&
limit=20
Geogebra
25. http://www.geogebratube.org/?lang=en
Math Open Reference
26. http://www.mathopenref.com/
Desmos
27. https://www.desmos.com/
Apply the distance formula to
calculate perimeter and area for
polygons on a coordinate plane.
Updated: 2/9/2016
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
Course: Geometry A
Department: Math
Grade(s): 9-12
Unit 2:
Proofs and
Constructions
Key Vocabulary: Points, Lines, Line Segments, Rays, Vertex, Angles, Adjacent, Linear Pair,
Essential Questions:
How can given information along with accepted definition and properties be
used to make valid conclusions?
What is a valid process that can be used to solve geometric problems?
(10 days)
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
Parallel Lines, Perpendicular Lines, Vertical Angles, Supplementary Angles, Complementary
Angles,, Corresponding Parts, Distance, Midpoint, Perimeter, Area, Slope, Slope-Intercept Form,
Polygon, Circle, Radius, Center, Transformation, Translation, Reflection, Rotation, Rigid Motion,
Congruence, Perpendicular Bisector, Angle Bisector, Formal Constructions, Image, Pre-Image,
Conditional Statements, Convers, Inverse, Contrapositive, Hypothesis, Conclusion, Algebraic
Properties of Equality, Postulate, Theorem, Prove, Given, Two-Column Proof, Paragraph Proof,
Conjecture, Counterexample, Deductive, Inductive, Contradiction, Symmetric Property,
Reflexive Property, Transitive Property
Core Content
(High School Standards)
Tier 3 Support
Use paragraph proofs and two
column proofs to prove theorems
about lines. Ex. Congruent
segments, segment addition, bisected
segments, parallel lines,
perpendicular lines.
Define vertical
angles, transversals,
alternate interior
angles,
corresponding
angles, and
perpendicular
bisectors.
□G.CO.A.1
Prove Line
Theorems
Prove Angle
Theorems
Construction
Proofs
G.CO.C.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.D.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.
Assessment
Formal
Use paragraph proofs and two
column proofs to prove theorems
about angles. Ex. Congruent angles,
angle addition,
supplementary/complementary
angles, bisected angles, angle
relationships in parallel lines and
transversals, angle relationships with
polygons
Use paragraph proofs and two
column proofs to prove theorems
about congruent figures.
Apply constructions to prove
properties of lines, angles, and
polygons.
Write conditional,
converse,
contrapositive, and
inverse statements.
Pre Test
Quizzes
Resources
Logic and Reasoning:
1. http://illuminations.nctm.org/Lesson.aspx?i
d=1444
2. http://illuminations.nctm.org/Lesson.aspx?i
d=2561
Unit Test
Informal
Checking for
Understanding
Questioning
Completion of
Project/Activity/
Assignments
Identify and apply
deductive and
inductive reasoning. Summarization
of Learning
Daily Exit Slip
3. http://kalamitykat.com/2010/08/29/alicein-wonderland-logic/
4. http://function-oftime.blogspot.com/2010/10/counterexampl
es-in-geometry.html
5. http://function-oftime.blogspot.com/2012/01/this-logicgame-needs-name.html
6. http://samjshah.com/2012/08/12/ifstudents-learn-then-weve-accomplishedsomething-part-i/
Proofs
7. http://ichoosemath.com/2011/11/22/intro
ducing-proof-using-formal-systems/
8. http://parkmath.org/2012/01/22/geometry
-follow-up-proof-in-a-bag/
Updated: 2/9/2016
Course: Geometry A
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
9. http://untilnextstop.blogspot.com/2011/03
/top-down-approach-to-proofs.html
10. http://untilnextstop.blogspot.com/search?q
=midsegment+proof
11. http://misscalculate.blogspot.com/2012/07
/made-4-math-1-popsicle-stick-proofs.html
Constructions
12. http://illuminations.nctm.org/Activity.aspx?
id=4154
Properties of Lines and Angles
13. http://www.projectmaths.ie/students/cdstrand1and2/strand2-geoandtrig-junior.asp
14. https://www.engageny.org/resource/geom
etry-module-1-topic-b-overview
College Preparatory Mathematics
15. http://www.cpm.org/technology/geometry/
Discovery Geometry Website with mini-lessons
16. http://math.kendallhunt.com/x19812.html
Wolfram Player
17. http://demonstrations.wolfram.com/educatio
n.html?edutag=High+School+Geometry&li
mit=20
Geogebra
18. http://www.geogebratube.org/?lang=en
Math Open Reference
19. http://www.mathopenref.com/
Desmos
20. https://www.desmos.com/
Updated: 2/9/2016
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
Course: Geometry A
Department: Math
Grade(s): 9-12
Unit 3:
Triangles and
Quadrilateral
Essential Questions:
Key Vocabulary:
What conditions are necessary to prove geometric figures are congruent?
How can properties of congruence, triangles, and quadrilaterals be used to solve
geometric problems?
(10 days)
Congruent
Triangle
Postulates
Properties of
Triangles
Applications
and Proofs with
Triangles
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□G.CO.A.1; G.CO.B.7; G.CO.C.9;
□G.CO.D.12; G.GPE.B.7
G.CO.B.8 Explain how the criteria for triangle
congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G.CO.C.10Prove 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.CO.C.11 Prove theorems about
Properties of
Quadrilaterals
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.
Applications
and Proofs of
Properties of
Parallelograms
geometric theorems algebraically. For example, prove or
disprove that a figure defined by four given points in the
coordinate plane is a rectangle; prove or disprove that the
point (1, √3) lies on the circle centered at the origin and
containing the point (0, 2).
G.GPE.B.4 Use coordinates to prove simple
Proofs for
Figures in a
Coordinate
Plane
Mathematical Practices
MP.1-8
Core Content
(High School Standards)
Rigid Motion, Formal Construction, Congruence, Corresponding Parts,
Distance, Midpoint, Parallel Lines, Perpendicular Lines, Bisector, Conditional Statements, Converse,
Inverse, Contrapositive, Hypothesis, Conclusion, Algebraic Properties of Equality, Postulate,
Theorem, Prove, Given, Two-Column Proof, Paragraph Proof, Conjecture, Counterexample,
Deductive, Inductive, Contradiction, Symmetric Property, Reflexive Property, Transitive Property,
Scalene, Isosceles, Equilateral, Trapezoid, Parallelogram, Rectangle, Square, Rhombus, Kite, ASA,
SAS, SSS, Triangle Sum Theorem, Base Angle Theorem, Median, Circumcenter, Centroid,
Diagonal, Equidistant
Tier 3 Support
Assessment
Resources
Formal
Prove congruence of triangles using
ASA, SAS, and SSS and connect the
definition of congruence to rigid
motions.
Use rigid motions to prove the
congruence of triangles by ASA,
SAS, and SSS.
Solve problems using congruent
triangles theorems in geometric
applications.
Apply formal proof methods to
prove properties of triangle.
Ex. Interior angles sum of 180
degrees, base angles of an isosceles
triangle are congruent, segment
joining midpoints of two sides is
parallel to third side, medians meet
at a point
Apply formal proof methods to
prove properties of quadrilaterals
and parallelograms.
Name triangles by
sides and angles
Understand
properties of angles
and segments in
triangles
Understand the
hierarchy of
quadrilaterals
1.
Pre Test
Quizzes
2.
Unit Test
3.
Informal
4.
Checking for
Understanding
5.
Questioning
Name quadrilaterals
by sides and angles
Understand
properties of
quadrilaterals,
diagonals, angles
and sides.
Completion of
Project/Activity/
Assignments
Summarization
of Learning
Daily Exit Slip
Triangle Congruency Proofs
http://www.absorblearning.com/media/atta
chment.action?quick=io&att=1336
http://illuminations.nctm.org/Lesson.aspx?i
d=2561
https://www.engageny.org/resource/geomet
ry-module-1-topic-d-overview
https://www.engageny.org/resource/geomet
ry-module-1-topic-e-overview
http://map.mathshell.org/materials/lessons.
php?taskid=452&subpage=concept
Triangle Properties
6. http://illuminations.nctm.org/Lesson.aspx?i
d=2195
7. http://illuminations.nctm.org/Activity.aspx
?id=4171
8. http://illuminations.nctm.org/Lesson.aspx?i
d=2339
9. http://mrhonner.com/archives/6153
Circumcenter/Orthocenter
10. http://www.mathopenref.com/constcircumc
enter.html
11. http://untilnextstop.blogspot.com/2011/03/l
earning-from-my-mistakes.html
12. http://untilnextstop.blogspot.com/2010/10/
orthocenter-curiosities.html
Updated: 2/9/2016
Course: Geometry A
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
Ex. Parallelogram properties,
congruent sides, congruent triangles
within, angles relationships, segment
relationships, properties of diagonals
Solve problems using properties of
parallelograms in geometric
applications.
Prove properties of triangles and
quadrilaterals given a figure in a
coordinate plane.
Tier 1+ H-L congruence and AAS
similarity
Quadrilateral/Parallelograms
13. http://illuminations.nctm.org/Lesson.aspx?i
d=2189
14. http://illuminations.nctm.org/Lesson.aspx?i
d=2469
15. http://education.ti.com/en/timathnspired/us/
detail?id=50D8F68B744F4327BFDCF02C
A613C503&sa=71A40A9FD9E84937B8C
6A8A4B4195B58&t=9D35ADD6DBEB4
B29B0005CAA54065AB6
16. http://www.mathsisfun.com/quadrilaterals.
html
17. https://www.engageny.org/resource/geomet
ry-module-1-topic-f-lesson-31
Quadrilateral Proofs and Properties
18. http://map.mathshell.org/materials/task
s.php?taskid=258&subpage=apprentic
e
19. http://map.mathshell.org/materials/task
s.php?taskid=270&subpage=apprentic
e
Review
20. https://www.engageny.org/resource/geomet
ry-module-1-topic-g-overview
College Preparatory Mathematics
21. http://www.cpm.org/technology/geometry/
Discovery Geometry Website with mini-lessons
22. http://math.kendallhunt.com/x19812.html
Wolfram Player
23. http://demonstrations.wolfram.com/educati
Updated: 2/9/2016
Course: Geometry A
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Geometry A 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: None
on.html?edutag=High+School+Geometry&
limit=20
Geogebra
24. http://www.geogebratube.org/?lang=en
Math Open Reference
25. http://www.mathopenref.com/
Desmos
26. https://www.desmos.com/
Updated: 2/9/2016