Common Core High School Mathematics: Transforming Instructional Practice for a New Era

1. Common Core High School Mathematics:Transforming Instructional Practice for a New Era School Year Session 3: October 16, 2013 Deconstructing Geometric Understanding 1.1

2. Agenda • Homework Discussion • Linking Claims and Evidence • Break • Precision in Geometry • Homework and closing remarks 1.2

3. Homework Discussion Activity 1: • Sit with others teaching the same content as you this semester. • One person places a task (original and modified versions) face up on the table. • Other group members study them individually, in silence, for 1 minute. • Discuss the modifications you see in the task. • Repeat, until everyone has had a chance to present. 1.3

4. Homework Discussion Activity 1: • Now that we have worked on task modification: • What do you notice about the work of modifying tasks? • What do you wonder about? • What do you want to know more about, and what keeps you up at night about this idea? 1.4

5. Learning Intentions & Success Criteria Learning Intentions: We are learning to use evidence from classroom sources to make claims about student understanding Success Criteria: We will be successful when we can identify and describe evidence for SBAC claims in given pieces of student work.

6. Linking Claims and Evidence Activity 2: Julie wants to fence in an area in her yard for her dog. After paying for the material to build her doghouse, she can afford to buy only 36 feet of fencing. She is considering various different shapes for the enclosed area. However, she wants all of her shapes to have 4 sides that are whole number lengths and contain 4 right angles. All 4 sides are to have fencing. What is the largest area that Julie can enclose with 36 feet of fencing? Support your answer by showing work that would convince Julie that your area is the largest. 1.6

7. Linking Claims and Evidence Activity 2: • Consider the student work from the NAEP item, Julie’s Fence. • With your group, create three claims: • A claim about most or all of these artifacts • A claim about some, but not all of these artifacts • A claim about few or none of these artifacts • Link each of your claims about the work to one of the four SBAC claim categories. • Claim 1: Concepts and Procedures • Claim 2: Problem Solving • Claim 3: Communicating and Reasoning • Claim 4: Modeling and Data Analysis 1.7

14. Linking Claims and Evidence Activity 2: • What claims would you have liked to have made about this set of work? • What would you need to do to be able to collect the evidence for those claims? 1.14

15. Learning Intentions & Success Criteria Learning Intentions: We are learning to use evidence from classroom sources to make claims about student understanding Success Criteria: We will be successful when we can identify and describe evidence for SBAC claims in given pieces of student work.

16. Break

17. Precision in Geometry Activity 3: • At your tables, come to consensus on a careful definition of each of the following: • A rigid motion • A reflection • A rotation • A translation 1.17

18. Precision in Geometry Activity 3: With your table group, find a way to model the particular rigid motion you have been given. You may use any tools or objects you can find in the room, including yourselves. Be prepared to justify your model by showing how you can connect it to the formal definition of your transformation. 1.18

19. Homework & Closing Remarks Activity 4: • Homework: • Read “Open-Ended Questions and the Process Standards” by Wendy Sanchez • Make any further modifications to your chosen tasks that you think desirable after today’s homework discussion. • Teach the final version of your tasks, and bring representative samples of student work to class on October 30. • Reflect on how you might incorporate the principles you are learning into the lesson or unit you have chosen for your main semester project. (Recall that this is a lesson or unit you plan to teach between November 20 and December 4.) 1.19