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Welcome to …

Join us for a professional development session focused on SMP qualities and practices for mathematical discourse. Explore solid shapes, nets, and measurement of solid shapes. Engage in lessons and reflections to improve your understanding and practice. Bring your ideas and stories of children's learning!

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Welcome to …

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  1. Welcome to …

  2. TODAY’S AGENDA • SMP Qualities • 5 Practices for Mathematical Discourse • Solid Shapes • Nets and Measurement of Solid Shapes • Lessons and Reflections

  3. Bring your ideas… • As a group of professionals we have made a commitment to helping children attain success in life and a voice in the world. • Many times the best part of these kinds of professional development is simply the chance to share ideas, raise questions, and work with other practitioners to improve our own understandings and practice. • Please bring your stories of children’s learning with you.

  4. Our Socio-mathematical Norms • Listen intently when someone else is talking avoiding distractions • Persevere in problem solving; mathematical and pedagogical • Solve the problem in more than one way • Make your connections explicit - Presentation Ready • Contribute by being active and offering ideas and making sense • Limit cell phone and technology use to the breaks and lunch unless its part of the task. • Be mindful not to steal someone else’s “ice cream” • Respect others ideas and perspectives while offering nurturing challenges to ideas that do not make sense to you or create dissonance. • Limit non-mathematical and non-pedagogical discussions

  5. Presentation Norms • Presenters should find a way to show mathematical thinking, not just say it • Presenters should indicate the end of their explanation by stating something like “Are there any questions, discussion, or comments?” • Others should listen and make sense of presenters’ ideas. • Give feedback to presenters, extend their ideas, connect with other ideas, and ask questions to clarify understandings

  6. The Standards for Mathematical PracticeStudent Reasoning and Sense Making about Mathematics Let’s list as many qualities as we can of the kinds of mathematically proficient student behaviors that exemplify the SMP’s. • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  7. 5 Practices for Orchestrating Productive Mathematics Discussions • Getting Started: Anticipating Students’ Responses and Monitoring Their Work

  8. Calling Plan Task Long distance Company “A” charges a base rate of $5.00 per month plus 4 cents a minute that you are on the phone. Long distance Company “B” charges a base rate of only $2.00 per month, but they charge you 10 cents per minute used. How much time per month would you have to talk on the phone before subscribing to Company “A” would save you money?

  9. Solve the task for yourself. • Discuss your ideas with your small group & prepare a justification and representation for your decision on chart paper. • Whole group presentations.

  10. Reading & Reflection • Read pages 31 – 42. • Consider questions #1 #2, #3 & #5 on the hand-out. • Discuss with a partner then with your group. • Be prepared to share your response to the question assigned to your group.

  11. Break Time

  12. What’s My Shape?

  13. All, Some, or No 1. _______ rectangles are squares. 2. _______ squares are rectangles. 3. _______ rhombuses are squares. 4. _______ squares are rhombuses. 5. _______ squares are parallelograms. 6. _______ parallelograms are squares. 7._______ rhombuses are rectangles. 8._______ trapezoids are parallelograms.

  14. Polygons • What is the definition of a polygon? • What is a “regular” polygon? • Which regular polygons could be used to “tessellate the plane”? What does this mean? http://illuminations.nctm.org/Activity.aspx?id=3533 • Why do some regular polygons tessellate the plane and others do not?

  15. Solid Shapes • What are solid shapes? • Locate/point out any solid shapes in the room. • These are also called three-dimensional shapes. What do we mean by one-dimensional, two-dimensional, and three-dimensional?

  16. Sorting 3-D Shapes • Consider a way to sort or group the 3-D shapes at your table; then work with a partner to devise a method of sorting the shapes. Share with your group. • Using the attribute hoops, construct a Venn diagram for your group & justify the structure of your diagram.

  17. Naming 3-D Shapes • Common 3-D Shapes • Cube; Rectangular Prism; Triangular Prism; Cylinder; Cone; Pyramid; Sphere • Polyhedron (plural is polyhedra) • Geometric solid with flat faces • Each face is a polygon • Platonic solids • Polyhedra • Each face is the same regular polygon • Same number of polygons meet at each vertex

  18. Attributes of 3-D shapes • Use the handout to record the names and the numbers of faces, vertices, and edges for several polyhedra. • Share your findings with the group. • Do you notice any patterns?

  19. Lunch

  20. Nets for 3-D Shapes • Cube is a 3-dimensional shape with six identical square faces. • Using the grid paper, how many patterns can you make that will fold into a cube? Make a sketch of each pattern you find on the recording sheet. Test each pattern by folding it into a box. • Work with a partner then share with your table group. • Determine the total area and perimeter for each pattern. • How do these compare for each pattern?

  21. Interactive Cube Net Site http://www.nctm.org/Classroom-Resources/Interactives/Cube-Nets/

  22. Questions About Cubes • Which nets have four squares in the middle? • Which ones have three squares in the middle? • Which ones have two squares in the middle? • And, more important, why are there only eleven possibilities?

  23. 11 Nets for Cubes

  24. Rectangular Prism • Working with a partner draw on grid paper a flat pattern for a rectangular prism that is not a cube. • Test the pattern by using . Describe the faces of the rectangular prism. • What are the dimensions of each face? What is the total area of the prism? What is the perimeter of the prism? • Compare your results with others.

  25. file:///Users/sherrykaylane/Desktop/Day%206%20Copies/Interactives%20.%203D%20Shapes%20.%20Prisms.webarchivefile:///Users/sherrykaylane/Desktop/Day%206%20Copies/Interactives%20.%203D%20Shapes%20.%20Prisms.webarchive

  26. Packaging Dilemma The Scrooge Shipping Company is looking to save money on the cost of shipping materials. To accomplish this, they have decided to use less material for the packages. Working with a partner and using the 1-centimeter cubes at your table, design a container that will allow for the maximum(greatest) number of cubes and the minimum(least) amount of packaging material.

  27. Break Time

  28. Math Content for our Classrooms • Each day we will spend time with grade level teams making lesson plans. • Each of us will make one plan that is part of a unit of plans the grade level team is working on. • Each plan must have the following: • Connected mathematics content focus from Ohio’s Mathematics Learning Standards • A focus SMP • Designed to Orchestrate Productive Mathematics Discussions (The 5 Practices)

  29. Math Content for our Classrooms Three checks must be made for the completion of lesson plans: Check 1) Consult with Sandy and/or Mary about the mathematics content of the lesson and explain to her its mathematical appropriateness. When the lesson is complete Sandy, our resident mathematician, will sign off on its content (SMC’s). Check 2) Consult with Sherry about the design of the lesson to promote mathematical discourse (5 Practices). Sherry must sign off on the lessons discourse elements. Check 3) Consult with Dr. Matney about the design of the lesson having a focus Standard for Mathematical Practice. Dr. Matney must sign off on the lessons mathematics proficiency elements (SMP’s) ?Questions about COMP Lesson Plans?

  30. Air of Appreciation We want to pass on to each generation a sense of learning how to appreciate life, others, and learning. Let’s spend some time sharing one thing or experience that we appreciate: Examples: I appreciated when Ray didn’t give up on solving that hard problem. It encouraged me to keep thinking for myself to make sense of it.

  31. Time of Reflection • On a sticky note tell us one thing you learned today. • Tell us one think you liked or one thing you are still struggling with.

  32. Stay Safe • Please help us put the room in proper order. • Please leave your name tents for next time.

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