Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Understanding Shape in Kindergarten and Grade 1 Common Core Leadership in Mathematics Tuesday, October 2012 This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,

CCSSM and Shape

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Geometry in Elementary Important Goals for Elementary Geometry: Geometric shapes, their components (e.g., sides, angles, faces), their properties, and their categorization based on those properties Composing and decomposing geometric shapes Spatial relations and spatial structuring

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, We are learning to … define triangles. understand student expectations of shape as defined by the standards in kindergarten to grade 1. We will be successful when we can … explain the mathematical content and language in K.G.2, K.G.4, and 1.G.1 and provide examples of the mathematics and language. Learning Intentions and Success Criteria

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standards for Mathematical Practice MP7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Predict what this standard means in the study of shape.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Getting Started With Triangles

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, What is a Triangle? On the 3 x 5 card As you think about shape, write a definition of a triangle.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Considering Triangle Characteristics Turn the card over.  Draw a triangle.  Draw another triangle that is different from the triangle you just drew.  Draw a third triangle that, again, is different from the triangles you just drew.  Finally, draw a fourth triangle that is different than any of the previous triangles.  What is different about the triangles? What is similar?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, CCSSM: Geometry Progression

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, CCSSM and Triangles As you think about student learning, consider levels of student reasoning and how students progress through levels of geometric understanding. K-6 Geometry Progression Document Read all of page 2 and stop when you come to page 3, Composing and Decomposing.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Levels of Geometric Thinking Visual/syncretic: Recognize shapes in ways that are visual, e.g., a rectangle “looks like a door.” Descriptive: Perceive properties of shapes, e.g., a rectangle has four sides, all its sides are straight, opposite sides have equal length. Analytic: Characterize shapes by their properties, e.g., a rectangle has opposite sides of equal length and four right angles. Abstract: Understand that a rectangle is a parallelogram because it has all the properties of parallelograms.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Geometry Research “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

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Tricky Triangles

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Tricky Triangles Goal…sort the shapes into 2 groups. “Triangles” and “Not Triangles” Process… Pull out a card (without looking). Show it to the table group. Explain why it is or isn’t a triangle. Pass the envelope… to the next person and repeat the process until all the shapes are sorted. Group Discussion… What defines a triangle?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Tricky Triangles Considering this activity, explain which triangles are tricky?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, CCSSM and Triangles As you are reading the Progression Document, be able to articulate the expectations for learning. K-6 Geometry Progression Document Read: Kindergarten - page 6 Grade 1 - page 8 (first paragraph)

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standards K.G.2, K.G.4, and 1.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.2. Correctly name shapes regardless of their orientations or overall size. Analyze, compare, create, and compose shapes. K.G.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). Reason with shapes and their attributes. 1.G.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.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standards K.G.2, K.G.4, and 1.G.1 Individually –Read the standards. –Highlight key words and key phrases. –Use your worksheet to draw a representation for each standard. Pairs –Compare highlighted ideas.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Big Ideas Kindergarten Two Perspectives on Space 1.The shapes of objects. 2.The relative position of objects. Grade 1 Differentiate between geometrically defining attributes (e.g. “hexagons have six straight sides”) and nondefining attributes (e.g. color, overall size and orientation).

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, MP7: Look for and make use of structure. Reflecting back on you initial thoughts about MP7, describe ways that the Tricky Triangle task exemplifies looking for structure?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Revisiting Your Triangle Definition Individually, review and revise your definition of a triangle. As a group, share definitions of triangles.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, We are learning to … define triangles. understand student expectations of shape as defined by the standards in kindergarten to grade 1. We will be successful when we can … explain the mathematical content and language in K.G.2, K.G.4, and 1.G.1 and provide examples of the mathematics and language. Learning Intentions and Success Criteria

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, CCLM Website