EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS (GPE) Translate between the geometric description and the equation for a conic section. 6.G.GPE.1 Derive the equation of a circle of center CC.G.GPE.1 Using and radius using the Pythagorean Theorem; CAD/CAM complete the square to find the center and software to radius of a circle given by an equation. design a product 6.G.GPE.2 Derive the equation of a parabola given a CC.G.GPE.2 Reading scientific focus and directrix. diagrams 6.G.GPE.3 (+) Derive the equations of ellipses and CC.G.GPE.3 Using CAD/CAM hyperbolas given the foci, using the fact that software to design the sum or difference of distances from the foci a product is constant. Use coordinates to prove simple geometric theorems algebraically. 6.G.GPE.4 Use coordinates to prove simple geometric CC.G.GPE.4 Proving or theorems algebraically. disproving that a figure defined by four given points in the coordinate plane is a rectangle; proving or disproving that the point (1, lies √3) on the circle centered at the origin and containing the point (0, 2) GEOMETRIC MEASUREMENT AND DIMENSION (GMD) Explain volume formulas and use them to problems. 6.G.GMD.1 Give an informal argument for the formulas for CC.G.GMD.1 Building and the circumference of a circle, area of a circle, measuring volume of a cylinder, pyramid, and cone. structures and Use dissection arguments, Cavalieri’s principle, and objects informal limit arguments. 6.G.GMD.2 (+) Give an informal argument Cavalieri’s CC.G.GMD.2 Building and principle for the formulas for the volume of a measuring sphere and other solid figures. structures and objects Visualize relationships between two-dimensional and three-dimensional objects.
EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS (GPE) Translate between the geometric description and the equation for a conic section. 6.G.GPE.1 Derive the equation of a circle of center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CC.G.GPE.1 Using CAD/CAM software to design a product 6.G.GPE.2 Derive the equation of a parabola given a focus and directrix. CC.G.GPE.2 Reading scientific diagrams 6.G.GPE.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. CC.G.GPE.3 Using CAD/CAM software to design a product Use coordinates to prove simple geometric theorems algebraically. 6.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. CC.G.GPE.4 Proving or disproving that a figure defined by four given points in the coordinate plane is a rectangle; proving or disproving that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2) GEOMETRIC MEASUREMENT AND DIMENSION (GMD) Explain volume formulas and use them to problems. 6.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. CC.G.GMD.1 Building and measuring structures and objects 6.G.GMD.2 (+) Give an informal argument Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. CC.G.GMD.2 Building and measuring structures and objects Visualize relationships between two-dimensional and three-dimensional objects.