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UCDMP Saturday Series 2012-13 The Vision of the Common Core: Changing Beliefs,

UCDMP Saturday Series 2012-13 The Vision of the Common Core: Changing Beliefs, Transforming Practice Saturday, March 16, 2013. Agenda. Overview – SMP’s #7 and #8 Exploring Conjectures – Volume Critical Attributes of 3D Shapes Critical Attributes of Quadrilaterals

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UCDMP Saturday Series 2012-13 The Vision of the Common Core: Changing Beliefs,

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  1. UCDMP Saturday Series 2012-13 The Vision of the Common Core: Changing Beliefs, Transforming Practice Saturday, March 16, 2013

  2. Agenda • Overview – SMP’s #7 and #8 • Exploring Conjectures – Volume • Critical Attributes of 3D Shapes • Critical Attributes of Quadrilaterals • Adjusting and Testing Conjectures Lunch • Exploring Shape s– Tangrams/Power Polygons • CCSS for Geometry – Progressions • Sum of the Angles of a Polygon • Closure, Reflections, and Feedback

  3. Wireless Access • Go to Moobilenet • Sign in information • Email address: ucdmp@wireless.com • Password: wireless

  4. SMP #6 Look for and make use of structure.

  5. SMP #7 Part of the beauty of mathematics is its structure.

  6. Examples 3 + 2 = 2 + 3

  7. Examples Place Value – you always add ones to ones, tens to tens, etc. Whole NumbersDecimals 246 + 37 2.46 + 3.7 246 2.46 + 37+ 3.7

  8. SMP #7 If students learn how and why math works AND why math works the way it does Then they begin to notice, look for, and anticipate how to use structure They become engaged in what it means to DO MATHEMATICS

  9. SMP #8 Look for and express regularity in repeated reasoning.

  10. SMP#8 The goal is for students to move past simply solving problems and find ways to • Generalize the methods they use • Determine shortcuts for procedures they use

  11. Examine Decompose a number less than 10 into pairs of numbers At first, students randomly find pairs After a while they start to organize their thinking

  12. Example 8 + 0 7 + 1 6 + 2

  13. Example • Suppose you have ¾ of a cake.

  14. Example • And you cut each piece into two. • What fraction do you have now?

  15. Example • What if you cut each piece in into 3 equal pieces instead?. • Now, what fraction do you have?

  16. Important Note • AVOID teaching shortcuts before students develop understanding • Instead provide examples and opportunities for students to discuss patterns that they are seeing

  17. Quadrilaterals What are the critical attributes of a quadrilateral? • Place all the shapes that are quadrilaterals onto the paper • Remove any shapes that are not quadrilaterals.

  18. Special Attributes Parallel sides • One set of parallel sides Trapezoid • Two sets of parallel sides Parallelogram

  19. Sort • Now sort your quadrilaterals • If it’s a trapezoid, place it on that paper • If it’s a parallelogram, place it on that paper • If it is neither of those, leave it on the quadrilateral paper.

  20. Special Attributes Next we look for an attribute that is always equal Let’s look at the trapezoids • Can you have 4 equal sides? • Can you have 4 equal angles? • So we are done sorting trapezoids.

  21. Special Attributes Now let’s look at the parallelograms • All sides are equal Rhombus • All angles are equal Rectangle

  22. Sort • Now sort your parallelograms • If it’s a rhombus, place it on that paper • If it’s a rectangle, place it on that paper • If it is neither of those, leave it on the parallelogram paper.

  23. Sorting • Are there any shapes that you had a problem deciding where to put them? • Why?

  24. Final sort • Find all of the shapes that are both rectangles and rhombuses. • What are these shapes called? • Squares have equal sides and equal angles

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