1. Secondary Mathematics Specialists
CCGPS Mathematics 8th Grade Update Webinar Unit 6: Linear Models and Tables February 14, 2014
James Pratt – Brooke Kline –
Secondary Mathematics Specialists
Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2. What are update webinars?
Update on the work of the 2013 Resource Revision Team
Overall revisions
Unit 6 revisions
Addressing areas which teachers have found to be more challenging
Resources
James

3. 2013 8th Grade Resource Revision Team
Samantha Clay APS
Shelly Bydlinski
Glynn Co. Schools
Kim Conley
Lee Co.
Joe Hardy
Bibb Co.
Mandi Campbell Floyd Co.
James

4. 8th Grade CCGPS Unit Revisions Webinar
Overview of
Comprehensive Course Guide
&
Unit 6: Linear Models and Tables
I hope you are excited about our 2nd year of CCGPS implementation. Our Resource Revision Team came from all over the state of GA to work for 8 days with a common goal: to make our CCGPS units more useful for teachers in the classroom. It is a living document. One that we hope will continue to improve as we dig deeper and gain a better understanding of our standards. This webinar will focus on the Comprehensive Course Guide and Unit 6.

5. 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.
Let’s first start with the 8th Grade Comprehensive Course Guide. We have added several sections to this document and hope that you will find it useful. For those of you that are familiar with Learning Village, you can access both the teacher and student version there; however, sometimes you may not have been able to access Learning Village or maybe you are a new teacher and you have not subscribed. Let’s look at other options.

6. Begin at www.georgiastandards.org
The georgiastandards.org web page will allow you to access Teacher Editions and Student Editions through Learning Village, but you may also access the units through SLDS if you have been trained to use this tool. By clicking on SLDS, you can find many helpful Modules that will walk you through how to use and get the most out of the system.

7. Accessing SLDS
Those familiar with SLDS can open a separate tab or window in your web browser and login to your district's Student Information System (Infinite Campus, School Max, Power Teacher, Tyler, etc.). Examples of widely-used Student Information Systems are shown. Next, select the link to the SLDS.

8. Accessing Resources through SLDS
2nd
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
4th
From here, first, you’ll click on the “Resources” tab at the top. Then, choose “search by subject”. Use the drop down boxes to choose your subject, grade level and course name. Next, click on “Get Resources”. Choose the “Teacher Tools” tab to view the unit frameworks.
3rd

9. Select the CCGPS ELA/Math Tab
To access the student versions of the framework tasks and the Comprehensive Course Guide, you may also go to georgiastandards.org. Click on the orange CCGPS ELA/Math tab up at the top.
Direct Link to Page

10. Select the Mathematics option under Browse CCGPS
Now go to Mathematics Located in the Orange box on the left

11. Select the 6-8 option in the Mathematics section
Choose your grade band. We are looking at 6-8.

12. Select the Grade 6 option
Now look at the blue box on the right. Click on the + sign in front of Grade 8. This will provide you with the dropdown menu of the 8th grade documents.

13. Select the Comprehensive Course Guide
Choose the Comprehensive Course Guide
Direct Link to Page

14. This is your Comprehensive Course Guide
I have included screen shots from the document so you know what you are looking for when you go exploring yourself.

15. 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
Standards are hyperlinked to the Flipbooks providing teaching strategies, misconceptions and prior knowledge. Formative Assessment Lesson information and videos are included. There are also internet resources available.

16. Flipbooks Click on blue hyperlink to access
The Flipbooks offer clarification
Very Large File (slow loading)
The Flipbooks are the result of a collaborative effort utilizing resources from the CCSS, Arizona DOE, Ohio DOE, and North Carolina DOE. The intention is to help teachers gain a better understanding of the standards. We have provided active links to this resource, but be patient while the document loads as it is very large.

17. 8th Grade Standards
All of the Grade 8 standards are listed in the course overview. Note the standard is in blue indicating this is where to click to go to the flipbook. I have selected the 2nd standard in Functions.

18. Standard Specific Information
This is a snapshot of part of the flipbook. Note that the flipbooks analyze each standard identifing the Standards for Mathematical Practice (SMPs) addressed by this standard, Instructional Strategies, Explanations and Examples, and Misconceptions to look out for.

19. 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.
Another section of the Comprehensive Course Overview that will be very helpful to teachers is the Task section. A table is provided to help delineate each type of task and how they should be used within the frameworks of each unit. This table is consistent across all grade levels and is provided based on feedback from teachers. Many Georgia teachers asked for explanations of the types of tasks used to facilitate instruction and mastery of standards. This particular unit includes Performance Tasks and Formative Assessment Lessons.

20. Formative Assessment Lessons (FALs)
Following the Task section, teachers will find detailed information in the FAL section with examples, lessons, a teaching manual, and links to videos of teachers using FALs.

21. Formative Assessment Lessons (FALs)
Formative Assessment Lessons (“Classroom Challenges”)
Developed by the Shell Center
Embedded in the FY14 Units, also available at
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.
One thing that I would like to stress is that the FALs are meant to be used in their entirety….not just the PowerPoint or just the game. They are intended to guide instructional decisions for the rest of the unit. They’re not intended to be graded, but more so used for feedback. They can be very beneficial in addressing student misconceptions. A link is provided here on this slide to the Shell Center, where all the FALs are located. Links are also imbeded in the framework units. Also, for further training using FALs, you may want to contact your RESA.

22. For the FALs click on this tab
For the Short Cycle Tasks click on this tab
When you go to the website looking for FALs click on Lesson tab. There are no Short Cycle Tasks in this unit, but when looking for Short Cycle Tasks click on Tasks tab. Don’t forget to make sure you are in the appropriate grade level.
Make sure to choose the Correct grade level

23. Internet Resources Webinar Information General Resources
Problem-Based Learning
Assessment and Instructional Support Resources
The next sections are dedicated to internet resources. These sections are designed to tie together many other areas of support offered by GADOE and other states implementing CCSS.

24. Examples of Resources
Again please note the link is in BLUE. By clicking on it, you will go directly to that resource. Some require logins. So check out these sites and if you find a resource that you feel would be helpful please post it to the wiki. The wiki address will be provided on the last slide if you are not familiar with it.

25. Unit 6 Linear Models & Tables
The focus of the remainder of this webinar will be Unit 5: Linear Functions.

26. 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 and the wiki
Observations made from personal experiences
We did have a slight change of format with the unit. Formative Assessment Lessons were added from the Shell Center. A few sections were added to the tasks, including SMPs and differentiation options. We received suggestions via and the wiki from all over the United States and those were also taken into account. In addition, we also brought our own views from personal experiences in our classrooms. This what we came up with.

27. Selected Terms and Symbols
We included two new links for definitions within the units…Common Core State Standards Mathematics Glossary and Common Core GPS Mathematics Glossary. While most of the definitions remained the same a few did change slightly.

28. 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.
The rest of the changes are reflected in the Teacher’s Edition. The Task Tables have been updated to include appropriate FALs. The FALs have been hyperlinked to the Math Shell website for your convenience. A short description of each task has also been provided along with corresponding standards.

29. Task Additions
Sugar Prices– Short Cycle Task - In this task, you must use a graph showing the prices and weights of bags of sugar to find the bag offering the best value for money..
Interpreting Distance-Time Graphs– FAL: Concept Development - This lesson is intended to help you assess how well students are able to interpret distance–time graphs &, in particular, to help you identify students who:
Interpret distance–time graphs as if they are pictures of situations rather than abstract representations of them.
Have difficulty relating speeds to slopes of these graphs.
Sports & Musical Instruments – Learning Task
Two-Way Tables – Learning Task
While this unit was long, it is now even longer. I think of it as a bonus….there are more options. A Short Cycle Task, A FAL, and 2 new Learning Task.

30. Short Cycle Task: SUGAR PRICES
Sugar Prices– Short Cycle Task - In this task, you must use a graph showing the prices and weights of bags of sugar to find the bag offering the best value for money.. Great task to check students understanding/ability to read a graph. A Rubric is provided.

31. Formative Assessment Lesson: INTERPRETING DISTANCE-TIME GRAPHS
The FAL Interpreting Distance-Time Graphs
Pre-Assessment: Journey to the Bus Stop, PPT, Match Story Card to Graph Card then include the Table Cards. Students share matches/poster with other groups. Take Post-Assessment: Journey to the Bus Stop

32. Formative Assessment Lesson: INTERPRETING DISTANCE-TIME GRAPHS

33. Learning Task: SPORTS & MUSICAL INSTRUMENTS
Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? To investigate this, each student in your class should answer the following two questions as you collect the data as a whole class:
Do you play a sport? (yes or no)
Do you play a musical instrument? (yes or no)
The Learning Tasks: Sports & Musical Instruments and Two-Way Tables provides various opportunities for students to create two-tables and investigate bi-variate data. An addition to all tasks is a list of the appropriate SMPs, possible misconceptions students may encounter, and a Differentation section for Acceleration and Remediation.

34. 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.
Remember: Use the wiki to share information with other teachers and ask questions. The web address for the wiki will be shared on the next slide. This is a living document. Please share anything you may have to enhance this unit or any other unit. The wiki is the teacher community page to share anything you have. The DOE CCGPS tab located at georgiastandards.org is static and viewable for anyone. Teacher editions and any updates or additional resources, including hot links, are only available through Learning Village.

35. THE WIKI

36. Feedback Your comments are greatly appreciated:
Your comments and feedback are greatly appreciated. Thank you!

37. Unit 6 Challenges
Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend’s house with a full battery. The pictures shows screenshots of the battery charge indicator after he plugs in the computer at 9:11 a.m.
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

38. Unit 6 Challenges
Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend’s house with a full battery. The pictures shows screenshots of the battery charge indicator after he plugs in the computer at 9:11 a.m.
Using the data and a scatterplot determine when Jerry can expect to have a fully charged battery?
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

39. Unit 6 Challenges (time since plugged in, battery charge)
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

40. Unit 6 Challenges (time since plugged in, battery charge) (0, 41)
(16, 56)
(25, 64)
(37, 74)
(44, 79)
(57, 86)
(66, 91)
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

41. Unit 6 Challenges (time since plugged in, battery charge) (0, 41)
(16, 56)
(25, 64)
(37, 74)
(44, 79)
(57, 86)
(66, 91)
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

42. Unit 6 Challenges (time since plugged in, battery charge) (0, 41)
(16, 56)
(25, 64)
(37, 74)
(44, 79)
(57, 86)
(66, 91)
James It appears that the line goes through the data points (16, 56) and (57, 87) so we can calculate the slope.
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

43. Unit 6 Challenges 𝑚= 87−56 57−16 𝑚= 31 41 ≈.76 Initial value close to
43.
James Calculating the slope and estimating the initial value.
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

44. Unit 6 Challenges 𝑚= 87−56 57−16 𝑚= 31 41 ≈.76 Initial value close to
43.
𝑏=.76𝑡+43
James Calculating the slope and estimating the initial value.
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

45. Unit 6 Challenges 𝑚= 87−56 57−16 𝑚= 31 41 ≈.76 Initial value close to
43.
𝑏=.76𝑡+43
James – graphically it shows that the battery will be charged about 75 minutes after it is plugged in.
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

46. Unit 6 Challenges 𝑏=.76𝑡+43 100=.76𝑡+43 57= .76𝑡 75=𝑡
James
Adapted from Illustrative Mathematics 8.SP Laptop Battery Charge

47. Brooke

49. Cell Phone
No Cell Phone
Total
MP3 Player
No MP3 Player
Brooke

50. Cell Phone
No Cell Phone
Total
MP3 Player 60 9 69
No MP3 Player 13 8 21 73 17
69+21= 73+17= 90
Brooke

51. Resources GaDOE Resources
Fall 2011 CCGPS Standards for Mathematical Practices Webinars -
Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB -
2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series -
Georgia Mathematics Teacher Forums -
CCGPS Mathematics Frameworks and Comprehensive Course Overviews -
Mathematics Formative Assessment Lesson Videos -
Brooke

52. 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.
Brooke

53. Resources CCGPS Resources Assessment Resources
Georgia Virtual Learning -
SEDL videos - or
Illustrative Mathematics -
Mathematics Vision Project -
Dana Center's CCSS Toolbox -
Tools for the Common Core Standards -
LearnZillion -
Assessment Resources
MAP -
Illustrative Mathematics -
CCSS Toolbox: PARCC Prototyping Project -
Smarter Balanced -
PARCC -
Online Assessment System -
Brooke

54. Resources Professional Learning Resources
Inside Mathematics-
Edutopia –
Teaching Channel -
Achieve -
Expeditionary Learning: Center for Student Work -
Blogs
Dan Meyer –
Robert Kaplinsky -
Estimation
Graphing Stories -
Books
Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Brooke

55. Estimation 180
Brooke

56. Estimation 180
Brooke

57. Estimation 180
Brooke

58. Graphing Stories
Brooke

59. Graphing Stories
Brooke

60. James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us
Feedback
James Pratt – Brooke Kline –
Brooke

61. James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us
Thank You!
Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 6-8 Mathematics listserve. Follow on Twitter!
Brooke Kline
Program Specialist (6‐12)
James Pratt Program Specialist (6-12)
James & Brooke
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.