CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Coordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry A
Unit 6: Connecting Algebra and Geometry Through
Coordinates
October 11, 2012
Session will be begin at 8:00 am
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CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Coordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry A
Unit 6: Connecting Algebra and Geometry Through
Coordinates
October 11, 2012
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary 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.
Welcome!
• 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
Feedback
http://ccgpsmathematics9-10.wikispaces.com/
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary 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 Eitel
Director, Assessment Administration
Assessment & Accountability
Office 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).
Mathematical Communication
The 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 Communication
Mathematical 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 Walk
Math Congress
Bansho (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 sensemaking of students rather than to
simply sanction particular
approaches as being correct or
demonstrate procedures for
solving predictable tasks.”
Stein, Engle, Smith, & Hughes
Mathematical Communication
When teacher talk dominates
whole-class discussion, students
tend to rely on teachers to
be 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.
Passive/receptive
Minimal student explanations, comparisons
Passive
Active
Transmission
Challenging
Research - Communication
Research 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 highquality student interaction
1. The use of rich math tasks
2. Justification of solutions
3. Students questioning one
another
4. Use of wait time
5. 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
PostAssessment
PreAssessment
• Misconceptions
• Understandings
• Feedback
• Discussion
• Explanations
Collaborative
Task
• Improvement
• Deeper
Understanding
Task Structure
PreAssessment
• Misconceptions
• Understandings
All three are
communication
• Feedback
• Discussion
• Explanations
Collaborative
Task
PostAssessment
• Improvement
• Deeper
Understanding
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.
4  (6) 10
PQ :

5
53
2
 10  (6)  4 4
QR :


03
3 3
0  (10) 10
RS :

5
20
2
4  ( 0) 4
SP :

52
3
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.
4  (6) 10
PQ :

5
53
2
 10  (6)  4 4
QR :


03
3 3
0  (10) 10
RS :

5
20
2
4  ( 0) 4
SP :

52
3
Two sets of parallel
sides. No perpendicular
sides.
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).
(2,3)
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from
A(-2, -3) to B(8, 7).
(2,3)
2
2
(2  x,3  y )
5
5
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from
A(-2, -3) to B(8, 7).
(2,3)
2
2
(2  x,3  y )
5
5
2
2
(2  (10),3  (10))
5
5
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from
A(-2, -3) to B(8, 7).
(2,3)
2
2
(2  x,3  y )
5
5
2
2
(2  (10), 3  (10))
5
5
(2  4,3  4)
Examples & Explanations
Find the coordinate of point T, that is 2/5 of the distance from
A(-2, -3) to B(8, 7).
(2,3)
2
2
(2  x,3  y )
5
5
2
2
(2  (10), 3  (10))
5
5
(2  4,3  4)
(2,1)
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.
AB
BC
AC
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2),
B(2, 5) and C(5, 6).
Determine the following lengths.
AB  (2  1) 2  (5  2) 2  1  9  10
BC
AC
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2),
B(2, 5) and C(5, 6).
Determine the following lengths.
AB  (2  1) 2  (5  2) 2  1  9  10
BC  (5  2) 2  (6  5) 2  9  1  10
AC
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2),
B(2, 5) and C(5, 6).
Determine the following lengths.
AB  (2  1) 2  (5  2) 2  1  9  10
BC  (5  2) 2  (6  5) 2  9  1  10
AC  (5  1) 2  (6  2) 2  16  16  32
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2),
B(2, 5) and C(5, 6).
Determine the following lengths.
AB  (2  1) 2  (5  2) 2  1  9  10
BC  (5  2) 2  (6  5) 2  9  1  10
AC  (5  1) 2  (6  2) 2  16  16  32
Perimeter is AB  BC  AC
10  10  32
Examples & Explanations
Determine the perimeter of a triangle with vertices A(1, 2),
B(2, 5) and C(5, 6).
Determine the following lengths.
AB  (2  1) 2  (5  2) 2  1  9  10
BC  (5  2) 2  (6  5) 2  9  1  10
AC  (5  1) 2  (6  2) 2  16  16  32
Perimeter is AB  BC  AC
10  10  32 or 3.16  3.16  5.65  11.97
Find the equation of the line that passes
through (5, 4) and is parallel to the line that
contains (1, 1) and (-3, 9).
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.
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 - 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.php
Illustrative 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
•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
•Blogs
Dan Meyer – http://blog.mrmeyer.com/
Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html
Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/
Resources
Learnzillion.com
•
•
•
•
•
•
Review
Common Mistakes
Core Lesson
Guided Practice
Extension Activities
Quick Quiz
Resources
Learnzillion.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.aspx
to join the 9-12 Mathematics email listserve.
Brooke Kline
Program Specialist (6‐12)
bkline@doe.k12.ga.us
James Pratt
Program Specialist (6-12)
jpratt@doe.k12.ga.us
These materials are for nonprofit educational purposes only.
Any other use may constitute copyright infringement.