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Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones MA.7.G.2.1 Block 33

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Learning Outcomes Understanding of Volume Find Surface Areas and Volumes for Prisms, Cylinders, Pyramids, Cones, and Spheres. Formulate possible formulas for volume for the 3-dimensional figures mentioned before Ana EscuderTeacher Quality Grant2

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Vocabulary needed polyhedron, edge, vertex, tetrahedron, regular polyhedron, bases, lateral faces lateral edges, prism, oblique prism, altitude, height, pyramid, height, cross- section sphere, great circle, cylinder, radius, right cylinder, oblique cylinder, altitude, cone Ana EscuderTeacher Quality Grant3

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GeoGebra files needed Rectangular_prism.zip Right_triangular_prism.zip Triangular_prism.zip Rectangula_pyramid.zip Triangular_pyramid.zip Cone_worksheets.ggb Cylinder_worksheet.ggb Sphere.zip Ana EscuderTeacher Quality Grant4

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Procedure Discuss the formula used to find the volume of a prism. Talk about what the "B" means in relation to the formula: area of the base, which is a rectangle. Discuss the dimensions needed in order to calculate volume: length and width of base and height of prism. Ana EscuderTeacher Quality Grant5

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Look at the GeoGebra File for a Rectangular Prism. Calculate the volume and surface area Changes to dimensions can be done easily by manipulating the sliders to create hundreds of examples. Formulas and solutions can be shown or hidden on the worksheets. Experiment how the volume and surface area change as you proportionately change the dimensions, using both an enlargement and a reduction. Is there a relationship to scale factor? If so, what is it? The same steps can be used for the rest of the files Ana EscuderTeacher Quality Grant6

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National Library of Virtual Manipulatives On the web, go to: – http://nlvm.usu.edu http://nlvm.usu.edu Click on the square: – 6-8 grade, Geometry Select the applet: How High – http://nlvm.usu.edu/en/nav/frames_asid_ 275_g_3_t_3.html?from=category_g_3_t_3. html Ana EscuderTeacher Quality Grant7

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How would you solve these problems? Ana EscuderTeacher Quality Grant8

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