Learning about Properties of Vectors and Vector Sums Using Dynamic Software: Components of a Vector

 Components of a Vector

This example illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties, as described in the Number and Operations Standard. Students manipulate a velocity vector to control the movement of an object in a gamelike setting. In this part, Components of a Vector, students will develop an understanding that vectors are composed of both magnitude and direction. In the second part, Sums of Vectors and Their Properties, students extend their knowledge of number systems to the system of vectors.

Your task is to explore how characteristics of the vector affect the movement of the car as you use the vector to "drive" the car around without crashing into the walls. Adjust the vector by dragging either endpoint, or move it by dragging the dot on the vector. How do your adjustments of the vector affect the numbers at the bottom of the screen? Now start the car by clicking on the "Start Car" button. Try to drive the car around the box without crashing. As you do this, consider the following questions:

• How do the numbers for direction and magnitude correspond to the appearance of the vector?

• How do those numbers correspond to the movement of the car?

• What happens when you move the vector into a new position using its midpoint?

• How can you make the car stop? What are the values of the vector's characteristics when this happens? What might this situation be called?

Now click the box to "Show Cyclone." Your goal is to chase after and attempt to "catch" the cyclone without crashing into the walls. Try to catch the cyclone by controlling the car's movement with the vector. Then reset the game and try to catch the cyclone using only the sliders at the bottom of the screen, without directly manipulating the vector.