Ginny Bohme Sam Buhler Linda Mannhardt 11/24/2018 Geometry Grade 6/7 Ginny Bohme Sam Buhler Linda Mannhardt Audience: grade 6-8 math teachers, special education teachers, curriculum directors , building administrators Teachers expected to already to have a working knowledge of the mathematical practice standards

Grade 6 Solve real-world and mathematical problems involving area, surface area, and volume. Cluster heading for the standards this PD highlights.

11/24/2018 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Ask teachers to highlight words or phrases in standard that may indicate what students will be able to do and understand Emphasize composing and decomposing shapes Authors' Name(s)

11/24/2018 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Ask teachers to highlight words or phrases in standard that may indicate what students will be able to do and understand Authors' Name(s)

Pause and Reflect Talk with your elbow partner 11/24/2018 Pause and Reflect Talk with your elbow partner What do you think the standard is expecting of students? Authors' Name(s)

Let’s Explore Begin the task on your own for 2-3 minutes 11/24/2018 Let’s Explore Begin the task on your own for 2-3 minutes Compare with your table mates On the chart paper record your group’s solution and thinking Be ready to present your solution Materials needed: Little Bo Peep task sheet, graph paper, pencils, rulers, chart paper, markers Questions to consider: what if students connected points in a convex polygon Authors' Name(s)

Pause and Reflect What skills were necessary to complete the task? 11/24/2018 Pause and Reflect What skills were necessary to complete the task? How did the various solutions relate to one another? How did the task address the standards? Which mathematical practices were evident? Have participants record their responses on the reflection sheet in their packet Questions to consider: what if students connected points in a way that doesn’t form a polygon Authors' Name(s)

11/24/2018 Considerations Task can address more than one standard in a domain or from multiple domains. Task should allow for multiple entry points. Pay attention to the mathematical practices in the student’s work. Authors' Name(s)

Grade 7 Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. Cube In grade 6 students have had experiences with 3-D shapes through nets and volume activites. Rectangular Prism

Slicing a Solid Describe the resulting face shape that will result from slicing a solid rectangular prism: parallel to the base perpendicular to the base at an angle through the prism Explain your thinking base Cubes, computers(optional), activity sheet, www.learner.org/courses/learningmath/geometry/session9/part_c/index.html May need to discuss end face. Base Cuts made parallel will take the shape of the base; cuts made perpendicular will take the shape of the lateral (side) face. Cuts made at an angle through the right rectangular prism will produce a parallelogram.

What’s Possible? Where could you slice a solid rectangular prism to create a triangle? Explain your thinking Could slice a cube to create a rectangle that is not a square?

Time to Explore Is it possible to create other polygons from slicing a cube? What are they? Are there any polygons you would not be able to create? How do you know? www.learner.org/courses/learningmath/geometry/session9/part_c/index.html www.wou.edu/~burtonl/flash/SandBox.html This applet could also be used for more advanced students

Classroom Implementation What would be your next step in the lesson? What tools would you make available to the students?

Which standard(s) in the 7th grade domain of Geometry does this address? Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

11/24/2018 Thank you!