their knowledge of number systems to the system of vectors.
Try the following:
High school students should not only explore more
formally the properties of number systems that they have already
encountered in the lower grades but also experience how those properties
extend into new systems, such as vectors. (See the Number and
Operations Standard.) Building on the experiences students had with a
single vector in the first part, this part gives them a second vector,
representing the velocity and direction of the wind, and asks them to
consider how the two vectors combine to affect the movement of the
plane. The third task allows a more formal look at vector
addition by showing the vector representing the sum of the two velocity
vectors. Students can see how changes in one of the summands affect the
sum; for example, as the angle of the red vector is increased, the angle
of the sum vector also increases. However, the relationship between the
summands and the sum is not easily seen unless the summands have the
same angle measure (in which case the lengths are added) or inverse
measures (in which case the lengths are subtracted). In the
fourth task, students can notice that vectors with opposite directions
and the same magnitude cancel each other out. In other words, when
"added," they result in the identity, implying that they are inverses of
each other. Likewise, students should note in the fifth task that if
the values of the two vectors are interchanged, the same sum results.
Thus, vector addition is commutative.
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