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CCGPS MathematicsUnit-by-Unit Grade Level WebinarCoordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry AUnit 6: Connecting Algebra and Geometry Through
CoordinatesOctober 11, 2012
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CCGPS MathematicsUnit-by-Unit Grade Level WebinarCoordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry AUnit 6: Connecting Algebra and Geometry Through
CoordinatesOctober 11, 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.
Expectations and clearing up confusion
• Intent and focus of Unit 6 webinar.• Framework tasks.• GPB sessions on Georgiastandards.org.• Standards for Mathematical Practice. • Resources. • http://ccgpsmathematics9-10.wikispaces.com/• CCGPS is taught and assessed from 2012-2013 and beyond.
• The big idea of Unit 6• The importance of mathematical communication
How can I help my students become more effective mathematical communicators?What does research say about communication?
• Resources
Welcome!
Feedbackhttp://ccgpsmathematics9-10.wikispaces.com/
James Pratt – [email protected] Brooke Kline – [email protected] Mathematics Specialists
My Favorite No
https://www.teachingchannel.org/videos/class-warm-up-routine
Wiki/Email Questions & Announcements
• Are Coordinate Algebra students expected to simplify radicals?
Estimate - Yes! Rewrite (Simplify) - No!
Wiki/Email Questions & Announcements
System Test Coordinators, Please note that we have posted today a revised EOCT Coordinate Algebra Study Guide. You can find the guide at the GaDOE webpage below:http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/EOCT-Guides.aspx
The purpose of this revised posting was to edit the information that appeared on pages 147 – 148 regarding strategies to fitting a line to data. The GaDOE Curriculum Division has determined that strategies for fitting a line to data may include estimation (“eye-balling”) and/or the use of technology. The previous version of the Study Guide specified that median-median was a required method for this purpose. However, that is not the case. As a result, the pages referenced above, and those that contained related problems, have been edited to clarify this point.
Please share this with the appropriate content experts in your local systems as you determine is appropriate. The GaDOE Curriculum Division’s math specialists will be sharing this information with their contacts in local systems as well.Thank you!
Tony EitelDirector, Assessment AdministrationAssessment & AccountabilityOffice of Curriculum, Instruction, and Assessment
Find the equation of the line that passes through (5, 4) and is parallel to the line that contains (1, 1) and (-3, 9).
Activate your Brain
Mathematical CommunicationThe development of students’ mathematical communication shifts in precision and sophistication throughout the primary, junior and intermediate grades, yet the underlying characteristics remain applicable across all grades.
CBS Mathematics
Mathematical CommunicationMathematical communication is an essential process for learning mathematics because through communication, students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments.
Ontario Ministry of Education
Mathematical Communication•Developing effective mathematical communication•Categories of mathematical communication•Organizing students to think, talk, and write•Updating the three-part problem-solving lesson
Gallery WalkMath CongressBansho (Board Writing)
Mathematical Communication“Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.”
Cobb, Wood, & Yackel
Mathematical Communication“The role of the teacher during whole-class discussion is to develop and to build on the personal and collective sense-making of students rather than to simply sanction particular approaches as being correct or demonstrate procedures for solving predictable tasks.”
Stein, Engle, Smith, & Hughes
Mathematical CommunicationWhen teacher talk dominates whole-class discussion, students tend to rely on teachers tobe the expert, rather than learning that they can work out their own solutions and learn from other students.
CBS Mathematics
What’s the big idea?•Deepen understanding of linear graphs and equations.•Deepen understanding of the Pythagorean Theorem.•Develop an understanding of distance between two points.•Develop an understanding of partitioning a directed line segment.• Standards for Mathematical Practice.
ImitativeBad Math?
Passive/receptive Bad Math?
Minimal student explanations, comparisons
Bad Math?
Passive Active
Transmission Challenging
Research - CommunicationResearch tells us that student interaction – through classroom discussion and other forms of interactive participation – is foundational to deep understanding and related student achievement. But implementing discussion in the mathematics classroom has been found to be challenging.
Dr. Catherine D. Bruce
Research - Communication•The value of student interaction•Challenges the teachers face in engaging students•The teacher’s role•Five strategies for encouraging high-quality student interaction
1. The use of rich math tasks2. Justification of solutions3. Students questioning one
another4. Use of wait time5. Use of guidelines for Math Talk
Mathematical Communication•Tips on Getting Started
1. Organizing the classroom learning environment
2. Preparing yourself mathematically
3. Coordinating student discussion and analysis of solutions
Coherence and Focus• K-8th
Finding perimeters of geometric figures Graphing on the coordinate plane Determining horizontal and vertical distances on the coordinate plane Pythagorean Theorem
• 10th-12th Transformations on the coordinate plane Coordinate proofs with geometric figures Coordinate proofs with quadratics and conics
Task Structure
• Misconceptions• Understandings
Pre-Assessment
Task Structure
• Misconceptions• Understandings
Pre-Assessment
All three are communication
Examples & Explanations
Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?
Examples & Explanations
Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?
Examples & Explanations
Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?
Find the slopes of the sides.
Examples & Explanations
Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?
Find the slopes of the sides.
3
4
25
)0(4:
52
10
02
)10(0:
3
4
3
4
30
)6(10:
52
10
35
)6(4:
SP
RS
QR
PQ
Examples & Explanations
Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?
Find the slopes of the sides.
Two sets of parallel sides. No perpendicularsides.
3
4
25
)0(4:
52
10
02
)10(0:
3
4
3
4
30
)6(10:
52
10
35
)6(4:
SP
RS
QR
PQ
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
)3,2(
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
)5
23,
5
22(
)3,2(
yx
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
))10(5
23),10(
5
22(
)5
23,
5
22(
)3,2(
yx
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
)43,42(
))10(5
23),10(
5
22(
)5
23,
5
22(
)3,2(
yx
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
)1,2(
)43,42(
))10(5
23),10(
5
22(
)5
23,
5
22(
)3,2(
yx
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
AC
BC
AB
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
AC
BC
AB 1091)25()12( 22
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
AC
BC
AB
1019)56()25(
1091)25()12(
22
22
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
321616)26()15(
1019)56()25(
1091)25()12(
22
22
22
AC
BC
AB
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
Perimeter is321616)26()15(
1019)56()25(
1091)25()12(
22
22
22
AC
BC
AB
321010
ACBCAB
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).
Determine the following lengths.
Perimeter is321616)26()15(
1019)56()25(
1091)25()12(
22
22
22
AC
BC
AB
97.1165.516.3.163or 321010
ACBCAB
Find the equation of the line that passes through (5, 4) and is parallel to the line that contains (1, 1) and (-3, 9).
Activate your Brain
Find the equation of the line that passes through (5, 4) and is parallel to the line that contains (1, 1) and (-3, 9).•Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.•The role of the teacher during whole-class discussion is to develop and the build on the personal and collective sense-making of students.•…learning that they can work out their own solutions and learn from other students.
Activate your Brain
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.
• Common Core Resources SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/Common 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://bit.ly/URwOFT
•Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.phpIllustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ PARCC - http://www.parcconline.org/ Online Assessment System - http://bit.ly/OoyaK5
Resources
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 Ontario Ministry of Education - http://bit.ly/cGZlce
Capacity Building Series: Communication in the Mathematics Classroom - http://bit.ly/acoWR9 What Works? Research into Practice - http://bit.ly/SRYTuM
•BlogsDan Meyer – http://blog.mrmeyer.com/Timon Piccini – http://mrpiccmath.weebly.com/3-acts.htmlDan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/
ResourcesLearnzillion.com
• Review• Common Mistakes• Core Lesson• Guided Practice• Extension Activities• Quick Quiz
ResourcesLearnzillion.com
~Thank you! Thank you! Thank you! This webinar was great, and the site has great resources that I can use tomorrow! I just shared it with everyone at my school! It is like going to a Common Core Conference and receiving all the materials for every session and having them in one place! I love it!
~I watch so many math videos for our common core lessons and I am speechless, how awesome all these small video clips are.
~Thanks for this. I attended the webinar last week and really like this site. I'm planning on having a PL session at school on Thursday.
https://attendee.gotowebinar.com/recording/2385067565478552832
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.aspxto join the 9-12 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.