Cluster Standard Practices Cluster Note: Informal arguments for area and Make sense of volume formulas can make use of the way in which area and problems and volume scale under similarity transformations: when one persevere in solving figure in the plane results from another by applying a them. similarity transformation with scale factor k, its area is times the area of the first. Similarly, volumes of solid figures scale Reason abstractly by under a similarity transformation with scale factor k. and quantitatively. G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, Construct viable pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. arguments and critique the reasoning of others. Essential Skills and Knowledge Model with See the skills and knowledge that are stated in the Explain volume mathematics. Standard. formulas and use them to solve Use appropriate problems. tools G.GMD.3 Use volume formulas for cylinders, pyramids, cones, strategically. and spheres to solve problems.★ Attend to precision. Note: This is an overarching standard that has applications in multiple units Look for and make Essential Skills and Knowledge use of structure. See the skills and knowledge that are stated in the Standard. Look for and express regularity in repeated reasoning. Visualize the relation G.GMD.4 Identify the shapes of two-dimensional cross-sections Make sense of between two of three dimensional objects, and identify three-dimensional problems and objects generated by rotations of two-dimensional objects. persevere in solving and them. dimensional Essential Skills and Knowledge objects. Ability to make connections between Reason abstractly
Cluster Standard Practices Explain volume formulas and use them to solve problems. Cluster Note: Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is times the area of the first. Similarly, volumes of solid figures scale by under a similarity transformation with scale factor k. G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. Essential Skills and Knowledge See the skills and knowledge that are stated in the Standard. G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★ Note: This is an overarching standard that has applications in multiple units Essential Skills and Knowledge See the skills and knowledge that are stated in the Standard. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Visualize the relation between two and objects. G.GMD.4 Identify the shapes of two-dimensional cross-sections of three dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Essential Skills and Knowledge Ability to make connections between Make sense of problems and persevere in solving them. Reason abstractly dimensional
GeometryFramework.docx