True or False?

1. True or False? • If it is a square, then it is a rhombus. • All squares are rectangles. • Some parallelograms are rectangles. • All parallelograms have congruent diagonals. • If it has exactly two lines of symmetry, it must be a quadrilateral. • If it is a cylinder, then it is a prism. • All prisms have a plane of symmetry. • All pyramids have square bases. • If a prism has a plane of symmetry, then it is a right prism.

2. Geometry and Measurement are Essential… Geometrymeans “earth measure,”and geometry, spatial reasoning, and measurement are topics that connect to each other and to other mathematics and that connect mathematics to real-world situations. ~NCTM

3. Big Ideas of Measurement • 1.Measurement involves a comparison of an attribute of an item or situation with a unit that has the same attribute. • 2.Meaningful measurement and estimation of measurements depend on personal familiarity with the unit of measure being used. • 3.Estimation of measures and the development of bench-marks help students increase familiarity with units. • 4.Measurement instruments are devices that replace the need for actual measurement units. • 5.Area and volume formulas provide a method of measuring these attributes by using only measures of length.

4. The Meaning and Process of Measuring • Concepts and skills — making comparisons — using physical models of measuring units — using measuring instruments • Nonstandard units and standard units: Reasons for using each • The role of approximation

5. Common Core State Standards: Grade 3 • Geometric measurement: recognize perimeter. • CCSS.Math.Content.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

6. Perimeter

7. Perimeter & Area • Connections to content and practices. • Flexibility in solution approaches, or, ways of making sense of the problem. • Student decision-making. • Familiarity with the ―type of problem.

8. Possibilities… Problem One. Your class is going to plant a garden in the playground. You have been given 100 feet of fencing to place around the perimeter of your garden. You want your garden to be as large as possible. What dimensions should your garden be? Problem Two. You have been asked to help build a sandbox for the kindergartners at your school. The perimeter of the sandbox should be 20 feet. If you want the sandbox to take up the least amount of space possible, what should the dimensions of the sandbox be?

9. CCSS & Make a task…. • Given a CCSSO (2010) standard, create a high cognitive demand task

10. The Knowledge Quartet Contingency Transformation Connection Foundation

11. The Knowledge Quartet Contingency – Unexpected, unplanned moments. Any time the teacher has to ‘think on her/his feet.’ Examples: • Unexpected* student responses and questions • *Teachers should anticipate likely responses, questions, etc! • What else? • Ways in which teachers deviate and respond during a lesson: (fill out on your handout) Rowland, T., Huckstep, P. & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281.

12. Contingency: The core 2 aspects • Deviation from Agenda: “Good” deviation can be described in two ways: 1) Why: the teacher deviates for a mathematical reason (as opposed to deviation that addresses time constraints or classroom management issues) and 2) How: the deviation focuses on relational understanding. • Responding to Students’ Ideas: There are two considerations: 1) the teacher must accurately respond to students’ comments, questions, answers and statements, and 2) the teacher’s responses should focus on relational understanding rather than instrumental.

13. Grade 4 Perimeter & AreaFocus on Contingency

14. Considering the lesson • In what ways did you observe aspects of Contingency? • Responding to Students’ Ideas: There are two considerations: 1) the teacher must accurately respond to students’ comments, questions, answers and statements, and 2) the teacher’s responses should focus on relational understanding rather than instrumental.

15. Geometry Chapter 20

16. Reading Response: 5 minutes • Side One: Explain the Van Hiele Levels of Thought in your own words • Side Two: What two activities did you want to try in a classroom?

17. The Greedy Triangle • Building understanding of concepts • Making connections • Bodily-kinesthetic learning • Novelty • Increase in engagement • http://www.corestandards.org/Math/Content/G

18. The 4 Goals of Geometry • Shape & Properties • Transformation • Location • Visualization

19. Objects of thought… What we are able to think about geometrically…(van Hiele Levels of Thought) Level 0 Level 1 Level 2 Level 3 Level 4Jigsaw Experts

20. A full lesson plan • Before (intro) • During (main activity) • After (summarize/closing) • CCSSO • Grade 3 • Reason with shapes and their attributes. • CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

21. Quadrilateral Perpendicular Parallel Four Angle Congruent

22. Mathematical Task Properties of Quadrilaterals

23. Can you come up with a complete definition for a quadrilateral? Extend your thinking…

24. Check for video….

25. Small Group New Idea Tryout

26. Midterms…

27. Exit Slip… • What three points do you want to remember? • Write one thing that squares your thinking… • What question still circles in your mind?

28. READ Chapter 15: Developing Fraction Concepts New Idea Tryout –Small Group Due 31st/ Nov 1 Extra Credit Coming soon For Next Week ….