ccgps mathematics unit-by-unit grade level webinar 8 th grade unit 1: transformations, congruence,...
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CCGPS MathematicsUnit-by-Unit Grade Level Webinar
8th Grade Unit 1: Transformations, Congruence, and Similarity
May 8, 2012
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CCGPS MathematicsUnit-by-Unit Grade Level Webinar
8th Grade Unit 1: Transformations, Congruence, and Similarity
May 8, 2012
James Pratt – [email protected] Kline – [email protected] Mathematics Specialists
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
Welcome!• Thank you for taking the time to join us in this discussion of Unit 1.• At the end of today’s session you should have at least 3 takeaways:
the big idea of Unit 1 something to think about…some food for thought
how might I approach this unit next fall? what is my conceptual understanding of the material in this unit?
a list of resources and support available for CCGPS mathematics
Welcome!
• For today’s session: read the standards read the unit downloaded and saved the documents from this session
• Ask questions and share resources/ideas for the common good.
Welcome!• Please provide feedback at the end of today’s session.
Feedback helps us become better teachers, and it helps you to reflect upon your learning. Feedback helps us as we develop the remaining unit-by-unit webinars. Please visit http://ccgpsmathematics6-8.wikispaces.com/ to provide us with your feedback, ask questions, and share your ideas and resources.
• After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars.
James Pratt – [email protected] Brooke Kline – [email protected] Mathematics Specialists
Clearing up confusion• This webinar focuses on CCGPS content specific to one grade level and one unit within that grade.• For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org.• For information about the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org.• CCGPS is taught and assessed from 2012-2013 and beyond. PARCC assessments begin in 2014-2015.• A list of resources will be provided at the end of this webinar.
Activate your Brain Are the following two figures congruent? Use transformations to justify your answer.
Activate your Brain Are the following two figures congruent? Use transformations to justify your answer.
1. Rotate
Activate your Brain Are the following two figures congruent? Use transformations to justify your answer.
1. Rotate2. Translate
Activate your Brain Are the following two figures congruent? Use transformations to justify your answer.
1. Rotate2. Translate3. Figures are congruent
because the second figure can be obtained from the first by a sequence of a rotation and a translation!
SEDL Common Core Support Video: MCC8.G.2
Sequence of Transformations to Demonstrate Congruence
http://secc.sedl.org/common_core_videos/index.php?action=view&id=781
What’s the big idea?• Enduring Understandings• Essential Questions• Key Standards• Overview
What’s the big idea?Unit 1: Transformations, Congruence and Similarity
Geometry• Understand congruence and similarity using physical
models, transparencies, or geometry software.
New Content• Transformation – came from 7th grade• Similarity – came from 7th grade• Congruence – not addressed in this manner
What’s the big idea?
• Developing deep understanding of transformations of geometric figures.• Using informal arguments to establish geometric facts.
Navigating a Unit•Table of Contents
OverviewStandardsEnduring UnderstandingsEssential QuestionsSelected Terms and SymbolsClassroom RoutinesStrategies for Teaching and LearningEvidence of LearningTasks
Navigating a Unit
What’s New?• Concepts and Skills to Maintain• Strategies for Teaching and Learning• Evidence of Learning
Navigating a Unit
What’s New?• Task Table
Task Type Grouping StrategyTask Description
Navigating a UnitWhat’s New?
• Classroom RoutinesSMP’s (analyzing, estimating, reasoning, describing patterns, defending, discussing, peer feedback, contentious discourse, answering, etc.)Collaborative skills (How collaborative are your collaborative activities?)Productive StruggleClassroom technology, materials…how to use materials in a productive manner.Journaling/NotebookDevelopment of own understandingThe regular use of routines is important to the development of students’ number sense, flexibility, fluency, collaborative skills and communication.
Navigating a UnitClassroom Routines
• What might all of this look like in the classroom?http://ccgpsmathematics6-8.wikispaces.com/
• Also check out:Inside Mathematics : Mathematical Community of Learners - http://www.insidemathematics.org/index.php/video-tours-of-inside-mathematics/classroom-teachers/157-teachers-reflect-mathematics-teaching-practicesEdutopia.org - Chris Optizhttp://www.edutopia.org/math-social-activity-cooperative-learning-vi
deohttp://www.edutopia.org/math-social-activity-sel
Unit 1 Transition Standard Teach 2012-13
MCC7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Coherence and Focus – Unit 1What are students coming with?
Coherence and Focus – Unit 1What foundation is being built?
Where does this understanding lead students?
Coherence and Focus – Unit 1View across grade bands
• K-7th Work with angles, lines of symmetry, and graphing geometric figures in the coordinate plane.Facts about supplementary, complementary, vertical, and adjacent angles.
• 9th-12th Describe transformations as functions.Connect congruence criteria to transformations.Formal proofs of congruence, similarity, and parallel lines cut by a transversal.
Examples & ExplanationsUnderstand congruence and similarity using physical models, transparencies, or geometry
software.
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create its
image at the coordinates (2x, 2y). What is the result?
C B
A
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create its
image at the coordinates (2x, 2y). What is the result?
C B
A
A: (4, 6)B: (7, 4)C: (4, 4)
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create its
image at the coordinates (2x, 2y). What is the result?
C B
A
A: (4, 6) A’: (8, 12)B: (7, 4) B’: (14, 8)C: (4, 4) C’: (8, 8)
A’
B’C’
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create a
second image at the coordinates (½x, ½y). What is the result?
A’
B’C’
A: (4, 6) A’: (8, 12)B: (7, 4) B’: (14, 8)C: (4, 4) C’: (8, 8)
C B
A
A’
B’C’
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create a
second image at the coordinates (½x, ½y). What is the result?
A’
B’C’
A: (4, 6) A’: (8, 12) A”: (2, 3) B: (7, 4) B’: (14, 8) B”: (3.5, 2)C: (4, 4) C’: (8, 8) C”: (2, 2)
C B
A
A’
B’C’
A”
B”C”
Examples & ExplanationsFor each vertex of the triangle in the form (x, y), create a
second image at the coordinates (½x, ½y). What is the result?
A’
B’C’
A: (4, 6) A’: (8, 12) A”: (2, 3) B: (7, 4) B’: (14, 8) B”: (3.5, 2)C: (4, 4) C’: (8, 8) C”: (2, 2)
C B
A
A’
B’C’
A”
B”C”
Examples & ExplanationsUse informal arguments to establish facts about:
the angle sum and exterior angle of triangles.the angles created when parallel lines are cut by a transversal.the angle-angle criterion for similarity of triangles.
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67° 23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67° 23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67°
23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p67°
23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67°23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67°23°
1 2
t
s
Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t
and s, find the measures of angles 1 and 2.
m
n
p
67° 23°
23° 67°
t
s
Examples & Explanations
Adapted from the Arizona department of Education
• Show that m 3 ∠ + m 4 ∠ + m 5 ∠ = 180˚
if and m are parallel lines and t1 & t2 are transversals.
• Find the m a ∠ , m b ∠ , and the m ∠c
if line n and segment yz are parallel.
n
Examples & ExplanationsUnderstand congruence and similarity using
physical models, transparencies, or geometry software.
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
SEDL Common Core Support Video: MCC8.G.2
Using a Physical Model to Demonstrate a Reflection
http://secc.sedl.org/common_core_videos/index.php?action=view&id=781
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
Examples & ExplanationsDescribe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there
more than one possible sequence?
1. Reflected the figure in the y-axis.2. Rotated the figure 90° clockwise about the point
(2, -5).3. Translated the figure vertically +10 units, or ten
was added to the y-coordinate of each point of the figure: (x, y) → (x, y + 10).
AssessmentHow could it look?
•Examples of how balanced assessments can be assembled.
http://map.mathshell.org/materials/tests.phpThe target audience for these example assessments are:
1. teachers who have already started to work on their student’s mathematical practice skills
2. designers of future CCSSM-aligned assessments
AssessmentHow could it look?
http://map.mathshell.org/materials/tests.php
Resource List
The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.
Resources• Common Core Resources
SEDL videos - https://www.georgiastandards.org/Common-Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/ Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Arizona DOE - http://www.azed.gov/standards-practices/mathematics-standards/ Ohio DOE - http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1704Common Core Standards - http://www.corestandards.org/ Tools for the Common Core Standards - http://commoncoretools.me/ Phil Daro talks about the Common Core Mathematics Standards - http://serpmedia.org/daro-talks/index.html
• BooksVan DeWalle, Elementary and Middle School Mathematics, Teaching Developmentally - College Level TextVan De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Resources• Professional Learning Resources
Inside Mathematics- http://www.insidemathematics.org/Annenberg Learner - http://www.learner.org/index.html Edutopia – http://www.edutopia.org Teaching Channel - http://www.teachingchannel.org
• Assessment Resources MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/ MAP - http://www.map.mathshell.org.uk/materials/index.php PARCC - http://www.parcconline.org/parcc-states
As you start your day tomorrow…Who dares to teach must never cease to learn ~ John Cotton Dana
http://www.youtube.com/watch?v=JEa0xpWi7C4
Thank You! Please visit http://ccgpsmathematics6-8.wikispaces.com/ to provide us with
your feedback, ask questions, and share your ideas and resources!
Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspxto join the 6-8 Mathematics email listserve.
Brooke KlineProgram Specialist (6 12)‐
James PrattProgram Specialist (6-12)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.