CCGPS Mathematics 8 th Grade Update Webinar Unit 4: Functions November 8, 2013 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.

What are update webinars? Update on the work of the 2013 Resource Revision Team  Overall revisions  Unit 4 revisions Addressing areas which teachers have found to be more challenging Resources

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

8 th Grade CCGPS Unit Revisions Webinar Overview of Comprehensive Course Guide & Unit 4: FUNCTIONS

8 th Grade Math Resource Revision Team Members Shelly Bydlinski - Glynn County School System Mandy Campbell- Floyd County School System Samantha Clay – Atlanta Public Schools Kim Conley - Lee County School System Joe Hardy – Bibb County School System

Create a Comprehensive Course Guide which would:  Provide an overview of the 8 th Grade Mathematics Curriculum  Provide clarification of CCGPS Mathematics Standards  Link together many sources of information pertinent to CCGPS 8 th Grade Math Update the Units by:  Increasing Task Options  Developing Differentiation Opportunities within each task. Resource Revision Team Goals

Accessing Resources through SLDS 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 1st 2nd 3rd 4th

This is your Comprehensive Course Guide

 Standards are hyperlinked to the Flipbooks providing teaching strategies, misconceptions, and prior knowledge  Formative Assessment Lesson (FAL) information and video links  Internet Resources Sections of Interest

Formative Assessment Lessons (FALs)

For the FALs click on this tab For the Short Cycle Tasks click on this tab Make sure to choose the Correct grade level

Unit 4 Functions

 Slight change of format  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 Overall Changes in the Unit

Selected Terms and Symbols

Note: While student editions of the units can still be found at only the Teacher’s Edition (found in the Learning Village and SLDS) include the Task Table.

A new section has been included in each task to list the appropriate Standards for Mathematical Practice (SMPs). STANDARDS FOR MATHEMATICAL PRACTICE: This task uses all of the practices with emphasis on: 2. Reason abstractly and quantitatively. 4. Model with mathematics. Formative Assessment Lesson: Modeling Situations with Linear Equations

The standards are hyperlinked to the CCGPS document which can also be found at

Common Misconceptions have been identified for each task to assist teachers in guiding the students to success.

Culminating Task: Sorting Functions functions/packet.pdf functions/packet.pdf

Culminating Task: Sorting Functions

Culminating Task: Sorting Functions Student Responses

Suggestions for differentiation have been added to each task.

 Use the Wiki to share information with other teachers and to ask questions.  This is a living document. 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 DOE CCGPS tab located at georgiastandards.org is static, viewable for anyone. Teacher editions and any updates or additional resources, including hot links, are only available through Learning Village.  If you are attending the Georgia Mathematics Conference at Rock Eagle in October, come visit us. Our session is Friday morning. Things to Remember

Your comments are greatly appreciated: Feedback

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). Let’s define a function which assigns to an input t the total amount of garbage, G, produced in that year. To find these values, you can look them up in the table. Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). How much garbage was produced in 2004? Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). How much garbage was produced in 2004? 249 million tons Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). In which year did the US produce 251 million tons of garbage? Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). In which year did the US produce 251 million tons of garbage? 2006 Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

The following table shows the amount of garbage that was produced in the US each year between 2002 and 2010 (as reported by the EPA). Draw a graph that shows this data. Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage t (years) G (million tons)

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F US Garbage

Below are two graphs that look the same. Note from the axis labels that the first graph shows the distance from home as a function of time and the second graph shows velocity as a function of time. Unit 3 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance

Below are two graphs that look the same. Note from the axis labels that the first graph shows the distance from home as a function of time and the second graph shows velocity as a function of time. Describe the graphs within context. Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person leaves the house and travels at a constant rate of speed.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person does not get further from the house, possibly is stopped.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person continues to travel away from the house, but slower than previous.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person travels back to the house, faster than leaving.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person stays at the house.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person leaves the house and travels at a constant rate.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person stays the same distance from home.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person returns home at the same speed as they left.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person starts at rest and speeds up at a constant rate.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person maintains a constant speed.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person begins to speed up again.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person quickly slows down.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person comes to a complete stop.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person accelerates at a constant rate.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person stays at a constant speed.

Unit 4 Challenges Adapted from Illustrative Mathematics 8.F Velocity vs. Distance The person slows down to come to a complete stop.

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 - Assessment-Lessons-Videos.aspx Assessment-Lessons-Videos.aspx Resources

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.

CCGPS Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -  LearnZillion - Assessment Resources  Online Assessment System -  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  Smarter Balanced -  PARCC - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Achieve -  Expeditionary Learning: Center for Student Work - Blogs  Dan Meyer –  Robert Kaplinsky - Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

Resources SMP 3 – Construct viable arguments and critique the reasoning of others  Student Sample Work  Feedback/Critique and Revision Expeditionary Learning

Feedback James Pratt – Brooke Kline –

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