CCSS 101: Standards for Mathematical Practice

1. CCSS 101: Standards for Mathematical Practice Class 3 March 14, 2011

2. Journal Review by Your Peers • Read and react to each other’s journal entries about the Standards for Mathematical Practice • Use Post-it-Notes to record your comments in each journal • Pass the journals to the right until you get your own journal back • Discuss as a group – What stands out after reading all the journals?

3. Learning Intentions We Are Learning To … • analyze students’ thinking on a Continuum of Student Thinking and Understanding. • advance students’ thinking by asking good questions and making adaptations and modifications to move students to the next stage or stages.

4. Success Criteria We will know we are successful when we can understand the components of the Continuum of Student Thinking and Understanding and fill in the form after analyzing student work.

5. Common Core State Standards Alignment • Present your task to the teachers at your table. • What did you see and hear when your students worked on this task? • Summarize the work that you brought for this task.

6. A Wisconsin Graphic of CCSS

7. Return to Chocolate and Cream A candy factory has a large vat into which workers pour chocolate and cream. Each ingredient flows into the vat from its own special hose, and each ingredient comes out of its hose at a constant rate. Workers at the factory know that it takes 20 minutes to fill the vat with chocolate from the chocolate hose, and it takes 15 minutes to fill the vat with cream from the cream hose. If workers pour both chocolate and cream into the vat at the same time (each coming full tilt out of its own hose), how long will it take to fill the vat? Before you find an exact answer to this problem, find an approximate answer, or find a range, such as “between…and…minutes.” Explain your reasoning. Look at packet of student work samples

8. Return to Chocolate and Cream • Continuum of Student Thinking and Understanding • Determine the stage of each student work sample • Advancing Student Thinking • What questions will I ask? • What modifications or adaptations will I do? • Developing Effective Questions

9. Common Core State Standards Alignment • Examine student work on “Chocolate and Cream”. • Sort the student samples according to their stage on the continuum • Complete part 2 of the continuum template

10. Common Core State Standards Alignment • Complete part 3 of the continuum template for the “Chocolate and Cream” samples.

11. Asking Questions Problem Comprehension Can students understand, define, formulate, or explain the problem or task? Can they cope with poorly defined problems? • What is the problem about? What can you tell me about it? • Would you please explain that in your own words? • What do you know about this part? • Is there something that can be eliminated or that is missing? • What assumptions do you have to make? Approaches and Strategies Do students have an organized approach to the problem or task? How do they record? Do they use tools (manipulatives, diagrams, graphs, calculators, computers, etc.) appropriately? • Where would you find the needed information? • What have you tried? What steps did you take? What did not work? • How did you organize the information? Do you have a record? • Did you have a system? A strategy? A design? • Would it help to draw a diagram or make a sketch? • How would it look if you used these materials? Solutions Do students reach a result? Do they consider other possibilities? • Is that the only possible answer? • How would you check the steps you have taken, or your answer? • Is there anything you have overlooked? • Is the solution reasonable, considering the context? • How did you know you were finished?

12. Summary We Are Learning To … • analyze students’ thinking on a Continuum of Student Thinking and Understanding. • advance students’ thinking by asking good questions and making adaptations and modifications to move students to the next stage or stages. We will know we are successful when we can understand the components of the Continuum of Student Thinking and Understanding and fill in the form after analyzing student work.

13. Your Student Work Samples • Continuum of Student Thinking and Understanding • Determine the stage of each student work sample • Advancing Student Thinking • What questions will I ask? • What modifications or adaptations will I do?

14. Break

15. Learning Intentions We are learning to recognize the second and third of the Standards for Mathematical Practices within a chosen Content Standard and identify those standards within a particular math task.

16. Success Criteria We will know we are successful when we can articulate how both a Content Standard and a Standard for Mathematical Practice are infused in a math lesson in the classroom.

17. New Common Task A look at the Practice Standards within the content Domain of Geometry Materials: Geo-boards and Dot Paper

18. What is Area? Turn and talk: what is your answer to this question?

19. Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

20. What did you do? Combining Principle: The total area of two (or more) non-overlapping shapes is the sum of their individual areas. Moving Principle: the area of a shape is not changed if the shape undergoes a rigid motion.

21. Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

22. Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

23. Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

24. Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

25. Standards for Mathematical Practice Standard #2: Reason abstractly and quantitatively. Standard #3: Construct viable arguments and critique the reasoning of others.

26. Practice Standard Discussion • What questions does your group have about these standards?

27. Linking Practice to the Classroom • What would this practice look like in a classroom? • Students would be… • Teachers would be…

28. What Content Standard Did We Address? Look for a Content Standard in the CCSS (Grades 6-8) that was addressed by today’s task.

29. What did we see? • What did you as students do to bring the standards alive? • What did the facilitator as a teacher do to bring the standards alive? • What else might you as teachers in your classroom do to bring the standards alive?

30. WI CCSS Visual • Identify other Standards for Mathematical Practices that you saw as we carried out today’s task. • Use specific examples to explain the connection between the content and practice standard you identified.

31. What other practices did you see?

32. Understanding Understanding • Some of the standards start with the word Understand • What does that verb mean in these math standards?

33. Summary We are learning to recognize the second and third Standards for Mathematical Practices within a chosen Content Standard and identify those standards within a particular math task. We will know we are successful when we can articulate how both a Content Standard and a Standard for Mathematical Practices are infused in a math lesson in the classroom.