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The Shape of Geometry for PreK-2 Teaching and Learning in the Common Core

The Shape of Geometry for PreK-2 Teaching and Learning in the Common Core. Lucia M. Flevares & Jamie R. Schiff. Session Goals .

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The Shape of Geometry for PreK-2 Teaching and Learning in the Common Core

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  1. The Shape of Geometry for PreK-2 Teaching and Learning in the Common Core Lucia M. Flevares & Jamie R. Schiff

  2. Session Goals 1. To explore your knowledge of the design and implementation of geometry experiences for students in the PK-2 years, using the Common Core Standards and the Ohio Pre-Kindergarten Content Standards for Mathematics 2. To map standards between the primary grades and back to the Pre-kindergarten years. 3. To share resources for lessons that will help meet the Common Core geometry goals for the prekindergarten and early elementary years.

  3. Agenda for the Hour • CCSS Geometry Background Knowledge: • What do yourteachers/students already know? • What do you still want to know? • Activity: Mapping out the standards • Identifying connections/gaps across grade levels • Focus on vocabulary • What is new to you? • Learning Progressions • Back mapping to Pre K • Conclusions

  4. Background Knowledge & Poll Questions • What do you, and your/ teachers/students already know about geometry in the early grades and the CCSS? • What do you still want to know? Table or Row Discussion • Nominate a person to share out your ideas.

  5. Learning Progressions "A learning progression is a carefully sequenced set of building blocks that students must master en route to mastering a more distant curricular aim. These building blocks consist of subskills and bodies of enabling knowledge" (Popham, 2007, p. 83)

  6. Backmapping • “The process of analyzing desired student outcomes (or learning objectives) to identify prerequisite skills and knowledge; starting with what students will know and be able to do at the end of a course and drilling down to what must be learned first, in order for the outcome to be successful.” • teachingtoday.glencoe.com/glossary

  7. Activity: Mapping Out the Standards • Problem/ challenge: With current students, we must always keep in mind that their understanding depends on previous experiences and current experiences then set the stage for future learning. Please: • (Re)join your small group • Read your instructions • Discuss for 10 minutes

  8. References Popham, W. J. (2007). The lowdown on learning progressions. Educational Leadership, 64, 83-4. teachingtoday.glencoe.com/glossary

  9. Prekindergarten: Spatial Sense • STANDARD STATEMENT: Demonstrate understanding of the relative positions of objects with terms such as in/on/under, up/down, inside/outside, above/ below, beside/between, in front of/ behind, and next to. • EXAMPLES • Says “My toy fell under the table,” or “I left my ball outside,” or “Sit down beside me.” • Navigates an obstacle course when the teacher says “go under the bridge” and then “go around the climber.” • Says, “My dad keeps the car inside the garage.” • Builds simple but meaningful “maps” using blocks and toys such as trees, cars, houses, and describes relative positions. (e.g., “The truck is beside the road.” “The dog is behind the house.”).

  10. Pre-Kindergarten: Identify and Describe Shapes STANDARD STATEMENT: Understand and use names of shapes when identifying objects. • EXAMPLES • Recognizes and names basic two-dimensional shapes, including, circle, square, rectangle, and triangle. • While playing a game of shape bingo, identify different shapes that are called out loud. • While playing with blocks, asks a friend, “Can I have another square block?” STANDARD STATEMENT: Names three-dimensional objects using informal, descriptive vocabulary. • EXAMPLES • Refers to a cube as a “box.” • Calls the cone “ice cream cone.” • Calls a sphere a “ball.”

  11. Pre-Kindergarten: Analyze, Compare and Create Shapes STANDARD STATEMENT: Compare two-dimensional shapes, in different sizes and orientations, using informal language. • EXAMPLES • Locates two-dimensional geometric shapes of differing size and orientation in the classroom environment. • Answers questions like “How do you know the shape is a triangle?” by describing the number of “lines” and “points.” • Identifies two-dimensional shapes by feel in a “feely box.” • Identifies a triangle whether sitting on its base or on its point. STANDARD STATEMENT: Create shapes during play by building, drawing, etc. • EXAMPLES • Draws a picture of his house using some basic shapes such as a rectangle for the building and a triangle for the roof and a circle for the sun. • Creates symmetrical block structures. • Draws shapes from memory. STANDARD STATEMENT: Combine simple shapes to form larger shapes. • EXAMPLES • Uses blocks to create larger shape structures. • Manipulates pattern blocks to form larger shapes. • Describes the shapes used to create new shapes.

  12. CCSS Kindergarten • Identify and describe shapes. • CCSS.Math.Content.K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. • CCSS.Math.Content.K.G.A.2 Correctly name shapes regardless of their orientations or overall size. • CCSS.Math.Content.K.G.A.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). • Analyze, compare, create, and compose shapes. • CCSS.Math.Content.K.G.B.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). • CCSS.Math.Content.K.G.B.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. • CCSS.Math.Content.K.G.B.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

  13. CCSS 1st Grade • CCSS.Math.Content.1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. • CCSS.Math.Content.1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape1. • CCSS.Math.Content.1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

  14. CCSS 2nd Grade • Reason with shapes and their attributes. • CCSS.Math.Content.2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. • CCSS.Math.Content.2.G.A.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. • CCSS.Math.Content.2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

  15. What’s New? • Participant responses • Connections between responses and implementation • Changes/ shifts not merely in terms of phrasings of standards & vocabulary but in terms of thinking about implementation. From ODE: • Coherence • Within & across grades • Focus: • Key ideas clearly identified • Expectation of deep rather than broad learning • Rigor: • Deep conceptual understanding • Skills and fluency • Application

  16. What’s New • Resources and Planning • www.illustrativemathematics.org • http://ohiorc.org/standards/commoncore/mathematics/ • K and up standards listed; • Activities linked to standards • Others you’ve found?

  17. Resources: Illustrative Mathematics.org

  18. Select a grade…

  19. Select a domain (like Geometry) …

  20. Look for Illustrations for Standards or Clusters of Standards Look for “see Illustrations”

  21. Select a task…

  22. View the task

  23. Conclusions • What would you share with a fellow educator? • What are you remaining concerns about implementing the CCSS in K-2?

  24. Our contact info: • Lucia M. Flevares • flevares.1@osu.edu • Jamie R. Schiff • schiff.64@osu.edu

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