Objective:
Students will reinforce their knowledge of transformations through active participation in "transformations of the classroom".
Discussion:
To conduct this activity, desks would be arranged in rows with each row having an equal number of desks (if there is not the right number of desks in the class to accomplish this, mark the spots where the desks would appear). If your room is not arranged in rows you can modify this activity to achieve the same results. A number will be placed at the four corners of each desk as in figure 1 to create a grid. Students will also have a copy of this grid and a list of transformations. Students will be asked to take on the identity of objects (or points) in a portion of a plane. Guided by the instructor, they will determine how the different transformations would affect their location or direction in the plane.
Activities:
1. Imagine you are an object in a section of the two abovedimensional plane. In whose desk would you be if you (and only you) were translated by the vector 36->29? Would you still be sitting by the same person?
2. Using this same vector, where would you be sitting if everyone were translated? What is the effect of this translation on the people at the front of each row? Would anyone be sitting in the desks at the back of each row? Why or why not?
3. What would happen if everyone were translated by the vector 42->1?
4. If our line of reflection contains the points 4 and 29, in whose desk would you be located if Anita's row and Glen's row were reflected about this line? Who would be right side up and who would be upside down and which direction would they be facing? What would be the result if everyone were reflected about this line?
5. If our line of reflection contains the points 22 and 28, where would you be located if everyone were reflected about this line? Would you be right side up or upside down and which direction would you be facing? Would everyone be located inside the given portion of the plane.
6. Using the point marked 26 as the center of rotation, what would happen if we rotated Amy, Chris, Carla and Jonathan 90 degrees? Where would they be sitting? In which direction would they be facing?
7. What would happen if 32 is our center of rotation and the whole class is rotated 360 degrees? Which direction would you be facing?
8. Notice our desks form a rectangle of length 6 desks, height 5 desks and area 30 desks squared. Using the point marked center as the center of dilation, what kind of object would be formed if our rectangle were dilated by a ratio of 1 to 2? Describe its proportions. What would happen to us if we were also dilated by this same ratio?