Download 2016-2017 Mathematics Curriculum Map Geometry, Q1

2016-2017 Mathematics Curriculum Map Geometry, Q1
Unifying Concept: Transformations, Congruence, Proof, and Constructions
Quarter 1
Target Standards are emphasized every quarter and used in formal assessment to evaluate student mastery.
Highly-Leveraged Standards1
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 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 polygons, 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.
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.
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.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.C.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-CO.C.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.
Additional Standards
Complementary Standards: (Standards to be
assessed in classroom and/or future benchmarks)
G-CO.D.12, 13
Standards for Mathematical Practice:
(quarterly focus)
Mathematically proficient students:
SMP 3. Construct viable arguments and critique
the reasoning of others.
SMP 4. Model with mathematics.
SMP 5. Use appropriate tools strategically.
SMP 6. Attend to precision.
Mathematical Practices Poster
6th – 12th Grade Literacy in History/Social
Studies, Science, and Technical Subjects Focus
Standards:
(http://www.azed.gov/standardspractices/files/2015/04/accs-6-12-ela-contentliteracy-standards-final10_28_2013.pdf)
9-10.RST.4
9-10.WHST.1a-1e
9-10.WHST.2c
9-10.WHST.3
9-10.WHST.4
Supporting Standards2
- There are no Supporting Target Standards for this quarter.
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Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality. This definition for highly-leveraged standards
was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA. http://www.millis.k12.ma.us/services/curriculum_assessment/brochures
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:05 PM
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2016-2017 Mathematics Curriculum Map Geometry, Q1
Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade Level Focus documents. They should encompass
a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35% for Supporting Cluster Instruction. See the Grade Level Focus documents at:
https://cms.azed.gov/home/GetDocumentFile?id=57069f7baadebe0bccd0a8b5
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Supporting Standards are related standards that support the highly-leveraged standards in and across grade levels.
*Highly-Leveraged standards in bold and supporting standards are normal text.
Adopted and Supplemental Texts
Big Ideas
Eureka Math/ Engage NY:
Module 1
Holt McDougal Geometry:
Chapter 1 – Sections 1-7
Chapter 2 – Section 7
Chapter 3 – Section 1-4
Chapter 4 – Sections 1-9
Chapter 5 – Sections 3 and 4
Chapter 6 – Sections 2 and 4
Chapter 9 – Sections 1-5
Instruction must be supplemented to meet the expectations of the standards.
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Additional Resources:
https://www.khanacademy.org
http://achievethecore.org
https://www.illustrativemathematics.org/
www.insidemathematics.org
https://learnzillion.com/resources/75114-math
http://maccss.ncdpi.wikispaces.net/ (Choose your grade level on the left)
http://www.pbslearningmedia.org/standards/1
http://nlvm.usu.edu/en/nav/vlibrary.html
http://nrich.maths.org
https://www.youcubed.org/week-of-inspirational-math/
http://illuminations.nctm.org/Lessons-Activities.aspx (choose grade level and
connect to search lessons)
http://www.yummymath.com/birds-eye-of-activities/
http://map.mathshell.org/tasks.php?collection=9&unit=HE06
http://www.shmoop.com/common-core-standards/math.html
http://www.njcore.org/standards?processing=true#
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Essential Concepts:
 The study of Geometry is based on three undefined terms: a point, a line, and a
plane. These three notions are used to define all other terms in geometry.
 Some transformations preserve distance and angle, and some do not.
 Figures with symmetry can be transformed onto themselves.
 Rotations, reflections, and translations can be developed using mathematical
definitions of general geometric terms.
 Using a variety of materials, we determine a sequence needed to carry a figure
onto another.
 Rigid motions can be used to determine if two figures are congruent.
 When figures are congruent, all corresponding parts (e.g., angles, segments,
and regions) are congruent.
 When certain corresponding parts of triangles are congruent, the triangles
themselves are congruent.
 When lines intersect, certain relationships among the created angles are always
true. The same is true of points on perpendicular bisectors of segments.
 In triangles, certain relationships among angles, sides, and other segments are
always true. (Triangle Sum Theorem, Isosceles Triangle Theorem, Midsegment
Theorem)
 In parallelograms, certain relationships among angles, sides, and other
segments are always true.
Essential Questions:
 What are the undefined terms in geometry and why are they undefined?
 Can you use these undefined terms to define angles, circles, parallel lines and
line segments?
 What is the difference between a rigid transformation and a non-rigid
transformation?
 What transformations are isometries?
 How is symmetry defined?
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2016-2017 Mathematics Curriculum Map Geometry, Q1
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https://hcpss.instructure.com/courses/162
https://www.desmos.com/
http://www.geogebra.org/
http://ccssmath.org/?page_id=1306
http://www.cpalms.org/Public/ToolkitGradeLevelGroup/Toolkit?id=14
 Can a figure have more than one type of symmetry?
 How do you draw the image of a figure under a reflection, rotation, and
translation?
 What mathematical definitions do we use to rotate, reflect, and/or translate so
that we can transform figures?
 What sequence of transformations will carry a figure onto another?
 How can congruence be represented through the transformations of figures?
 What is required to show that two triangles are congruent?
 What can we conclude about two triangles that are congruent?
 How do triangle congruence criteria follow from the rigid motion definition of
congruence?
 What relationships between angles formed by intersections of lines are always
true?
 What is true about the endpoints of a segment and its perpendicular bisector?
 What relationships among angles, sides, and other segments in a triangle are
always true?
 What relationships among angles, sides, and other segments in parallelograms
are always true?
Vocabulary
AAS (angle-angle-side congruence)
acute triangle
alternate exterior angles
angle
angle of rotation
arc
ASA (angle-side-angle congruence)
base
base angles
bisect
bisector
center of rotation
centroid
circle
circumcenter
circumference
Additional Resource: http://www.graniteschools.org/mathvocabulary/
dilation
midpoint
distance
midsegment
end point
non-rigid transformation
equiangular
obtuse triangle
equiangular triangle
orthocenter
equidistant
output
equilateral
parallel lines
equilateral triangle
parallelogram
expansion
perpendicular
exterior angle
perpendicular lines
plane
horizontal stretch
point
hypotenuse
point of symmetry
image
pre-image
incenter
quadrilateral
initial point
radius
input
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:05 PM
rigid motion
rigid transformation
rotation
rotational symmetry
rotations
same-side interior angles
SAS (side-angle-side congruence)
scalene triangle
sequence of transformations
sides of an angle
square
SSS (side-side-side congruence)
supplementary
supplementary angles
symmetry
terminal point
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2016-2017 Mathematics Curriculum Map Geometry, Q1
collinear/noncollinear
complementary angles
composition of transformations
consecutive angles
contraction
corresponding angles
corresponding parts
CPCTC (corresponding parts of
congruent triangles are congruent)
CPFTC (corresponding parts of
congruent figures are congruent)
diagonal
diameter
interior angle
isometry
isosceles triangle
leg
line
line of reflection
line of symmetry
line segment
linear pair
locus
mapping
ray
rectangle
reflection
reflectional symmetry
reflections
regular polygon
remote angle
rhombus
right angle
right triangle
transformation
translation
transversal line
trapezoid
undefined term
vector
vertex angle
vertex of an angle
vertical angles
vertical stretch
Interdisciplinary Connections
Multicultural Math Connections:
https://www.deltacollege.edu/dept/basicmath/Multicultural_Math.htm
http://www.edchange.org/multicultural/sites/math.html
http://users.wfu.edu/mccoy/mgames.pdf
http://www.ericdigests.org/1996-1/more.htm
A Course in Multicultural Mathematics
Integrating Mathematics of Worldwide Cultures into K-12
Teaching Mathematics through Multicultural Literature
http://www.nea.org/tools/lessons/47756.htm
https://www.teachervision.com/
Math Modeling Projects
https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkT
QEsfqouLWNNC6Z4/pub?output=html
Literacy Connections:
http://mathsolutions.com/wpcontent/uploads/1995_Writing_in_Elem_Grades.pdf
http://www.edutopia.org/blog/four-tips-writing-math-classroom-heatherwolpert-gawron
http://files.eric.ed.gov/fulltext/ED544239.pdf
http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_1_burns.pdf
Writing Prompts for Math
http://writingfix.com/wac/numberfix.htm
http://www.nea.org/tools/lessons/47756.htm
https://www.teachervision.com/
http://msms.ehe.osu.edu/2010/05/20/teaching-with-trade-books-math/
http://letsreadmath.com/math-and-childrens-literature/
Assessment Guides and Resources
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http://www.azed.gov/assessment/files/2015/12/math-pld-geometry.pdf
http://achievethecore.org/category/1020/mathematics-assessments
http://www.azed.gov/assessment/azmeritsupportmaterials/
http://www.ccsstoolbox.org/
http://www.insidemathematics.org/tools-for-educators
http://map.mathshell.org/materials/index.php
http://www.orglib.com/home.aspx
http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWor
k/default.htm?s=Z3JhZGVzPTgmc3ViamVjdD0y
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Instructional Resources
DOK Levels
http://www.azed.gov/assessment/files/2014/11/dok-levels.pdf
DOK Stems
http://www.azed.gov/assessment/files/2014/11/dok-question-stems.pdf
Hess’s Matrix
http://static.pdesas.org/content/documents/M2-Activity_2_Handout.pdf
Bloom’s Taxonomy
http://www.bloomstaxonomy.org/Blooms%20Taxonomy%20questions.pdf
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2016-2017 Mathematics Curriculum Map Geometry, Q1
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https://www.illustrativemathematics.org/8
https://hcpss.instructure.com/courses/99
http://www.cpalms.org/Public/ToolkitGradeLevelGroup/Toolkit?id=14
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:05 PM
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