Examples, Left Poster

The three examples illustrated on this poster are: Linear Combinations of Vectors, Properties of Summation, and Arc Length Exercise. Each of these interactive Flash programs are used in my Precalculus II class.

When students run the Linear Combination of Vectors SCO, they get 3 random vectors, one of which is an integer linear combination of the other two vectors. Then the student is asked to duplicate and if needed negate the other two vectors and put them in position to add up to the third vector. This program reinforces the idea of geometric vector addition, which is a concept that students sometimes struggle with when they are first introduced to vectors.

Properties of Summation, helps reinforce the idea of algebraic properties that work with summation notation. Right now, this program focuses on assessing understanding rather than teaching the idea. Someday, I plan to add an instructional phase to the program where students can explore and discover the properties for themselves.

After students learn about the definition of a radian, they are ready to calculate the arc length of a circular sector since they have already learned about the area of a circle. It is a challenge for most students to put the concepts of area, proportion, and radians together to figure the arc length of a circular sector when they are given the angle in degrees and the area of that sector. Meeting that challenge helps them master critical concepts that are needed to understand radian angles.

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