CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
May 7, 2013
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CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
May 7, 2013
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.

• Intent and focus of Unit 1 webinar.
• Framework tasks.
• GPB sessions on Georgiastandards.org.
• Standards for Mathematical Practice.
• Resources.
• http://ccgpsmathematics9-10.wikispaces.com/

What is a Wiki?
http://ccgpsmathematics9-10.wikispaces.com/

Welcome!
•
•
 Why do SSS, ASA, & SAS work? Why does AA work?
•
•

Feedback http://ccgpsmathematics9-10.wikispaces.com/
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary Mathematics Specialists

Parent Communication
• Explanation to parents of the need for change in mathematics
• What children will be learning in high school mathematics
• Parents partnering with teachers
• Grade level examples
• Parents helping children learn outside of school
• Additional resources http://www.cgcs.org/Page/244

Parent Communication
• An overview of what children will be learning in high school mathematics
• Topics of discussion for parentteacher communication regarding student academic progress
• Tips for parents that will help their children plan for college and career http://www.achievethecore.org/leadership-tools-commoncore/parent-resources/

Parent Communication
• An overview of what children will be learning in high school mathematics
• Topics of discussion for parentteacher communication regarding student academic progress
• Tips for parents that will help their children plan for college and career http://www.achievethecore.org/leadership-tools-commoncore/parent-resources/

Wiki/Email Questions
MCC9-12.G.CO.6
What’s the difference between 8 th grade MCC8.G.2 and what we do in
Analytic Geometry?
MCC9-12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Wiki/Email Questions
MCC9-12.G.CO.10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Can you provide more information about this standard:
1. Do we need the students to be able to prove the medians of a triangle meet at a point?
2. Do the students need to know centroid, incenter, circumcenter, and orthocenter?
3. Do the students need to know how to apply each proof listed in this standard to “skill based” problems?

• Cost: $50 for GCTM members and $60 for GCTM non-members
• Travel expenses will be reimbursed for all participants who complete the academy and are Georgia certified K-12 educators under contract with a Georgia school
• Registration will opened on April 1, 2013
• Registration closing dates:
 Academy 1 – May 15, 2013
 Academy 2 – May 22, 2013
 Academy 3 – May 29, 2013
 Academy 4 – June 5, 2013
• Payments must be received prior to the closing date of registration

• Visit www.gctm.org
for more details concerning these quality professional development opportunities
• Call 1-855-ASK-GCTM (ext 4) for questions about the academy
• Peggy Pool – GCTM Vice President for Regional Services and Director of Academies, Academies2013@gctm.org

In each of the following diagrams, two triangles are shaded. Based on the information given about each diagram, decide whether there is enough information to prove that the two triangles are congruent.
In circle O, 𝐴𝐵 is congruent to 𝐶𝐷
ABCD is a parallelogram
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

The two triangles are congruent by SAS:
ABCD is a parallelogram
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

The two triangles are congruent by SAS:
We have 𝐴𝑋 ≅ 𝐶𝑋 and 𝐷𝑋 ≅ 𝐵𝑋 since the diagonals of a parallelogram bisect each other, and ∠ AXD ≅ ∠ CBX since they are vertical angles.
ABCD is a parallelogram
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

The two triangles are congruent by SAS:
We have 𝐴𝑋 ≅ 𝐶𝑋 and 𝐷𝑋 ≅ 𝐵𝑋 since the diagonals of a parallelogram bisect each other, and ∠ AXD ≅ ∠ CBX since they are vertical angles.
Alternatively, the two triangles are congruent by ASA:
ABCD is a parallelogram
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

The two triangles are congruent by SAS:
We have 𝐴𝑋 ≅ 𝐶𝑋 and 𝐷𝑋 ≅ 𝐵𝑋 since the diagonals of a parallelogram bisect each other, and ∠ AXD ≅ ∠ CBX since they are vertical angles.
ABCD is a parallelogram
Alternatively, the two triangles are congruent by ASA:
∠ DAX ≅ ∠ BCX and ∠ ADX ≅ ∠ CBX since they are opposite interior angles. 𝐴𝐷 ≅ 𝐵𝐶 since opposite sides of a parallelogram are congruent.
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

Triangles are congruent.
Triangle BOA is the result of reflecting triangle COD across the perpendicular bisector of AD
In circle O, AB is congruent to CD
Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

What’s the big idea?
• Understand congruence in terms of rigid motions.
• Understand similarity in terms of similarity transformations.
• Prove theorems involving similarity.
• Prove geometric theorems.
• Make geometric constructions.

What’s the big idea?
Standards for Mathematical Practice

What’s the big idea?
• SMP 3 – Construct viable arguments and critique the reasoning of others
 Student Sample Work
 Feedback/Critique and Revision
Expeditionary Learning http://elschools.org/student-work/butterfly-drafts

Coherence and Focus
• K-8 th
 Identification of figures in different orientations
 Ratios and proportions
 Drawing of geometric figures with specific characteristics
 Transformations
 Basic congruence and similarity
• 10 th -12 th
 Transformations of functions
 Trigonometric Functions

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Show that there is a translation of the plane which maps A to D
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Show that there is a translation of the plane which maps A to D
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Show that there is a rotation of the plane which does not move
D and which maps B ’ to E.
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Show that there is a rotation of the plane which does not move
D and which maps B ’ to E.
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Show that there is a reflection of the plane which does not move D or E and which maps C ’’ to F.
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ ABC ≅ △ DEF
Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations
The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.
Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Examples & Explanations
The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.
Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Examples & Explanations
The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.
Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Proofs in CCGPS
Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two ‐ column format, and using diagrams without words.
Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning.
http://www.mathematicsvisionproject.org/secondary-two-mathematics.html

Examples & Explanations
In the picture below 𝐴𝐷 and 𝐵𝐶 intersect at X. 𝐴𝐵 and 𝐶𝐷 are drawn forming △ AXB and △ CXD.
The lengths AX, XB, CX, and DX satisfy the equation 𝐴𝑋
𝐵𝑋
=
𝐷𝑋
𝐶𝑋
A
C
X
D
B
Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Examples & Explanations
In the picture below AD and BC intersect at X. AB and CD are drawn forming △ AXB and △ CXD.
The lengths AX, XB, CX, and DX satisfy the equation 𝐴𝑋
𝐵𝑋
=
𝐷𝑋
𝐶𝑋
Are the two triangles similar, if so describe the sequence of transformations
.
Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Examples & Explanations
The lengths AX, XB, CX, and DX satisfy the equation 𝐴𝑋
𝐵𝑋
=
𝐷𝑋
𝐶𝑋
Rotate △ ABX 180 degrees about point X, so
∠ AXB coincides with ∠ DXC. Then dilate △ ABX by a factor of 𝐷𝑋
𝐴𝑋
. This moves A to D, since
𝐴𝑋(
𝐷𝑋
)=𝐷𝑋
𝐴𝑋
, and likewise moves B to C. Therefore △AXB is similar to △DXC
Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

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 http://secc.sedl.org/common_core_videos/index.php

Resources http://www.shodor.org/interactivate/

Resources http://www.illustrativemathematics.org/

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 Mathematicshttp://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
 Expeditionary Learning: Center for Student Work http://elschools.org/student-work
• Blogs
 Dan Meyer – http://blog.mrmeyer.com/
 Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html
 Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/

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