1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 5th Grade Unit 5: Geometry and the Coordinate Plane November 15, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

2. Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to share your feedback.http://ccgpsmathematicsK-5.wikispaces.com/ After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist

3. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fifth Grade Unit 5: Geometry and the Coordinate Plane November 15, 2012 Turtle Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

4. Welcome! Thank you for taking the time to join us in this discussion of Unit 5. At the end of today’s session you should have at least 3 takeaways:  What the research says about developing understanding.  Ideas to support student and teacher understanding.  Content specific to Unit 5.

5. The intent of this webinar is to bring awareness to:  the development of foundational coordinate graphing understanding.  the mathematics of graphing relationships.  the underlying structure of a task. We will view task structure by looking at a performance task for Unit 5 during this webinar.

6. What’s Unit 5 all about? The coordinate system in the first quadrant of the coordinate plane How to organize information on the coordinate plane How to recognize numerical patterns How to represent and interpret relationships on the coordinate plane

7. What should students bring from previous grades? Knowledge of various graph types Understanding that graphs are a visual representation of information (data) Familiarity with transfer of data between charts and graphs Ability to interpret graphs Knowledge of numerical patterns and relationships

8. Here’s the skinny- The short version is happening right now. The long version is here: http://commoncoretools.me/wp- content/uploads/2012/06/ccss_progression_g_k6_201 2_06_27.pdf

9. What’s Unit 5 all about? The coordinate system in the first quadrant of the coordinate plane

10. What’s Unit 5 all about? The coordinate system in the first quadrant of the coordinate plane

11. What’s Unit 5 all about? How to organize information on the coordinate plane

12. What’s Unit 5 all about? How to organize information on the coordinate plane

13. What’s Unit 5 all about? How to recognize numerical patterns

14. What’s Unit 5 all about? How to recognize numerical patterns

15. What’s Unit 5 all about? How to represent and interpret relationships on the coordinate plane

16. Visual Representations A major task for any student engaged in problem solving is to translate the quantitative information in a problem into a symbolic equation (an arithmetic/algebraic statement) necessary for solving the problem. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16

17. Visual Representations Visual representations help students solve problems by linking the relationships between quantities in the problem with the mathematical operations needed to solve the problem. Visual representations include tables, graphs, number lines, and diagrams such as strip diagrams, percent bars, and schematic diagrams. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16

18. Visual Representations Recommendations by WWC to assist students in their development and use of visual representations: Select visual representations that are appropriate for students and the problems they are solving. Use think-alouds and discussions to teach students how to represent problems visually. Show students how to convert the visually represented information into mathematical notation. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16

19. What’s Unit 5 all about? Visual models- Yep. I think we get this now.

20. Performance Task: What’s the Better Buy?

21. A new amusement park has just opened in your town and you want to make sure you get as many rides as possible for your money. The park has two cost plans for visitors. Each plan includes a fee for admission and an additional charge for each ride. It’s up to you to decide which plan works best for you. Check out Plan A and Plan B in the boxes beside the graph. Complete the table for each plan to generate ordered pairs and create a graph to represent your results. Be sure to add numbers to the x and y axis before plotting your points. Highlight each plan with a different color. Review your results and create an argument for which plan you feel is the better buy.

23. What’s the Better Buy? What’s the goal of this task? What might you add? How might you increase student choice/entry points?

24. Performance Task: What’s the Better Buy? How can you structure the task so that it works for your classroom? Intro task- start with task and create a rubric. Edit task if necessary to better fit your students. Students work independently while you circulate and ask questions, take notes Set benchmarks along the way to keep students moving forward, help kids to organize their workflow

25. Performance Task: What’s the Better Buy? Refer students back to rubric all along the way to help kids to organize their thinking and improve their work. Choose strategically which student ideas offer opportunities for “mid-stream minilessons”. Question more than you answer. Listen more than you talk. If you are recording your thinking, you are modeling your expectation for them.

26. Looking at a Task: https://www.teachingchannel.org/videos/algebra-lesson- planning?fd=1

27. Horizontal and vertical connections Strategies apply everywhere, in multiple contexts Integration of content areas ensures connections and relational thinking Multiple steps builds understanding and deeper thinking Work the culminating task collaboratively with colleagues so you know where your kids need to go, and what they might have difficulty with

28. Rubric How might a rubric be made by your students? Different criteria- you can choose! Standards (for sure) Organization Clarity Student behavior

29. Interested? http://www.teachervision.fen.com/teaching-methods- and-management/rubrics/4586.html http://www.teachervision.fen.com/teaching-methods- and-management/rubrics/4586.html http://faculty.mwsu.edu/west/maryann.coe/coe/Projects/ epaper/rubrics.htm http://faculty.mwsu.edu/west/maryann.coe/coe/Projects/ epaper/rubrics.htm http://sblc.registereastconn.org/greatrubrics.pdf http://www.schrockguide.net/assessment-and- rubrics.html http://www.schrockguide.net/assessment-and- rubrics.html http://www.scholastic.com/teachers/article/making- most-rubrics http://www.scholastic.com/teachers/article/making- most-rubrics

30. Effective Feedback Sharing thinking

31. Culmination of the unit, not the grade.

32. Food for thought: “ I’ve learned a lot from watching good teachers. The most important thing I’ve learned: adopt the mantra “ Just the answer isn’t good enough.” I watched teachers transform passive students into thinkers because of this simple idea. This expectation, that a teacher sets at any point in the year, opens up doors to all of the SMP’s (not every one every day – but many every day). In those classes, because “ just the answer isn’t good enough,” kids made sense of the mathematics they were doing, reasoned to justify that their answer was correct, critiqued their work and others’, used tools and made models of the mathematics that was happening, used some measure of precision as they explained their thinking, and sometimes found structure (even a few teachers found this) in their own repeated reasoning.” From a math coach friend…

34. Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback!http://ccgpsmathematicsK-5.wikispaces.com/ Turtle Gunn Toms Program Specialist (K-5) tgunn@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! join-mathematics-k-5@list.doe.k12.ga.us Follow on Twitter! Follow @GaDOEMath Follow @turtletoms (yep, I’m tweeting math resources in a very informal manner)