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CCGPS Mathematics6th Grade Update Webinar
Unit 2: Rate, Ratio and Proportional Reasoning Using Equivalent Fractions
September 13, 2013
James Pratt – [email protected] Brooke Kline – [email protected] 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 2 revisions
• Addressing areas which teachers have found to be more challenging• 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
Unit 2
Task Chart- Ashley Powell
SMP’s, Strategies and Misconceptions – Janet Kennedy
Unit 2 changes – Beverly Harvey
FALs for Unit 2 (Guide for FALs along with specific information on the two FALs in this unit. – Anne 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.
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 2
Standards for Mathematical Practice, Strategies Misconceptions
Unit 2
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, Strategies and Misconceptions
Unit 2
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, Strategies and Misconceptions
Unit 2
Strategies
The Strategies in this unit were greatly enhanced with some helpful explanations and samples.
Standards for Mathematical Practice, Strategies and Misconceptions
Unit 2
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. It was the teams hope that math teachers in our state will find this information useful when writing lesson plans and being effective teachers in the their classroom
Types of Tasks Unit 2
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 - No changes to the tasks in the unit Only unit not to have additions/deletions and
big changes Changes made to make the student pages
more user friendly Misconceptions added to most individual task
as well as unit
Look for changes in Units 3-7. We will discuss those changes in detail during those webinars.
FALSFormative Assessment Lessons
• Developed by the MARS, Shell Center
• To Inform Instruction• 2/3 into a unit• Preferably not graded
2 Types of FALs Called “Classroom Challenges” in the
new revision by Shell. GaDOE will continue to refer to this type of informing activity as Formative Assessment Lessons
Concept Development FALs Problem Solving FALS
Concept Development and Problem Solving FALs Given 2/3 of the way through a unit Pre and Post assessments Teachers give feedback to pre-
assessment and use it to group students Accessible to all students Not graded Make effective use of Standards for
Mathematical Practice
Concept Development FALs Intended to assess and develop
understanding of fundamental concepts Feedback given after collaborative task
but before post-assessment Students may be grouped based on
common misconceptions from pre-assessment
Problem Solving FALs Intended to assess and develop capacity
to select and deploy mathematical knowledge in non-routine contexts
Feedback is given as part of the task Students may be grouped based on
different approaches to pre-assessment task
First 6th Grade FAL is in Unit 2 (There are Two!) Addresses:
SMP 1. Make sense of problems and persevere in solving them.
SMP 2. Reason abstractly and quantitatively.
SMP 4. Model with mathematics.
6.RP Understand ratio concepts and use ratio reasoning to solve problems.
Also…Addresses:
SMP 1. Make sense of problems and persevere in solving them.
SMP 2. Reason abstractly and quantitatively.
SMP 3. Construct viable arguments and critique the reasoning of others.
SMP 4. Model with mathematics.
6.RP Understand ratio concepts and use ratio reasoning to solve problems.
6.G Solve real-world and mathematical problems involving area, surface area and volume.
Note the quick links to sections of the task on the side bar.
What do I need to do to get started on this first FAL – Traveling to School?
1. Print the FAL; print copies of pages S-1 through S-5 for students.
2. Before the lesson, students work individually on the pre-assessment task- Sharing Gasoline Costs.
3. Review their work and write questions to help students improve their work. Note the Common Issues, pg.T-3
4. During the lesson, students work in 2’s or 3’s on the task.
1. They plan a strategy, share ideas on chart paper2. They examine samples of other student work (provided)3. Teacher notes strategies used
5. In whole class discussion, share and compare strategies
Preparation: 6th grade Example Each small group needs a piece of poster paper,
markers, a copy of each of the Sample Solutions to Discuss
There are slides provided to support the task Proposed Time:
20 minutes before the lesson (pre-assessment) 80 minute lesson 20 minutes for follow-up lesson
FALs are accessible at the MAP website http://map.mathshell.org.uk/materials/index.php
Short Cycle Tasks Located under the Tasks tab Short tasks To be graded Rubrics provided Often student work samples provided
None at this time for unit 2 – first 6th grade SCT is in Unit 5
Instructions and detailed information is available under the “Instructions” tab
Training is Available The Mathematics Specialists at the
RESAS offer training in using the FALS, Short Cycle Tasks, and other resources from the
Mathematics Design Collaborative.
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.
Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below.
Assume Julianna walked at a constant speed. Complete the table and plot Julianna’s progress in the coordinate plane.
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
Assume Julianna walked at a constant speed. Complete the table and plot Julianna’s progress in the coordinate plane.
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below.
How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile?
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile?
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile?
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below.
Next year Julianna is planning to walk for seven hours. If she walks at the same speed next year, how many miles will she walk?
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
Next year Julianna is planning to walk for seven hours. If she walks at the same speed next year, how many miles will she walk?
Unit 2 Challenges
Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Unit 2 Challenges
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Unit 2 Challenges
1scoop1quart
=𝑥 scoops2quarts
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Unit 2 Challenges
1scoop1quart
=𝑥 scoops2quarts
→2scoops2quarts
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Unit 2 Challenges
1scoop1quart
=𝑥 scoops2quarts
→2scoops2quarts
1quart4cups
=2quarts𝑐 cups
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Unit 2 Challenges
1scoop1quart
=𝑥 scoops2quarts
→2scoops2quarts
1quart4cups
=2quarts𝑐 cups
→2quarts8cups
Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder?
Emily needs 8 cups of water.
Unit 2 Challenges
1scoop1quart
=𝑥 scoops2quarts
→2scoops2quarts
1quart4cups
=2quarts𝑐 cups
→2quarts8cups
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
• 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/ 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)
James PrattProgram Specialist (6-12)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
