1. Class 4: Part 1 Common Core State Standards (CCSS) Class April 4, 2011

2. Reading – Chapter 8 Implementing Talk in the Classroom: Getting Started Five Principals of Productive Talk Principle 1: Establishing and Maintaining a Respectful, Supportive Environment Principle 2: Focusing Talk on the Mathematics Principle 3: Providing for Equitable Participation in Classroom Talk Principle 4: Explaining Your Expectations About New Forms of Talk Principle 5: Trying Only One Challenging New Thing at a Time

3. Journal Review by Your Peers Read and react to each other’s journal entries about the five principals of productive talk 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?

4. Learning Intentions We Are Learning To … Understand the Common Core State Standards Alignment Task Reflect on how the mathematical tasks we select address the Standards for Mathematical Practice and Content Standards

5. Success Criteria We will know we are successful when we can explain to others the Common Core State Standards Alignment Task and when we can identify the Standards for Mathematical Practice and Content Standards in the mathematical tasks we teach.

6. Common Core State Standards Alignment Task 3 Present your completed Task 3 to the teachers at your table, briefly reviewing the task and student work. Why did you select the task you did? What did the students’ work reveal? What did you see and hear when your students worked on this task?

7. Common Core Alignment Task 3 Discuss differences/ similarities between the three tasks in relation to the Standards for Mathematical Practices.

8. Final Project Review CCSS Project Questions about expectations?

9. Developing Geometric Reasoning: Grades 3-5 Common Core State Standards (CCSS)

10. Learning Intentions We Are Learning To: Examine how students’ understanding of geometry develops through defined stages, the van Hiele Model. Consider implications for instruction to move students along in developing their geometric reasoning. Compare, contrast, and connect properties of quadrilaterals.

11. Success Criteria We will know we are successful when we can articulate how Mathematical Practice Standards 1, 2 and 5— sense making, reasoning, and tools—are infused in mathematical tasks or lessons for a standards’ content progression.

12. Wisconsin Common Core Standards

13. Domain Cluster Standards Content strand across grades: Geometry “Big Idea” that groups together a set of related standards. Statements that define what students should understand and be able to do at a grade level.

14. A Content Standards Progression Domain: Geometry Clusters: 3: Reason with shapes and their attributes 4: Draw and identify lines and angles, and classify shapes by properties of their lines and angles 5: Classify 2-dimensional figures into categories based on their properties Standards: 3.G.1, 3.G.2, 4.G.1, 4.G.2, 4.G.3, 5.G.3, 5.G.4

15. van Hiele Levels of Geometric Reasoning Level 0: Visualization Recognize figures as total entities, but do not recognize properties. Level 1: Analysis (Description) Identify properties of figures and see figures as a class of shapes. Level 2: Informal Deduction Formulate generalizations about relationships among properties of shapes; Develop informal explanations.

16. van Hiele Levels of Geometric Reasoning Level 3: Deduction Understand the significance of deduction as a way of establishing geometric theory within an axiom system. See interrelationship and role of undefined terms, axioms, definitions, theorems and formal proof. See possibility of developing a proof in more than one way. Level 4: Rigor Compare different axiom systems (e.g., non-Euclidean geometry). Geometry is seen in the abstract with a high degree of rigor, even without concrete examples.

17. How do students progress in developing geometric reasoning? How would you recognize each of these levels of thinking in your students’ work? Considering the first three levels, where would you place the majority of the lessons that you teach?

18. “I believe that development is more dependent on instruction than on age or biological maturation and that types of instructional experiences can foster, or impede, development.” Pierre M. van Hiele

19. Quadrilateral Sorting Activity Facilitator: Give all a voice.Recorder: Take notes on recording sheet. Directions 1. Remove a card from the envelope. 2. Sort the quadrilateral shapes by the directions on the card. 3. Record the sort and discussion on the recording sheet. 4. Push all of the shapes back into a pile. 5. Pass the envelope to the left and repeat steps 1–4 with the next card.

20. Property Criteria all right angles at least one right angle both pairs of opposite sides congruent both pairs of opposite sides parallel both pairs of opposite angles congruent congruent diagonals diagonals bisect each other at least one pair of parallel sides exactly one pair of parallel sides

21. What is a Trapezoid? Some authors choose to define trapezoid as a quadrilateral with at least one pair of parallel sides. That definition is more inclusive and leads to the conclusion that all parallelograms are trapezoids.

22. Trapezoid definitions Everyday MathExpressionsScott Foresman A quadrilateral that has exactly one pair of parallel sides ( K & 1st) A quadrilateral with at least one pair of parallel sides. (5th) A quadrilateral with one pair of parallel sides. (3rd & 4th) A quadrilateral with only one pair of parallel sides. (5th) A quadrilateral that has exactly one pair of parallel sides

23. Maybe by Middle School? CMPGlencoeHolt A quadrilateral with at least one pair of opposite sides parallel. (6th) A quadrilateral with one pair of opposite sides parallel. (7th) A quadrilateral with one pair of parallel sides. (8th) A quadrilateral with exactly one pair of parallel opposite sides. A quadrilateral with exactly one pair of parallel sides.

24. Parallelogram Definitions Everyday MathExpressionsScott Foresman A quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are congruent. Opposite angles in a parallelogram have the same measure. (K-2nd) A quadrilateral in which both pairs of opposite sides are parallel and opposite angles are congruent. (3rd-5th) A quadrilateral with both pairs of opposite sides parallel. (3rd & 4th) A quadrilateral in which opposite sides are parallel. (5th) A quadrilateral with both pairs of opposite sides parallel.

25. True or False A square is a special kind of rectangle. It is a rectangle in which all four sides are the same length A parallelogram is a special kind of trapezoid. It is a trapezoid with two pairs of parallel sides.

26. True or False A rhombus is a special kind of kite. It is a kite in which all four sides are the same length.

27. Reflect How do these tasks engage you in the content learning infused with practices? (Mathematical Practices Standards 1, 2, 5) How do these tasks help you to better understand the mathematics? Standards: 3.G.1, 3.G.A, 4.G.1, 4.G.2, 4.G.3, 5.G.3, 5.G.4

28. Big Ideas of Geometry Two- and three-dimensional objects can be described, classified and analyzed by their attributes. Objects can be oriented in an infinite number of ways. The orientation of an object does not change the other attributes of the object. Some attributes of objects (e.g. area, volume, perimeter, surface area) are measurable and can be quantified using unit amounts. Objects can be constructed from or decomposed into other objects. In particular, any polygon can be decomposed into triangles.

29. Development Through the van Hiele Levels Level is not affected by biological age. Level is affected by degree of experience. In order to progress through the levels, instruction must be sequential and intentional. When instruction (or materials or vocabulary, etc.) is at an inappropriate level, students will not be able to understand the instruction. They may be able to memorize it, but with no understanding of material.

30. What other practices were infused in the content learning? Provide specific examples.

31. Summary We were learning to recognize three of the Standards for Mathematical Practices—sense making, reasoning, and tools— within a chosen Content Standards progression. 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.