CCGPS Mathematics 8 th Grade Update Webinar Unit 5: Linear Functions December 13, 2013 James Pratt – [email protected] Brooke Kline –...

CCGPS Mathematics8th Grade Update Webinar

Unit 5: Linear FunctionsDecember 13, 2013

James Pratt – [email protected] Brooke Kline – [email protected] 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 5 revisions

• Addressing areas which teachers have found to be more challenging• Resources

2013 8th Grade Resource Revision Team

Samantha Clay APS

Shelly BydlinskiGlynn Co. Schools

Kim Conley Lee Co.

Joe Hardy Bibb Co.

Mandi Campbell Floyd Co.

8th Grade CCGPS Unit Revisions

WebinarOverview of

Comprehensive Course Guide&

Unit 5: Linear Functions

8th 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 8th Grade Mathematics Curriculum

Provide clarification of CCGPS Mathematics Standards Link together many sources of information pertinent

to CCGPS 8th Grade MathUpdate the Units by:

Increasing Task Options Developing Differentiation Opportunities within each

task.

Resource Revision Team Goals

Begin at www.georgiastandards.org

Accessing SLDS

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

1st2nd

3rd

4th

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

Direct Link to Page

Select the Comprehensive Course Guide

Located on the 6-8 math section of www.georgiastandards.org

Designed to provide clarification of CCGPS Mathematics Standards

Organized to link together many sources of information pertinent to CCGPS 8th Grade Math

8th Grade Comprehensive Course Guide

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

Click on blue hyperlink to access The Flipbooks offer clarification Very Large File (slow loading)

Flipbooks

8th Grade Standards

Standard Specific Information

Task DescriptionsScaffolding 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 5Linear Functions

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

Overall Changes in the Unit

Lines and Linear Equations – In this lesson students translate between equations and graphs and interpret speed as the slope of a linear graph.

Solving Real-Life Problems: Baseball Jerseys – In this lesson, students interpret a real-life situation and represent the variables

mathematically.

Formative Assessment Lessons

Also, if you did not use the FAL, Modeling Situations with Linear Equations, from Unit 4 you might want to look at using it in Unit 5.

This task can be used in either Unit 4 or Unit 5.

We decided to put it in Unit 4 so that teachers could see it earlier rather than later and decide when/if they want to use it.

Formative Assessment Lessons

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.

Lets look at a Task: What’s My Line

Lets look at a Task: What’s My Line?

Lets look at a Task: What’s My Line?

Lets look at a Task: What’s My Line?

Lets look at a Task: What’s My Line?

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:

http://ccgpsmathematics6-8.wikispaces.com/home

Feedback

Eva, Carl, and Maria are computing the slope between pairs of points on the line shown below.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Slopes Between Points on a Line

Eva finds the slope between the points (0, 0) and (3, 2). Carl find the slope between the points (3, 2) and (9, 6). Maria finds the slope between the points (3, 2) and (9, 6).

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Slopes Between Points on a Line

Why should the slope be the same for the three students?

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Slopes Between Points on a Line

We can see that the blue and the green triangles are congruent since we can translate the green triangle up along the line until it lines up with the blue triangle.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Slopes Between Points on a Line

We can dilate the blue triangle by a factor of 2 to line it up with the red triangle.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Slopes Between Points on a Line

Lines and have the same slope. The equation of line is . Line passes through the point .

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Proportional relationships, lines, and linear equations

Lines and have the same slope. The equation of line is . Line passes through the point .

What is the equation of line ?

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Proportional relationships, lines, and linear equations

Lines and have the same slope. The equation of line is . Line passes through the point .

What is the equation of line ?

Therefore slope of line is

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Proportional relationships, lines, and linear equations

Lines and have the same slope. The equation of line is . Line passes through the point .

What is the equation of line ?

Therefore slope of line is Since M passes through the point(0,-5), the equation for the line M is

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Proportional relationships, lines, and linear equations

The equation for the line M is or or or or or or any other equivalent equation.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.EE Proportional relationships, lines, and linear equations

Graph both functions below and list as many differences between the two functions as you can.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.F Introduction to Linear Functions

Graph both functions below and list as many differences between the two functions as you can.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.F Introduction to Linear Functions

Graph both functions below and list as many differences between the two functions as you can.

The blue graph is a straight line, the red graph is curved.The term is squared in the red function, and not in the blue.The blue function has a constant slope, the red function does not.

Unit 5 Challenges

Adapted from Illustrative Mathematics 8.F Introduction to Linear Functions

• 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://ccgpsmathematics6-8.wikispaces.com/ CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative-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 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/ 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/LearnZillion - http://learnzillion.com/

• Assessment Resources Online Assessment System - http://bit.ly/OoyaK5 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/

Resources

www.gavirtuallearning.org/Resources.aspx No password required!

Georgia Virtual Learning

Georgia Virtual Learning

Georgia Virtual Learning

Georgia Virtual Learning

Georgia Virtual Learning

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 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/

• Books Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

Feedbackhttp://www.surveymonkey.com/s/WZKG5G2

James Pratt – [email protected] Brooke Kline – [email protected]

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 KlineProgram Specialist (6‐12)

[email protected]

James PrattProgram Specialist (6-12)

[email protected]

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