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+ Agenda CCSS Standards for Mathematical Practice CCSS Grade Level Overviews Differentiation Van Hiele & Mosaic Puzzles Menu Slices and FALs Lunch Breakout Groups 3

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1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 4

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Grouping the Practices William McCallum Standards for Mathematical Practice Tucson, April

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+ Grouping the Practices SMP Pairs 1 & 6 ; 2 & 3 ; 4 & 5 ; 7 & 8 Discuss with your SMP partner the similarities and differences between the two practices in the K-1 posters and then the middle school posters. Discuss with your SMP partner why these two practices have been grouped together. Share highlights of your partner talk with your table. Whole group discussion 7

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+ Geometry Across Grade Levels In your team of 8: Read one of the overview handouts (K/1; 2/3; 4/5, 6, 7, 8, Algebra, Geometry) Circle, underline, or, highlight any geometry concepts and other big ideas that support geometrical reasoning. Share the progression of geometry with your table, beginning with the K/1 overview. Popcorn share out and clarifying questions. 9

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+ CCSS-Mathematics Content standards: paint the Big Picture of the domain flesh out the domain are not a checklist are independent of Californias 1997 math standards 10

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+ Differentiation Please read Malcolm Swans Improving Learning in Mathematics: Challenges and Strategies Discuss at your table: highlights from the article. anything that resonated with you. questions that arose while reading. Whole Group Debrief 11

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+ Setting the Stage for Geometry Take a few minutes to think about and represent in some way [diagraming, webbing, listing, organizing] what you believe are the big ideas in Geometry. Pair/Share your ideas with an elbow partner Group Popcorn Sharing 12

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+ Setting the Stage for Geometry Please read the excerpts from Van de Walle and Burns. Discuss at your table: highlights from the article. anything that resonated with you. questions that arose while reading. Whole Group Debrief 13

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+ Van Hiele Levels 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 Teaching Children Mathematics 14

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+ Van Hiele Levels Please read Van Hieles Levels of Geometric Reasoning Level 0 Recognition Level 1 Analysis Level 2Informal Deduction Level 3 Formal Deduction Level 4 Rigor 15

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+ Level 0 Shapes are what they look like Students recognize and name figures based on the global visual characteristics of the figure. Its a square because it looks like a house. These shapes go together because theyre pointy or theyre fat. 16

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+ Work of 10th grader 17

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+ Work of 10th grader 18

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+ Instruction at Level 0 Sorting and Classifying-see how shapes are alike and different Variety of shapes- minimize the effect of irrelevant features. Build activities around specific properties so students start to understand and see them naturally. 19

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+ Questions at Level O Lets see if thats true for other rectangles. Can you draw a triangle that does not have a right angle? In general students should be challenged to see if observations made about a particular shape apply to other similar shapes. 20

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+ Level 1- Analysis Students start to see classes of shapes (instead of a rectangle, all rectangles) Start to see properties of shapes or list of attributes They have trouble with subcategories or sifting through the attributes, such as seeing that squares are also rectangles, quadrilaterals, parallelograms. 21

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+ Whats a rectangle? 6th graders were asked: Can a parallelogram be both a rectangle and a rhombus? 22

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+ Whats a rectangle? 6th graders were asked: Can a parallelogram be both a rectangle and a rhombus? 23

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+ Whats a rectangle? 6th graders were asked: Can a parallelogram be both a rectangle and a rhombus? 24

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+ Student Finds Correct Attributes 25

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+ Student Finds Correct Attributes 26

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+ Other Students Did not notice that Blobbies had 4 sides. Failed to notice that Blobbies had circles in the middle or thought all shapes with circles in the middle were Blobbies. Students used irrelevant properties like parallel sides. Students couldnt sort with 2 attributes. 27

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+ Instruction at Level 1 Focus on properties rather than mere identification. Think about classes: all rectangles, all prisms. 28

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+ Questions at Level 1 Questions that involve reasoning: If the sides of a four-sided shape are all congruent, will you always have a square? How do you know? Can you find a counterexample? How do you know? 29

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+ Instruction at Level 2 Make and test hypotheses and conjectures. Examine properties of shapes to determine necessary and sufficient conditions. Use language of informal deduction: all, some, none, if-then, what if, etc. Encourage students to attempt informal proofs. 30

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+ Implications for Instruction Handout Students working at the recognition or visual level needed activities like… Students working at this analysis stage need activities like… Students working at abstraction or informal deduction are ready for… 31

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+ Mosaic Puzzle Please cut out the puzzle pieces and explore their relationships. 32

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+ Mosaic Puzzle Find all the pieces that can be made from two other pieces. Find all the pieces that can be made from three other pieces. How many different shapes can be made with a pair of pieces? 33

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+ Mosaic Puzzle What two shapes make a parallelogram? What other two pieces make this shape? Do they also work flipped over? Can you make a parallelogram with three pieces? Hint: Try pieces 1,2 and 5; make it in a different way with these 3 pieces. Also try pieces 1,2, 5 flipped over 34

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+ BREAK Time !! 35

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+ Problem of the Month (POM) and Slices SVMI morning sessions provide: Opportunities to experience the development of specific mathematical content through the grade levels. POMs and Menu Slices provide: multiple entry points to mathematics opportunity for extension, development, and differentiation an opportunity to analyze and synthesize the progression of mathematics within domains September and October POMs November and December Menu Slices 36

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+ Geometry Menu Slices Choose a color from the pile on your table. Go to corresponding color Menu Station 2- and 3- Dimensional Shapes Location and Position Transformations and Symmetry Visualization, Spatial Reasoning, and Modeling Work through all the activities in the slice. Complete the Learning Log 37

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+ Geometry Menu Slices Return to your table. Share Learning Log for the Slice you experienced with your table. Whole Group Discussion 38

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Lunch Please be back in 45 minutes 39

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+ Breakout Sessions K Algebra - HS 40

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+ 3-5 afternoon session 41

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+ Spatial Visualization Number Talks Dot Patterns 2-D Geometry 3-D Geometry 42

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Dot Patterns How Many Dots? How did you see it? 43

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2-D Geometry What are the shapes? How did you see them? 44

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+ 3-D Geometry How many cubes? How did you see them? 45

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+ Teacher Techniques Individual Think Time Signals - e.g. Use of Thumbs Pair/Share Whole Group Share Out 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk 3 x 5 Card Formative Assessment: two different strategies for solving problem And the conversation continues … Individual Think Time Signals - e.g. Use of Thumbs Pair/Share Whole Group Share Out 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk 3 x 5 Card Formative Assessment: two different strategies for solving problem And the conversation continues … 46

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+ Teacher Tools Overhead Transparencies Charts Butcher Paper Recordings White Boards Document Reader Smart Boards 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk And the conversation continues … Overhead Transparencies Charts Butcher Paper Recordings White Boards Document Reader Smart Boards 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk And the conversation continues … 47

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+ 4 Triangle Problem 48

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+ Roping in Quadrilaterals 49

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+ MARS tasks related to Geometry 50

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+ MARS for next time (Measurement) Work the task Think about where your students will be successful Predict misconceptions Administer the task to your students Bring back the work in December. 51

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