The interactive figure in this activity can help students understand the Pythagorean relationship and gives them experience with transformations that preserve area but not shape. 6.6 Comparing Properties of the Mean and the Median through the use of Technology Using interactive software, students can compare and contrast properties of measures of center, specifically these tasks illustrate how changes in data values influence the mean and median. When students change the data values, the interactive figure immediately displays the mean and median of the new data set. Experimenting with this software helps students compare the utility of the mean and the median as measures of center for different data sets, as discussed in the Data Analysis and Probability Standard . 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 the first 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. This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. These activities allow high school students to study modeling in greater depth, as described in the Algebra Standard . In the first part, Modeling the Situation, an interactive environment is used to become familiar with the parameters involved and the range of results that can be obtained.