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Coordinates & Vectors Unit
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"A mathematician is a machine for turning coffee into theorems."--Paul Erdös Worth Being Familiar With
Commutativity and associativity of vector addition, with the ability to draw examples showing both properties at work.
Similarly, a geometrical interpretation of both scalar multiplication and the associativity of scalar multiplication. Important to Know and Do
Both pictorial and component-based vector addition and scalar multiplication (see above). Given a coordinate grid, students should be able to draw more than one representation of a given vector, and given a representation, write it in Cartesian or polar component form. Students should also be able to construct vectors when given information in other forms or interpret their meanings, e.g. "The Red Queen walks northwest at 5 m/s" or "The White Knight moved from a2 to c3." "Enduring" Understanding
Where vectors can be used and what they can represent. Examples from physics abound, and students should be able to give both appropriate and inappropriate (or "overkill") uses of vectors. In the Tweedledee and Tweedledum word problem (see Essential, Unit & Entry-Level Questions) vectors can certainly be used, but the problem can be solved solely with scalars. |
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