Secondary Mathematics Specialists CCGPS Mathematics Coordinate Algebra Update Webinar Unit 6: Connecting Algebra and Geometry Through Coordinates November 8, 2013 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Secondary Mathematics Specialists Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

What are update webinars? Update on the work of the 2013 Resource Revision Team Overall revisions Unit 6 revisions Addressing areas which teachers have found to be more challenging Resources James

2013 CA Resource Revision Team Brooke

Coordinate Algebra/Acc CA Comprehensive Course Overview Located on the 9-12 math section of www.georgiastandards.org Designed to provide clarification of CCGPS Mathematics Standards Organized to link together many sources of information pertinent to CCGPS Coordinate Algebra/Accelerated Coordinate Algebra

Begin at www.georgiastandards.org Direct Link to Page

Select the CCGPS ELA/Math Tab Direct Link to Page

Select the Mathematics option under Browse CCGPS Direct Link to Page

Select the 9-12 option in the Mathematics section Direct Link to Page

Expand the Coordinate Algebra Course Direct Link to Page

Select the Comprehensive Course Overview Expande Coordinate Algebra Direct Link to Page

This screen should appear when you select Comprehensive Course Overview Direct Link to Page

Table of Contents Outlines the Major areas of Focus for the Course Fully Interactive when viewed via internet Hover over a section and select to access the section quickly This fully interactive page will provide teachers with ease of access to the information that they need

Sections of Interest Flipbook Access: Detailed Information About Each Standard Unit Descriptions: Overview Webinar Information Assessment Resources and Instructional Support Resources Internet Resources Curriculum Map These sections are designed to tie together many other areas of support offered by GADOE and other states implementing CCSS

Formative Assessment Lessons (FALs) Follow the Task section, teachers will find detailed information in the FAL section with examples and links to videos of teachers using FALs

CCGPS Math Wiki Space

Coordinate Algebra EOCT Released Items Released Items Housed in the Assessment Division of GADOE http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/Coordinate%20Algebra%20Released%20Items%20Booklet.pdf Released Items Commentary Housed in the Assessment Division of GADOE http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/Coordinate%20Algebra%20Released%20Items%20Commentary.pdf There are 20 released items and commentary about each item available for Coordinate Algebra

EOCT Released Item Commentary

EOCT Released Item #16

Solution to item #16 𝐺𝑃 𝑃𝐻 = 3 2 2𝐺𝑃=3𝑃𝐻 2 −1−𝑥, 5−𝑦 =3 𝑥−1, 𝑦+1 G (-1,5) P (x,y,) H (1,-1) 2𝐺𝑃=3𝑃𝐻 2 −1−𝑥, 5−𝑦 =3 𝑥−1, 𝑦+1 2 −1−𝑥 =3 𝑥−1 -2-2x = 3x – 3 5x = 1 X = 0.2 2 5−𝑦 =3 𝑦+1 10 – 2y = 3y + 3 5y = 7 Y = 1.4 𝑻𝒉𝒆 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆𝒔 𝒐𝒇 𝒑𝒐𝒊𝒏𝒕 𝑷 𝒂𝒓𝒆 (𝟎.𝟐, 𝟏.𝟒)

Data on Released Item #16

Sample Item From EOCT Study Guide http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/EOCT%20Coordinate%20Algebra%20Study%20Guide%20Revised%20August%202013.pdf From CA EOCT Study Guide Pg 187

Solution to EOCT Study Guide Example From CA EOCT Study Guide Pg 188

Unit 6 Frameworks Show how this released item relates back to the Frameworks for Unit 4

Partitioning in Unit 6 “New York City”

Purpose of Tasks Problem-Based-Learning--Check out Dan Meyer, Robert Kaplinksy’s websites Provide several entry points to the standards. Teachers should review all tasks in a given unit to determine which tasks would be appropriate for their students.  Tasks can be adapted to fit the needs or your classroom.    Most standards are covered by various tasks

Goals of Unit Revisions More user-friendly Provide teachers with task summaries Give teachers tools necessary to quickly analyze tasks Provide tasks from different sources

Updates to Unit Frameworks TASK TABLE Outlines the tasks by type, content and standard. Provides suggested times Hyperlinks to PDFs and Word Docsv

Updates to Unit Frameworks

Unit 6 Partition a line segment Determine slope and equations of parallel and perpendicular lines Use slope and distance formula to prove simple geometric theorems in the coordinate plane

Equations of Parallel and Perpendicular Lines Task Basic Content Addressed New York City Slopes of Special Pairs of Lines Euler’s Village Partition a line segment into a given ratio Determine slopes of parallel and perpendicular lines Write equations of parallel and perpendicular lines given an equation of a line and a point not on that line

Geometric Properties on the Coordinate Plane Task Basic Content Addressed Geometric Properties in the Plane Equations of Parallel & Perpendicular Lines (FAL) Square (Short Cycle Task) Surveillance of the Village (Culminating Task) Use slope and distance formula to prove simple geometric theorems algebraically Find perimeter and area of polygons in a coordinate plane Use equations of parallel and perpendicular lines to form geometric figures

Square (Short Cycle Task) This short task focuses on using the distance formula and slope formula to determine if the points graphed will form the sides of a square.

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. At this point, I know that a rectangle has four right angles and opposite sides that are the same length. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. At this point, I know that a rectangle has four right angles and opposite sides that are the same length. I need to show that adjacent sides are perpendicular, by using their slopes. I need to show the lengths of opposite sides are equal. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3 Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. I need to show that adjacent sides are perpendicular, by using their slopes. Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3 Slope of 𝑄𝑅 = 6−(−3) −3−9 = −9 12 = −3 4 Slope of 𝑅𝑆 = −7−(−3) 6−9 = 4 3 Slope of 𝑆𝑃 = −7−2 6−(−6) = −9 12 = −3 4 James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3 Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. I need to show that adjacent sides are perpendicular, by using their slopes. Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3 Slope of 𝑄𝑅 = 6−(−3) −3−9 = −9 12 = −3 4 Slope of 𝑅𝑆 = −7−(−3) 6−9 = 4 3 Slope of 𝑆𝑃 = −7−2 6−(−6) = −9 12 = −3 4 The slopes of adjacent sides are opposite reciprocals of each other so the lines are perpendicular. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. I need to show the lengths of opposite sides are equal. 𝑃𝑄= (−6− −3 ) 2 + (2−6) 2 = (−3) 2 + (−4) 2 = 25 =5 𝑄𝑅= (9− −3 ) 2 + (−3−6) 2 = (12) 2 + (−9) 2 = 225 =15 𝑅𝑆= (9−6) 2 + (−3−(−7)) 2 = (3) 2 + (4) 2 = 25 =5 𝑆𝑃= (6− −6 ) 2 + (−7−2) 2 = (12) 2 + (−9) 2 = 225 =15 James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Opposite sides have the same length. Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. I need to show the lengths of opposite sides are equal. 𝑃𝑄= (−6− −3 ) 2 + (2−6) 2 = (−3) 2 + (−4) 2 = 25 =5 𝑄𝑅= (9− −3 ) 2 + (−3−6) 2 = (12) 2 + (−9) 2 = 225 =15 𝑅𝑆= (9−6) 2 + (−3−(−7)) 2 = (3) 2 + (4) 2 = 25 =5 𝑆𝑃= (6− −6 ) 2 + (−7−2) 2 = (12) 2 + (−9) 2 = 225 =15 Opposite sides have the same length. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain. At this point, I know that a rectangle has four right angles and opposite sides that are the same length. Adjacent sides are perpendicular and the lengths of opposite sides are equal, therefore the quadrilateral is a rectangle. James 8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Unit 6 Challenges Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7). Brooke

Resources GaDOE Resources Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx 2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Georgia Mathematics Teacher Forums - http://ccgpsmathematics9-10.wikispaces.com/ CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative-Assessment-Lessons-Videos.aspx Brooke

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. Brooke

Resources CCGPS Resources Assessment Resources Georgia Virtual Learning - http://www.gavirtuallearning.org/Resources.aspx SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.html Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Tools for the Common Core Standards - http://commoncoretools.me/ LearnZillion - http://learnzillion.com/ Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.php Illustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/ PARCC - http://www.parcconline.org/ Online Assessment System - http://bit.ly/OoyaK5 Brooke

LearnZillion Revised http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go A more “user friendly” version of the Learnzillion lessons support learning new strategies, sharing with parents, helping absent students. Brooke

LearnZillion Choose grade band: Choose domain: Choose topic/strand http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go Choose grade band: Choose domain: Choose topic/strand and standard: Brooke

LearnZillion http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go Brooke

LearnZillion “Quick Codes” http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go Brooke

Resources Professional Learning Resources Blogs Books 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 Ontario Ministry of Education - http://bit.ly/cGZlce Achieve - http://www.achieve.org/ Expeditionary Learning: Center for Student Work - http://elschools.org/student-work Blogs Dan Meyer – http://blog.mrmeyer.com/ Robert Kaplinsky - http://robertkaplinsky.com/ Books Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8 Brooke

James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Feedback http://www.surveymonkey.com/s/WZKG5G2 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Brooke

James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us Thank You! Please visit http://ccgpsmathematics9-10.wikispaces.com/ to share your feedback, ask questions, and share your ideas and resources! Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx to join the 9-12 Mathematics email listserve. Follow on Twitter! Follow @GaDOEMath Brooke Kline Program Specialist (6‐12) bkline@doe.k12.ga.us James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us James & Brooke These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.