ccgps mathematics unit-by-unit grade level webinar coordinate algebra & accelerated coordinate...

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 – jpratt@doe.k12.ga.usBrooke Kline – bkline@doe.k12.ga.usSecondary 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 – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usSecondary 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)

bkline@doe.k12.ga.us

James PrattProgram Specialist (6-12)

jpratt@doe.k12.ga.us

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.