CCGPS Mathematics
8th Grade Update Webinar
Unit 7: Solving Systems of Equations
March 14, 2014
James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us
Secondary Mathematics Specialists
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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 7 revisions
• Addressing areas which teachers
have found to be more challenging
• Resources
2013 8th Grade Resource Revision Team
Shelly Bydlinski
Glynn Co.
Schools
Mandi Campbell
Floyd Co.
Kim Conley
Lee Co.
Samantha Clay
APS
Joe Hardy
Bibb Co.
8th Grade
CCGPS Unit Revisions
Webinar
Overview of
Comprehensive Course Guide
&
Unit 7: Solving Systems of Equations
Resource Revision Team Goals
Create a Comprehensive Course Guide which would:
 Provide an overview of the 8th Grade Mathematics
Curriculum
 Provide clarification of CCGPS Mathematics Standards
 Link together many sources of information pertinent to
CCGPS 8th Grade Math
Update the Units by:
 Increasing Task Options
 Developing Differentiation Opportunities within each task.
Begin at www.georgiastandards.org
Accessing SLDS
Accessing Resources through SLDS
1st
2nd
4th
3rd
 Click on the
“RESOURCES” tab at the
top
 Choose “Search by
Subject”
• Using the drop down
boxes, choose your
Subject, Grade Level,
and Course Name
 Click “Get Resources”
 Choose the “Teacher
Tools” tab
Select the CCGPS ELA/Math Tab
Direct Link to Page
Select the Mathematics option under
Browse CCGPS
Select the 6-8
option in the Mathematics section
Select the Grade 6 option
Select the Comprehensive Course Guide
Direct Link to
Page
This is your Comprehensive Course Guide
Sections of Interest
 Standards are hyperlinked to the Flipbooks
providing teaching strategies,
misconceptions, and prior knowledge
 Formative Assessment Lesson (FAL)
information and video links
 Internet Resources
Flipbooks
 Click on blue hyperlink to access
 The Flipbooks offer clarification
 Very Large File (slow loading)
8th Grade Standards
Standard Specific Information
Task Descriptions
Scaffolding Task - Tasks that build up to the learning task.
Learning Task - Constructing understanding through deep/rich contextualized problem solving
tasks.
Practice Task - Tasks that provide students opportunities to practice skills and concepts.
Performance Task - Tasks which may be a formative or summative assessment that checks for
student understanding/misunderstanding and or progress toward the standard/learning goals at
different points during a unit of instruction.
Culminating Task - Designed to require students to use several concepts learned during the unit to
answer a new or unique situation. Allows students to give evidence of their own understanding
toward the mastery of the standard and requires them to extend their chain of mathematical
reasoning.
Achieve CCSS- CTE - Designed to demonstrate how the Common Core and Career and Technical
Classroom Tasks - Education knowledge and skills can be integrated. The tasks provide teachers
with realistic applications that combine mathematics and CTE content.
Short Cycle Task - Designed to exemplify the performance targets that the standards imply. The
tasks, with the associated guidance, equip teachers to monitor overall progress in their students’
mathematics.
Formative Assessment Lesson (FAL) - Lessons that support teachers in formative assessment
which both reveal and develop students’ understanding of key mathematical ideas and
applications. These lessons enable teachers and students to monitor in more detail their progress
towards the targets of the standards.
Formative Assessment Lessons
(FALs)
Formative Assessment Lessons
(FALs)
• Formative Assessment Lessons (“Classroom Challenges”)
• Developed by the Shell Center
• Embedded in the FY14 Units, also available at
http://map.mathshell.org.uk/materials/lessons.php
• Intended to guide instructional decisions for the rest of the unit
• Not intended to be graded, but for feedback
• Very beneficial to addressing student misconceptions
• Additional FALs are in the editing process.
For the FALs click on
this tab
For the Short Cycle
Tasks click on this tab
Make sure to choose the
Correct grade level
Internet Resources
• Webinar Information
• General Resources
• Problem-Based Learning
• Assessment and Instructional
Support Resources
Examples of Resources
Unit 7
Solving Systems of
Equations
Overall Changes in the Unit
 Slight change of format
 Inclusion of Formative Assessment Lessons from the Shell
Center
 Included Standards for Mathematical Practice (SMPs) for
each Task and differentiation options
 Suggestions sent by educators from all over the United
States via email and the wiki
 Observations made from personal experiences
Selected Terms and Symbols
Note: In the Teacher’s Edition (found in the
Learning Village), the Task Table includes hyperlinks
to the Formative Assessment Lessons (FALs). The
links are also found on the individual task pages
within the unit.
Task Additions
 Fencing: Short Cycle Task – In this task, you must
figure out the cost of building fences from fence
posts and wooden panels.
 Optimization Boomerang: FAL – Use system of
equations to find the maximum amount of money
which could be raised.
 Classifying Solutions to Systems of Equations: FAL
– Classify solutions to a pair of linear equations by
considering their graphical representations.
Let’s take a closer look at a Performance
Task in Unit 8: Playing with Straws
A new section has been included in each
task to list the appropriate Standards for
Mathematical Practice (SMPs).
The standards are hyperlinked to the CCGPS
document which can also be found at
www.georgiastandards.org
Common Misconceptions have been
identified for each task to assist teachers
in guiding the students to success.
Playing With Straws
Differentiation, including both Extensions and
Intervention/Scaffolding, have also been
provided for this task and other tasks in Unit 8.
Things to Remember
 Use the Wiki to share information with other
teachers and to ask questions.
 These units are living documents. Please share
anything you may have to enhance this or any
unit. The Wiki is the teacher community page to
share anything you have.
THE WIKI
Feedback
Your comments are greatly appreciated:
http://ccgpsmathematics6-8.wikispaces.com/home
Unit 7 Challenges
The local swim center is making a special offer. They
usually charge $7 per day to swim at the pool. This
month swimmers can pay an enrollment fee of $30 and
then the daily pass will only be $4 per day.
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
The local swim center is making a special offer. They
usually charge $7 per day to swim at the pool. This
month swimmers can pay an enrollment fee of $30 and
then the daily pass will only be $4 per day.
Determine which deal is best.
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
The local swim center is making a special offer. They
usually charge $7 per day to swim at the pool. This
month swimmers can pay an enrollment fee of $30 and
then the daily pass will only be $4 per day.
Normal rate: 𝑚 = 7𝑑
Special rate: 𝑚 = 4𝑑 + 30
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
Normal rate: 𝑚 = 7𝑑
Special rate: 𝑚 = 4𝑑 + 30
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
Normal rate: 𝑚 = 7𝑑
Special rate: 𝑚 = 4𝑑 + 30
7𝑑 = 4𝑑 + 30
3𝑑 = 30
𝑑 = 10
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
Normal rate: 𝑚 = 7𝑑 : best for 10 days or less
Special rate: 𝑚 = 4𝑑 + 30 : best for more than 10
days
Adapted from Illustrative Mathematics 8.EE Summer Swimming
Unit 7 Challenges
http://bit.ly/1eRkTWR
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
Unit 7 Challenges
Find the equations of line 𝑚 and line 𝑙.
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
Unit 7 Challenges
Find the equations of line 𝑚 and line 𝑙.
Line 𝑚 goes through (0,0) and (1,1)
𝑦=𝑥
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
Unit 7 Challenges
Find the equations of line 𝑚 and line 𝑙.
Line 𝑚 goes through (0,0) and (1,1)
𝑦=𝑥
Line 𝑙 goes through (12,1) and (1,0)
Slope: -2
y-intercept: 2
𝑦 = −2𝑥 + 2
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
Unit 7 Challenges
Point 𝑃 is at the intersection of line 𝑚 and line 𝑙.
𝑦=𝑥
𝑦 = −2𝑥 + 2
𝑥 = −2𝑥 + 2
3𝑥 = 2
𝑥 = 23
𝑦 = 23
(23, 23)
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
Unit 7 Challenges
http://bit.ly/1fEOdeu
Adapted from Illustrative Mathematics 8.EE Folding a Square into Thirds
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-FormativeAssessment-Lessons-Videos.aspx
Resources
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
• CCGPS 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
 LearnZillion - http://learnzillion.com/
 ShareMyLesson - http://www.sharemylesson.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
sharemylesson.com
http://www.sharemylesson.com/teaching-resources/
sharemylesson.com
http://www.sharemylesson.com/teaching-resources/
sharemylesson.com
http://www.sharemylesson.com/teaching-resources/
sharemylesson.com
http://www.sharemylesson.com/teaching-resources/
Resources
• Professional Learning Resources
 Inside Mathematics- http://www.insidemathematics.org/
 Edutopia – http://www.edutopia.org
 Teaching Channel - http://www.teachingchannel.org
 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/
 Estimation 180 - http://www.estimation180.com/
 Graphing Stories - http://graphingstories.com/
• Books
 Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Feedback
http://www.surveymonkey.com/s/WZKG5G2
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Thank You!
Please visit http://ccgpsmathematics6-8.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 6-8 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.