**Title:** Learning about Properties of Vectors and Vector Sums Using Dynamic Software

**Description:**
In this two-lesson unit, from Illuminations, students manipulate a velocity vector to control the movement of an object in a gamelike setting. They develop an understanding that vectors are composed of both magnitude and direction, and extend their knowledge of number systems to the system of vectors.

**Standard(s): **

[MA2013] PRE (9-12) 5: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., **v**, |**v**|, ||**v**||, v). [N-VM1]

[MA2013] PRE (9-12) 7: (+) Solve problems involving velocity and other quantities that can be represented by vectors. [N-VM3]

[MA2013] PRE (9-12) 8: (+) Add and subtract vectors. [N-VM4]

[MA2013] PRE (9-12) 9: (+) Multiply a vector by a scalar. [N-VM5]

[MA2013] AM1 (9-12) 1: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., **v**, | **v** |, | |**v**| |), including the use of eigen-values and eigen-vectors. [N-VM1] (Alabama)

[MA2013] AM1 (9-12) 2: (+) Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). [N-VM3] (Alabama)

[MA2013] AM1 (9-12) 3: (+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. [N-VM4a] (Alabama)

[MA2013] AM1 (9-12) 4: (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [N-VM4b] (Alabama)

[MA2013] AM1 (9-12) 5: (+) Understand vector subtraction **v** - **w** as **v** + (-**w**), where (-**w**) is the additive inverse of **w**, with the same magnitude as **w** and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise, including vectors in complex vector spaces. [N-VM4c] (Alabama)