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CCGPS Mathematics 7 th Grade Update Webinar Unit 1: Operations with Rational Numbers August 9, 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.

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What are update webinars? Update on the work of the 2013 Resource Revision Team Overall revisions Unit 1 revisions Addressing areas of concern Resources

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th Grade Resource Revision Team

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7th Grade Resource Revision Team Tiffany Evans – Eastbrook MS, Whitfield Co. Leigh Kitchens – Henry Co. MS, Henry Co. Elizabeth Oliver – Okefenokee RESA McKendree Ramsell – Russell MS, Barrow Co. Amanda Wilhelm – ET Booth MS, Cherokee Co.

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Unit 1: Numbers and Operations 7th grade Mathematics

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7 th Grade Comprehensive Course Overview Located on the 6-8 math section of Designed to provide clarification of CCGPS Mathematics Standards Organized to link together many sources of information pertinent to CCGPS 7 th Grade Standards The comprehensive course overviews in grades 6-8 are similar to “grade level overviews” in k-5. They have been created for coordinate algebra and analytic geometry as well, making them a great tool for vertical alignment.

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Begin at Direct Link to Page

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Select the CCGPS ELA/Math Tab Direct Link to Page

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Select the Mathematics option under Browse CCGPS Direct Link to Page

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Select the 6-8 option in the Mathematics section

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Expand the 7th Grade Course

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Select the Comprehensive Course Overview Expande Coordinate Algebra

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Flipbooks (located within the Comprehensive Course Overview) Bold words will provide access to the Common Core Flipbooks The Flipbooks offer clarification of standards Hover mouse over FLIPBOOKS heading to follow a direct link to the entire document Very Large File (slow loading)

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Links to Flipbook Teachers can access the general information associated from the Flipbook with a particular standard by hovering the mouse over the standard number (page 2 of the Comprehensive Course Overview)

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Standards for Mathematical Practices Mathematical Practices are listed with each task to highlight the importance of connecting the SMPs to teaching and learning. Teachers should not overlook the Standards for Mathematical Practice. The SMPs are just as important as the content standards. Using the framework tasks often in the classroom will ensure that SMPs are being addressed and emphasized.

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Formative Assessment Lessons You’ll also see these called “Classroom Challenges” or CCs The purpose of the FAL is to show teachers where their students are in the progression towards mastery of a concept. Emphasis is placed on student responsibility for learning through “productive struggle” on challenging tasks. Teacher role during a FAL is to facilitate students’ solutions, ideas, and reflections through questioning…not to provide answers and solutions. FALs should be done about 2/3 of the way through a unit. Two or three days before doing a FAL in class, the pre- assessment will need to be administered to students.

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Formative Assessment Lessons (FALs)

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Rationale for revisions of 7 th grade Math Unit 1 Frameworks Prior to revisions: – The introductory segment was too lengthy and not “teacher-friendly”; couldn’t be consumed efficiently, so many teachers would skip this section. – Some standards were overrepresented by tasks while other standards had no aligned task. – Many of the student versions of tasks had directions that needed to be more detailed. – Student versions lacked structure making it difficult for students to know exactly what was being asked of them. – Unit 1 lacked many tasks that incorporated positive and negative rational numbers; many specifically used integers only.

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Rationale for revisions of 7 th grade Math Unit 1 Frameworks After revisions: – Tasks include student versions that allow for more organized responses and often offer examples – Teacher guides have more extensive explanations of how to use tasks in the classroom – Differentiation suggestions have been incorporated – Many additional resources and materials are suggested to supplement tasks – Links and explanations for Formative Assessment Lessons and Short Cycle Tasks provided by Shell Centre – Emphasis on SMPs and formative assessment

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Specific Task Comments and Explanations Things to look for: Identified standards within the Task Table as well as SMPs added within individuals tasks Common Misconceptions section added within each task Differentiation and additional resources to help modify tasks to meet the needs of your students

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Task Table Notes

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Operations of Integers: Appendix of Additional Resources for Unit 1

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Just A Friendly Reminder… The Unit 1 Frameworks are meant to be seen as GUIDELINES – Take from the frameworks what you need for your students to be successful – Note that there are more tasks included within the unit – It is not feasible nor expected to complete all of the assigned tasks within an academic year

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3 – (-2) Areas of Concern

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3 – (-2) + = 0 Areas of Concern

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3 – (-2) + = 0 Areas of Concern

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3 – (-2) + = 0 Remove two negative chips. Areas of Concern

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3 – (-2) + = 0 Remove two negative chips …but I do not have two negative chips to remove! Areas of Concern

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3 – (-2) + = 0 Areas of Concern

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3 – (-2) + = 0 You can now remove two negative chips! Areas of Concern

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3 – (-2) + = 0 Areas of Concern

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3 – (-2) + = 0 Which leaves you with five positive chips! Areas of Concern

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3 – (-2) + = 0 Which leaves you with five positive chips! 3 – (-2) = Areas of Concern

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Making sense of division… Partitive Division – If the number of groups is known and you are trying to find the number in each group. (learner.org) Ex: You have six dollars and you want to divide it equally among 3 groups. Quotative Division – If the number in each group is known and you are trying to find the number of groups. (learner.org) Ex: You have six dollars and you want to give 3 dollars to each group. 6 ÷ 3 (Partitive) = = 2 (in each of the 3 groups) 6 ÷ 3 (Quotative) = = 2 (groups of 3) Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s) Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s) 6 ÷ -3 Areas of Concern

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Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s) 6 ÷ -3 I’m stuck because I can’t make -3 groups (partitive) nor can I determine how many -3’s are in 6 (quotative)! Areas of Concern

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Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? Areas of Concern

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Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? Remove one set of -3. Areas of Concern

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Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? Remove a second set of -3. Areas of Concern

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Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? 2 sets of -3 were removed to make 6 or -2 sets (removing 2 sets) of -3 were used to make 6. 6 ÷ -3 = -2 Areas of Concern Teaching Student-Centered Mathematics Van de Walle and Lovin

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Assessment July 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: Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123http://www.gadoe.org/External-Affairs-and- Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

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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; and will include a variety of item types, such as performance-based and multiple- choice items. The press release in its entirety can be found at: Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123http://www.gadoe.org/External-Affairs-and- Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

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Assessment We 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)

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GaDOE Resources Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx 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 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 https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Georgia Mathematics Teacher Forums - CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx 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 https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative- Assessment-Lessons-Videos.aspx Resources

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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.

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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

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Professional Learning Resources Inside Mathematics- Annenberg Learner - Edutopia – Teaching Channel - Ontario Ministry of Education - Achieve - Blogs Dan Meyer – Timon Piccini – Dan Anderson –

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Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

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Thank You! Please visit 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 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.

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