Possible CCGPS standards to relate to Taxicab Geometry
Analytic Geometry
MCC9-12.G.GPE.1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
MCC9-12.G.GPE.2 - Derive the equation of a parabola given a focus and directrix.
MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graphy, by hand in simple cases and using technology for more complicated cases.
MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Advanced Algebra
MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
MCC9-12.A.CED. 3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
MCC9-12.G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Pre-Calculus
MCC9-12.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.
Advanced Mathematical Decision Making
MAMDMG1 - Students will create and use two- and three-dimensional representations of authentic situations
MCC9-12.G.GPE.1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
MCC9-12.G.GPE.2 - Derive the equation of a parabola given a focus and directrix.
MCC9-12.F.IF.7 - Graph functions expressed symbolically and show key features of the graphy, by hand in simple cases and using technology for more complicated cases.
MCC9-12.F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Advanced Algebra
MCC9-12.A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
MCC9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
MCC9-12.A.CED. 3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
MCC9-12.A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
MCC9-12.G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Pre-Calculus
MCC9-12.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.
Advanced Mathematical Decision Making
MAMDMG1 - Students will create and use two- and three-dimensional representations of authentic situations