Download 2016-2017 Mathematics Curriculum Map Geometry, Q3

2016-2017 Mathematics Curriculum Map Geometry, Q3
Unifying Concept: Dilations, Similarity, Proof and Trigonometry
Target Standards are emphasized every quarter and used in formal assessment to evaluate student mastery.
Highly-Leveraged Standards1
G-SRT.A.1a 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.A.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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.
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.
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.
Supporting Standards2
- There are no Supporting Target Standards for this quarter.
Quarter 3
Additional Standards
Complementary Standards: (Standards to be
assessed in classroom and/or future benchmarks)
G-MG.A.1, 3
Standards for Mathematical Practice: (quarterly
focus)
Mathematically proficient students:
SMP 1. Make sense of problems and persevere in
solving them.
SMP 2. Reason abstractly and quantitatively.
SMP 3. Construct viable arguments and critique the
reasoning of others.
SMP 4. Model with mathematics.
SMP 7. Look for and make use of structure.
SMP 8. Look for and express regularity in repeated
reasoning.
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.RST.7
9-10.WHST.1a-1e
1
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
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
2
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.
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:07 PM
Page 1
2016-2017 Mathematics Curriculum Map Geometry, Q3
Adopted and Supplemental Texts
Big Ideas
Eureka Math/ Engage NY:
Module 2
Holt McDougal Geometry:
Chapter 4 – Section 5
Chapter 5 – Sections 1 and 7
Chapter 7 – Sections 1-6
Chapter 8 – Sections 1-4
Instruction must be supplemented to meet the expectations of the standards.
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#
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
Essential Concepts:
 Dilations are transformations that preserve angle measure but not distance.
 When figures are similar, corresponding angles are congruent and
corresponding segments are proportional.
 There are criteria that allow the conclusion two triangles are similar.
 In triangles, certain relationships among sides and other segments are always
true.
 Applying the concepts of congruent and similar triangles when comparing
geometric figures allows us to find measures of corresponding parts of those
figures.
 The angles in right triangles are related to the ratios of the side lengths.
 The sine and cosine of complementary angles are related.
 Right triangles properties can be applied to solve problems.
Essential Questions:
 What are the key properties of dilations?
 How do dilations affect the various parts of a figure and their relationship to
each other?
 How do you draw the image of a figure under a dilation?
 What does it mean for two figures to be similar?
 How do triangle similarity criteria follow from similarity transformations?
 What relationships among sides and other segments in a triangle are always
true?
 How does the use of congruency and similarity concepts allow us to model
relationships between geometric figures?
 How do the ratios of the side lengths of right triangles relate to the angles in the
triangle?
 What is the relationship of the cosine and the sine of two complementary
angles?
 What does it mean to "solve" a triangle?
Vocabulary
AA similarity (angle-angle)
AAS
adjacent
altitude
angle bisector
angle measure
arc functions
Additional Resource: http://www.graniteschools.org/mathvocabulary/
congruence
image
contraction
inverse
corresponding parts
isometric
corresponding sides
isosceles right triangle
cosecant
mapping
cosine
median
cotangent
opposite
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/11/2016 3:07 PM
SAS
scale factor
secant
similar
similarity
similarity ratio
similarity transformation
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2016-2017 Mathematics Curriculum Map Geometry, Q3
ASA
betweenness
center of dilation
cofunction
collinearity
complementary
dilation
expansion
geometric mean
HL
hypotenuse
identity transformation
perpendicular bisector
preimage
proportion
proportional
Pythagorean Theorem
ratio
sine
solve a triangle
SSS
tangent
trigonometric ratio
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_CoDzyDFeJimZxnhgwOVsWk
TQEsfqouLWNNC6Z4/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-heather-wolpertgawron
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
Instructional Resources
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/TasksUnitsStudentWo
rk/default.htm?s=Z3JhZGVzPTgmc3ViamVjdD0y
https://www.illustrativemathematics.org/8
https://hcpss.instructure.com/courses/99
http://www.cpalms.org/Public/ToolkitGradeLevelGroup/Toolkit?id=14
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
TUSD Department of Curriculum and Instruction
Revised 5/11/2016 3:07 PM
Curriculum 3.0
Page 3