K-6, Geometry Focus Area 2: Decompose & Compose Focus Area 3: Spatial Structuring Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success Wednesday, July 20, 2016 2:15 p.m. – 4:00 p.m.

Learning Intentions and Success Criteria We are learning about The 2nd and 3rd areas of focus for Geometry. Spatial structuring Decomposing and composing shapes. We will be successful when we can… Identify activities that focus on spatial structuring and decomposing and composing shapes.

K-6 Geometry Progressions Read 2 sections of the K-6 Geometry Progressions First, read the Overview of Composing and Decomposing – p.3 – p4. Stop at Spatial Structuring. Continue reading on p.8 Grade 1. Starting with paragraphs 2, 3, and 4. What is the happening in the early grades around composing and decomposing shapes?

1.G.1 and 1.G.2 Reason with shapes and their attributes. 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. 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 shape.4 4Students do not need to learn formal names such as “right rectangular prism.”

How many different ways are there to cover? Use pattern blocks to fill the open patterns. What thinking did you engage in as you worked to cover each pattern with different blocks? They learn to substitute one composite shape for another congruent composite composed of different parts. P. 8 What would you be monitoring for in order to know if students are mastering this skill?

Building A Wall: What is he doing? What does he understand?

What mathematical reasoning is in play? What did we see as we watched the student work? What did we hear from the student? What instructional moves were made to support a focused discussion about the mathematics? This provides an opportunity to connect to the classification of shapes. It also connects to the sentence on pg. 8 about developing sophistication of language based on attributes and properties. What if we didn’t ask those questions. Stop playing after student describes the wall. What is the purpose of this activity? What should students be talking about as they work together? What do you think the student understands about why his building a wall? Continue to play the video. What new information did we learn about the student? What instructional moves were made to leverage the matheamtics? How is this student working to meet the standard 1.G.1 and 1.G. 2

Compose and Decompose What experiences are you prioritizing next year in your classroom that will support the idea of composing and decomposing? As students work ….. What might you be looking for? What might you be listening for? Use the same notebook page as the van Hiele reflections.

Focus Area 3: Spatial Structuring Read the first two paragraphs of Spatial Structuring and Spatial Relations in the K-6 Geometry Progressions, p. 4-5. Share your understanding of Spatial Structuring with your shoulder partner. Provide examples of it in your grade level.

Exploring Spatial Structuring First, put the rectangles in order from smallest to largest. Use tiles to justify the order of the rectangles. Adjust the order of the rectangles based on your findings with the tiles. How did you engage in spatial structuring to determine the order of your rectangles? B and E are about the same… Structure of C vs B

Reason with shapes and their attributes. 2. G. 2 Reason with shapes and their attributes. 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. What mathematical ideas are addressed in this standard? Read Grade 2 Progressions: Page 11 Paragraphs 2 and 3. Measurement is one idea that is addressed in this standard. The process of identifying an attribute, finding a unit and iterating a unit is acutally the process of measuring. Do you have to count to identify which shape is larger?” Could fill one and move over to cover another shape or – compare the fillings of one shape onto another shape.

Structuring Task: Student Work

Spatial Structuring: Student Work Individually study the student work samples. With a partner discuss, What misunderstandings and understands can you identify in the students’ work? What is your evidence for these misunderstandings and understandings?

Classification of Shapes Spatial Visualization Essential Understandings of Geometry Classification of Shapes Features or properties of geometric shapes can be analyzed and described to define and refine classification schemes with growing precision. Spatial Visualization Spatial relationships and spatial structuring involves developing, attending to, and learning how to work with imagery, as well as to specify locations. Geometry is the branch of mathematics that addresses spatial sense and geometric reasoning. Transformations Transformation involves working with geometric phenomena in ways that build on spatial intuition by explaining what does and does not change when moving and altering the objects and the space that they occupy.

PRR: Spatial Structuring In your 3-5 Essential Understandings book… Read about Spatial Structuring on Pages 104 – 110. What did you learn about the importance of spatial structuring? What did you learn about Isaac? How does this information impact how your work with students?

Learning Intentions and Success Criteria We are learning about The 2nd and 3rd areas of focus for Geometry. Spatial structuring Decomposing and composing shapes. We will be successful when we can… Identify activities that focus on spatial structuring and decomposing and composing shapes.

Core Mathematics Partnership Project Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.