An informal limit argument for the circumference or area of a circle is performed by fitting n-gons of increasing number of sides into a circle to approximate the circumference or area of the circle. Example: Dissect a circle into increasingly more the slices into a shape “pizza slices”, arranging that approximates a parallelogram; find the area of the parallelogram to approximate the area of the circle (height of the parallelogram = r, base of the parallelogram = G.GMD.3 Use volume formulas for See the skills and knowledge Note: This is an overarching standard that has cylinders, pyramids, cones, and that are stated in the applications in multiple units spheres to solve Standard. Students should solve real-world application problems.★(additional) problems using volume formulas for cylinders, pyramids, cones and spheres. (see resources) G.GMD.4 Identify the shapes of Ability to make connections Use hands-on kits or computer generated graphics cross-sections of three- between two-dimensional to demonstrate cross-sections. Have students objects, and identify figures such as rectangles, predict and experiment with other two-dimensional three-dimensional objects generated squares, circles, and shapes. by rotations of two-dimensional triangles and Use an old fashioned carousel slide holder as a objects. *(additional) figures such as base. Prepare cardboard cut-outs of the cylinders, spheres, pyramids shapes to be rotated. Add a tab to and cones each base to insert in the carousel. Rotate the carousel to demonstrate the various 3-D results.
An informal limit argument for the circumference or area of a circle is performed by fitting n-gons of increasing number of sides into a circle to approximate the circumference or area of the circle. Example: Dissect a circle into increasingly more “pizza slices”, arranging the slices into a shape that approximates a parallelogram; find the area of the parallelogram to approximate the area of the circle (height of the parallelogram = r, base of the parallelogram = G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★(additional) See the skills and knowledge that are stated in the Standard. Note: This is an overarching standard that has applications in multiple units Students should solve real-world application problems using volume formulas for cylinders, pyramids, cones and spheres. (see resources) G.GMD.4 Identify the shapes of cross-sections of three- objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. *(additional) Ability to make connections between two-dimensional figures such as rectangles, squares, circles, and triangles and figures such as cylinders, spheres, pyramids and cones Use hands-on kits or computer generated graphics to demonstrate cross-sections. Have students predict and experiment with other two-dimensional shapes. Use an old fashioned carousel slide holder as a base. Prepare cardboard cut-outs of the shapes to be rotated. Add a tab to each base to insert in the carousel. Rotate the carousel to demonstrate the various 3-D results.
Geometry_U3_UP_Extending_to_Three_Dimensions_12_10.docx