LEONA QSI Curriculum Map
Geometry B 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A
Course: Geometry B
Department: Math
Grade(s): 9-12
Unit 4:
Similarity
(10 days)
Essential Questions:
What properties can be identified between similar geometric figures?
How can similar geometric figures be used to solve real world problems?
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
Core Content
(High School Standards)
Key Vocabulary:
Transformations, Reduction, Enlargement, Corresponding Parts, 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, Dilation, Center, Proportional, Ratio, Scale
Factor, Similarity, Center of Dilations, Mid-Segment
Tier 3 Support
Assessment
Resources
Formal
Dilations
Triangle and
Polygon
Similarity
Applications
and Proofs of
Similarity
G.SRT.A.1a Verify experimentally the properties of
dilations given by a center and a scale factor:
a. 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.
b. The dilation of a line segment is longer or shorter in the
ratio given by the scale factor.and
G.SRT.A.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.A.3 Use the properties of similarity
transformations to establish the AA criterion for two triangles
to be similar.
Describe the effects and the
properties of figures that have been
dilated about the origin and other
points.
Given a ratio identify a point on a
line segment between two given end
points that partitions the segment in
a given ratio.
Recognize and identify that the
corresponding sides of the dilated
objects are parallel and that line
going through the center of the
figures are unchanged.
G.SRT.B.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.B.5 Use congruence and similarity criteria for
triangles to solve problems and to prove relationships in
geometric figures.
Understand and apply scale factor
through dilations of geometric
figures.
Prove that two figures are similar
using dilations.
G.GPE.B.6 Find the point on a directed line segment
between two given points that partitions the segment in a
given ratio.
Mathematical Practices
MP.1-8
Understand and determine that
corresponding sides are proportional
and corresponding angles are
congruent in similar figures.
Make connections between dilations
Draw dilated
figures using a
scale factor.
Identify
corresponding parts
of geometric
figures.
Write ratios and
simplify.
1.
Pre Test
2.
Quizzes
3.
Unit Test
http://nlvm.usu.edu/en/nav/frames_asid_296
_g_4_t_3.html?open=activities&from=topic
_t_3.html
http://tube.geogebra.org/student/m157262
http://tube.geogebra.org/student/m449131
Informal
4.
5.
Checking for
Understanding
6.
http://www.absorblearning.com/media/attac
hment.action?quick=hr&att=1270
7.
http://www.absorblearning.com/media/attac
hment.action?quick=hq&att=1268
8.
http://www.nctm.org/standards/content.aspx
?id=26770
http://illuminations.nctm.org/Lesson.aspx?id
=3165
Questioning
Set up proportions
and solve for a
variable.
Dilations
http://www.cpm.org/flash/technology/panto
graphv1.2.swf
https://share.ehs.uen.org/node/12485
Completion of
Project/Activity/
Assignments
Summarization
of Learning
Daily Exit Slip
9.
10. http://math.kendallhunt.com/documents/dg4/
condensedlessons/dg4cl_895_11.pdf
11. http://www.cpm.org/pdfs/information/sampl
eChapters/CCG%20Ch%203%20TV.pdf
Similarity in Polygons
12. http://illuminations.nctm.org/Lesson.aspx?id
=2469
13. http://fawnnguyen.com/listerine-fuji-water2/
Updated: 2/9/2016
Course: Geometry B
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Geometry B 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A
and angle properties between similar
figures.
Prove that the congruence of two
angles leads to similarity in two
triangles.
Prove that two triangles are similar
by AA, SAS, and SSS criteria.
Prove a line parallel to one side of a
triangle divides the other two sides
of the triangle proportionally.
Use properties of similar figures to
solve problems and applications of
similarity.
Similarity in Triangles
14. http://cpm.org/technology/general/similarity
/
15. http://demonstrations.wolfram.com/ATriang
leFormedByTheCentersOfThreeCircles/
16. http://www.cpm.org/technology/CCG/Ch3/
AAA_Similarity.html
17. http://www.cpm.org/technology/CCG/Ch3/S
AS_Similarity_v3.html
18. http://www.cpm.org/technology/CCG/Ch3/S
SA_Similarity.html
19. http://www.cpm.org/technology/CCG/Ch3/S
SS_Similarity.html
20. http://map.mathshell.org/materials/download
.php?fileid=1257
21. http://map.mathshell.org/materials/download
.php?fileid=1372
22. http://www.mathopenref.com/similartriangle
s.html
23. http://threeacts.mrmeyer.com/besttriangle/
24. http://map.mathshell.org/materials/lessons.p
hp?taskid=429#task429
25. http://demonstrations.wolfram.com/TheRati
oTheorem/
26. http://illuminations.nctm.org/Lesson.aspx?id
=1672
27. EngageNY
https://www.engageny.org/resource/geometr
y-module-2
28. http://www.mathematicsvisionproject.org/up
loads/1/1/6/3/11636986/sec2_mod6_simtrig
_tn_83113.pdf
29. Discovery Geometry Website with minilessons
Updated: 2/9/2016
LEONA QSI Curriculum Map
Geometry B 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A
Course: Geometry B
Department: Math
Grade(s): 9-12
http://math.kendallhunt.com/x19812.html
30. http://www.illustrativemathematics.org/
Unit 5:
Key Vocabulary:
Essential Questions:
What unique properties are found in right triangles?
Right Triangles What are trigonometric ratios and how are they related to similar right triangles?
How can right triangles and their properties be used to solve problems?
(12 days)
Right Triangle
Similarity
Trigonometry
Applications
and Proofs with
Right Triangles
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
G.SRT.B.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.B.5 Use congruence and similarity criteria for
Core Content
(High School Standards)
G.SRT.C.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.C.7 Explain and use the relationship between
the sine and cosine of complementary angles.
G.SRT.C.8 Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in applied
problems. (★)
Mathematical Practices
MP.1-8
Tier 3 Support
Resources
Assessment
Formal
Use properties of right triangles to
solve problems. Including special
right triangle properties in triangles
of 45-45-90, and 30-60-90.
triangles to solve problems and to prove relationships in
geometric figures.
Transformations, Corresponding Parts, Postulate, Theorem, Prove, Given, TwoColumn Proof, Paragraph Proof, Conjecture, Counterexample, Deductive, Inductive, Contradiction, Symmetric
Property, Reflexive Property, Transitive Property, Right Triangle, Distance Formula, Dilation, Proportional, Ratio,
Scale Factor, Similarity, Pythagorean Theorem, Hypotenuse, Opposite Side, Adjacent Side, Sine, Cosine,
Tangent, Trigonometry, Trigonometric Ratios, Inverse Trigonometry
Show that the relationship between
the side ratios of similar right
triangles are the same and related to
their corresponding angles, which
leads to the definition of
trigonometric ratios for acute angles.
Prove the Pythagorean theorem
using the properties of similar right
triangles.
Use trigonometric ratios and the
Pythagorean theorem to solve
problems and applications of right
triangles.
Understand and explain the
relationship between trigonometric
Define
complementary and
supplementary,
obtuse, acute, and
right angles.
Identify the parts of
a right triangle
(hypotenuse, legs).
Use the
Pythagorean
theorem to solve for
a side length of a
right triangle.
Use the
Pythagorean
theorem to identify
if a triangle is a
right triangle.
1.
http://www.nbclearn.com/nfl/cuecard/51220
Pre Test
Quizzes
2.
Unit Test
3.
Informal
4.
Checking for
Understanding
5.
Questioning
Completion of
Project/Activity/
Assignments
6.
7.
8.
Summarization
of Learning
9.
Daily Exit Slip
Proofs of the Pythagorean Theorem
http://www.cimt.plymouth.ac.uk/projects/me
pres/book8/y8s3act.pdf
http://map.mathshell.org/materials/tasks.php
?taskid=276&subpage=expert
http://www.cpm.org/flash/technology/pytha
goreanv1.2.swf
http://nlvm.usu.edu/en/nav/frames_asid_164
_g_4_t_3.html?open=instructions&from=to
pic_t_3.html
Trigonometric Functions
http://illuminations.nctm.org/hsactivity/
http://illuminations.nctm.org/Lesson.aspx?id
=2493
http://www.teachengineering.org/view_activ
ity.php?url=http://www.teachengineering.or
g/collection/cub_/activities/cub_navigation/c
ub_navigation_lesson03_activity2.xml
http://www.teachengineering.org/view_lesso
n.php?url=collection/uno_/lessons/uno_hand
held/uno_handheld_lesson01.xml
10. http://www.cpm.org/technology/CCG/Ch4/L
eaning_Tower_of_Pisa.html
Updated: 2/9/2016
LEONA QSI Curriculum Map
Geometry B 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A
Course: Geometry B
Department: Math
Grade(s): 9-12
functions (especially with the sine
and cosine of complementary
angles).
Unit 6:
Circles
(8 days)
Similarity and
Circles
Inscribed
Angles, Radii,
and Chords
Constructions
with Circles
Essential Questions:
What unique properties are found in circles?
How can circles and their properties be used to solve problems?
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□G.CO.D.13 Construct an equilateral triangle, a
square, and a regular hexagon inscribed in a circle.
○G.C.A.1 Prove that all circles are similar.
○G.C.A.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.A.3 Construct the inscribed and circumscribed
circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
○G.GPE.A.1 Derive the equation of a circle of given
Circles in a
Coordinate
Plane
center and radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle given by an
equation.
G.GPE.B.4 Use coordinates to prove simple
Core Content
(High School Standards)
Prove that all circles are similar.
Solve problems using the
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.
Constructions with circles
Write equations of circles given the
center and radius. Prove or disprove
a given point lies on the circles.
Relate it to the Pythagorean
theorem.
11. http://demonstrations.wolfram.com/HowFar
CanOneSeeFromAHeight/
12. EngageNY
https://www.engageny.org/resource/geometr
y-module-2
13. http://www.cpm.org/pdfs/information/sampl
eChapters/GC_Ch4_2006_TV.pdf
14. http://www.illustrativemathematics.org/
Key Vocabulary: Postulate, Theorem, Prove, Given, Two-Column Proof, Paragraph Proof,
Conjecture, Counterexample, Deductive, Inductive, Contradiction, Symmetric Property, Reflexive
Property, Transitive Property, Dilation, Proportional, Ratio, Scale Factor, Similarity, Pythagorean
Theorem, Circle, Center, Diameter, Radius, Semi-Circle, Circumference, Area, Chord, Secant,
Tangent, Minor Arc, Major Arc, Arc Length, Arc Measure, Inscribed, Circumscribed, Central
Angle, Intercepted Arc, Point of Tangency
Tier 3 Support
Know where Pi
came from (as a
ratio of
circumference to
diameter)
Define the parts of
a circle (radius,
diameter,
circumference,
center)
Resources
Assessment
Circle Parts and Properties
Formal
Pre Test
1.
Quizzes
2.
Unit Test
3.
Informal
Checking for
Understanding
Questioning
Completion of
Project/Activity/
Assignments
http://demonstrations.wolfram.com/Geometr
icElementsOfACircle/
http://illuminations.nctm.org/Lesson.aspx?id
=2417
http://illuminations.nctm.org/Lesson.aspx?id
=3777
Circles and Triangles
4.
5.
6.
7.
Summarization
of Learning
8.
http://map.mathshell.org/materials/lessons.p
hp?taskid=403&subpage=problem
http://illuminations.nctm.org/Lesson.aspx?id
=2219
http://map.mathshell.org/materials/download
.php?fileid=696
http://illuminations.nctm.org/Lesson.aspx?id
=2374
Circles in Coordinate Plane
http://map.mathshell.org/materials/download
.php?fileid=1202
Updated: 2/9/2016
Course: Geometry B
Department: Math
Grade(s): 9-12
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).
Mathematical Practices
MP.1-8
LEONA QSI Curriculum Map
Geometry B 2014-2015
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A
Tier 1+
Introduce unit circle relating trig
functions and converting from
degrees to radians.
Daily Exit Slip
9.
http://map.mathshell.org/materials/download
.php?fileid=1247
10. EngageNY
https://www.engageny.org/resource/geometr
y-module-5
11. http://www.illustrativemathematics.org/
Updated: 2/9/2016