CCGPS Mathematics6th Grade Update Webinar

Unit 1: Number System FluencyAugust 9, 2013

James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usSecondary 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 1 revisions

• Addressing areas of concern • Resources

2013 6th Grade Resource Revision Team

6th Grade Math Resource Revision Team

Tonya Burt- Lincoln County Middle School

Anne Miller Gay – MS Math Coach, Camden County

Beverly Harvey- Ebenezer MS, Effingham County

Janet Kennedy – Kittredge Magnet School, Dekalb County

Ashley Powell – Marietta 6th Grade Academy, Marietta City

6th Grade Math Resource Revision Team

Webinar Guide

Comprehensive Course GuideTonya Burt

FAL assessment and short cycle taskAnne Miller Gay

Unit 1

Task Chart- Ashley Powell

SMP’s and Misconceptions – Janet Kennedy

Unit 1 changes – Beverly Harvey and Anne Miller Gay

6th grade Math 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 6th Grade Math

6th Grade Comprehensive Course Overview

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 6th Grade Math

Begin at www.georgiastandards.org

Direct Link to Page

Select the CCGPS ELA/Math Tab

Direct Link to Page

Select the Mathematics option under Browse CCGPS

Direct Link to Page

Select the 6-8 option in the Mathematics section

Direct Link to Page

Select the Grade 6 option

Direct Link to Page

Direct Link to Page

Select the Comprehensive Course Guide

This is your Comprehensive Course Guide

Flipbooks

Bold words will provide access to the Common Core Flipbooks

The Flipbooks offer clarification Very Large File (slow loading)

Direct link to Flipbook

Content Domain Flipbook Resources

Active links to standard resources

Standard Specific Information

Each Standard is Linked to Flipbook information

Select the Standard to gain quick access to clarification without having to scroll through

multiple pages

Standards for Mathematical Practice • Active Links Provided

to Videos and Information on the Standards for Mathematical Practice

• Active Links Provided for EACH Standard for Mathematical Practice

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.

Formative Assessment Lessons (FALs)

Formative Assessment Lessons (FALs)

Formative Assessment Lessons (“Classroom Challenges”)Developed by the Shell CenterEmbedded in the FY14 Units, also available at http://map.mathshell.org.uk/materials/lessons.php Usually 2/3 into a unit

Intended to guide instructional decisions for the rest of the unit Not intended to be graded, but for feedback

Plan is to have at least one per unit

Details coming in Unit 2, when the first available 6th grade FAL occurs

Short Cycle Tasks

Also from the Shell Center (Mathematics Assessment Project web site)

“Tasks” tab: Short assessments with rubricsIncluded in each unit as available

“Mathematical skills and practices might be assessed partly in isolation, partly under scaffolded conditions, and partly when students face substantial problems without scaffolded support. We call tasks that assess these three different types of performance novice, apprentice, and expert tasks respectively”

Other Sections of Interest

• Unit Descriptions• Webinar Information• Assessment Resources and

Instructional Support Resources

• Internet Resources• Curriculum Map

Examples of ResourcesAssessment Resources and Instructional Support Resources The resource sites listed below are designed to support the instructional and assessment needs of teachers. All BLUE links will direct teachers to the site mentioned. • CCGPS Frameworks are "models of instruction" designed to support teachers in the implementation of the Common Core Georgia Performance Standards (CCGPS). The Georgia Department of Education, Office of Standards, Instruction, and Assessment has provided an example of the Curriculum Map for each grade level and examples of Frameworks aligned with the CCGPS to illustrate what can be implemented within the grade level. School systems and teachers are free to use these models as is; modify them to better serve classroom needs; or create their own curriculum maps, units and tasks.

• The Teacher Resource Link (TRL) is an application that delivers vetted and aligned digital resources to Georgia’s teachers. TRL is accessible via the GaDOE “tunnel” in conjunction with LDS using the single sign-on process. The content is aligned to Common Core Georgia Performance Standards, Georgia Performance Standards, and National Education Technology Standards and pushed to teachers based on course schedule.

• Georgia Online Assessment (OAS) System Teachers can use the OAS as a tool for Assessment for Learning. Student results on assessments help teachers identify learner needs and strengths and inform instructional practices. Robust reports also allow teachers to communicate with students and parents about learner goals, intentions, and outcomes. The OAS helps with a cycle of assessments, instruction, feedback, and communication that allows teachers, students, and parents to be confident with instructional success. Teachers will be particularly interested in the Formative Item Bank.

• Webinar support and links will direct teachers to archived webinars as well as links to join or view upcoming webinars.

• Course/Grade Level WIKI spaces are available to post questions about a unit, a standard, the course, or any other CCGPS math related concern. Shared resources and information are also available at the site.

• CRCT Resources are available to provide more information for the CRCT as provided by the GaDoe.

• Georgiastandards.org provides a gateway to a wealth of instructional links and information. Open the Common Core GPS tab at the top to access specific math resources for CCGPS.

• Formula Sheet is the formula sheet found on the GaDoe website and the formula

sheet used on the CRCT.

Examples of Resources• Webinar support and links will direct teachers to archived webinars as well as

links to join or view upcoming webinars.

• Course/Grade Level WIKI spaces are available to post questions about a unit, a standard, the course, or any other CCGPS math related concern. Shared resources and information are also available at the site.

• CRCT Resources are available to provide more information for the CRCT as provided by the GaDoe.

• Georgiastandards.org provides a gateway to a wealth of instructional links and information. Open the Common Core GPS tab at the top to access specific math resources for CCGPS.

• Formula Sheet is the formula sheet found on the GaDoe website and the formula sheet used on the CRCT.

TasksUnit 1

Standards for Mathematical Practice and Misconceptions

Unit 1

Specific Standards for Mathematical Practice

A step was taken by the team to incorporate in each unit specific Standards for Mathematical Practice. Instead of listing the eight general SMPs repeatedly throughout the units, we chose the standards that were most relevant with terminology specific to the task.

For example in the TASK: UNDERSTANDING THE LONG DIVISION ALGORITHM the following standards were listed:

Before- 1. Make sense of problems and persevere in solving them.

Now-1. Make sense of problems and persevere in solving them. Students make sense of multi-digit division problems using the standard algorithm. Students represent this visually through a base-ten chart.

Standards for Mathematical Practice and Misconceptions

Unit 1

Before-4. Model with mathematics. Now-4. Model with mathematics. Students will model multi-digit division with base-ten charts.

Before- 5. Use appropriate tools strategically.

Now-5. Use appropriate tools strategically. Students will use visual tools (base-ten charts) for of multi-digit division.

Before- 7. Look for and make use of structure. Now-7. Look for and make use of structure. Students examine the relationship between the dividend, quotient, and divisor in a multi-digit division problem using the base-ten chart.This addition of specific standards is an important bonus for the classroom teacher.

Standards for Mathematical Practice and Misconceptions

Unit 1

Misconceptions

The team added misconceptions to each unit as documented by research. This addition was in-line with other states, as we previewed other states’ documents.

The misconceptions in unit 1 are listed with examples. The misconceptions are:The addition of specific standards for mathematical practice for each task and specific misconceptions to each unit are just a few of the many improvements we hope the math teachers in our state will find useful in writing lesson plans and being effective teachers in their classroom.

Standards for Mathematical Practice and Misconceptions

Unit 1

MisconceptionsThe misconceptions in unit 1 are listed with examples. The misconceptions are:

Types of Tasks Unit 1

Types of Tasks (Chart in each unit)

Each task is listed in a chart with the task type, content addressed and standard the task will address.

• Learning Task/Scaffolding Task

• Performance Task• Formative Task/Formative

Assessment lesson• Summative Performance

Tasks - unchanged Finding Common Factors Back to School Let’s Distribute Dividing Fractions Understanding Algorithms Do it Yourself

Secret Number Clues reformatted A key to #9

Fractional Divisors more detail in the answer key

Estimating is the Root of Fluency introduction teacher notes

Culminating Task: Pick and Number, Any Number All standards for unit 1 Clarify directions

Understanding the Long Division Algorithm New Task Designed to have students model and

explain Based on place value

Grouping and regrouping Leads to understanding the ‘standard

algorithm’ NS.2 – Fluently divide multi-digit

numbers using the standard algorithm.

Dividing Fractions with Modeling New Task More Practice with modeling dividing

fractions

Things to Remember 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 is static, viewable for anyone. Teacher pages and any updates or additional resources, including hot links, are only available through Learning Village.

Tonya and Chrissy are trying to understand the following story problem for

serving of rice is of a cup. I ate 1 cup of rice. How many servings of rice did I eat?

To solve the problem, Tonya and Chrissy draw a diagram divided into three equal pieces, and shade two of those pieces.

Areas of Concern

Adapted from Illustrative Mathematics 6.NS.1 Cup of Rice

Tonya says, “There is one - cup serving of rice in cup, and there is cup of rice left over, so the answer should be 1 ervings.”Chrissy says, “I heard someone say that the answer is servings . Which answer is right?”Is the answer ? Explain your reasoning using the diagram.

Areas of Concern

Adapted from Illustrative Mathematics 6.NS.1 Cup of Rice

Areas of Concern

Adapted from Illustrative Mathematics 6.NS.1 Cup of Rice

13𝑐𝑢𝑝

23𝑐𝑢𝑝

12𝑠𝑒𝑟𝑣𝑖𝑛𝑔

1𝑠𝑒𝑟𝑣𝑖𝑛𝑔

Illustrative Mathematics - http://www.illustrativemathematics.org/

5/3 ÷ 1/2How many halves are in five-thirds?

Areas of Concern

5/3 ÷ 1/2How many halves are in five-thirds?

Areas of Concern

5/3 ÷ 1/2How many halves are in five-thirds?

Areas of Concern

5/3 ÷ 1/2How many halves are in five-thirds?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

5/3 ÷ 1/2How many sets of 1/2 are in 5/3?

Areas of Concern

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1/3

3

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Teaching Student-Centered MathematicsVan de Walle and Lovin

AssessmentJuly 22, 2013 – State School Superintendent Dr. John Barge and Gov. Nathan Deal announced today that Georgia is withdrawing from the Partnership for Assessment of Readiness for College and Careers (PARCC) test development consortium. Instead, the Georgia Department of Education (GaDOE) will work with educators across the state to create standardized tests aligned to Georgia’s current academic standards in mathematics and English language arts for elementary, middle and high school students. Additionally, Georgia will seek opportunities to collaborate with other states. The press release in its entirety can be found at: http://www.gadoe.org/External-Affairs-and-Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

Assessment As GaDOE begins to build new assessments, please note that our Georgia assessments:will be aligned to the math and English language arts state standards;will be high-quality and rigorous;will be developed for students in grades 3 through 8 and high school;will be reviewed by Georgia teachers;will require less time to administer than the PARCC assessments;will be offered in both computer- and paper-based formats; andwill include a variety of item types, such as performance-based and multiple-choice items.The press release in its entirety can be found at: http://www.gadoe.org/External-Affairs-and-Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

AssessmentWe will continue to work with Georgia educators, as we have in the past, to reconfigure and/or redevelop our state assessments to reflect the instructional focus and expectations inherent in our rigorous state standards in language arts and math. This is not a suspension of the implementation of the CCGPS in language arts and math.

~ Dr. John Barge(excerpt from a letter to state Superintendents from Dr. Barge)

• 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 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 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

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/

• Blogs Dan Meyer – http://blog.mrmeyer.com/ Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/

Feedbackhttp://ccgpsmathematics6-8.wikispaces.com/

James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usSecondary Mathematics Specialists

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)

bkline@doe.k12.ga.us

James PrattProgram Specialist (6-12)

jpratt@doe.k12.ga.us

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