Geometric Explorations with Linear Equations
![Picture](/uploads/3/1/6/0/31605851/2336005.png?357)
Materials Needed
Access to Geometer's Sketchpad Software, computer lab, paper, pencil.
Sequence of Lesson
Warm-up: Have the class think about the types of functions that they have looked at so far. If possible, have them open up some of their old GSP work. Now ask them what would happen if you placed a vertical line somewhere on the graph. Would there be any geometric shapes created? Ask that they put down one, two, or three vertical lines on one of their graphs, and ask they they look to see how many shapes they can discover. The shapes the students will be looking for are those bounded by the function, the vertical lines the students place, and the x-axis. They are likely to find some combination of triangles, rectangles, and trapezoids. Have them color in the shapes that they find.
See the figure.
After giving them a few minutes to color in their polygons, ask them to see if they can find the area!
Description: Now, have the students recall how to find areas of shapes. Are they able to find the areas of some of the shapes that they made on their graph? Assist the students who are having a hard time getting started. (Note that this subject is addressed in our introductory video)
Post-Activity: Have the class discuss their what seemed to cause each type of shape to occur and the class’s methods for solving the polygons they made in their graphs. For example, rectangles only occur in constant functions. Three types of shapes should have come up, triangles, trapezoids and squares. A discussion of the different ways to look at finding the area of the trapezoid might come up.
Access to Geometer's Sketchpad Software, computer lab, paper, pencil.
Sequence of Lesson
Warm-up: Have the class think about the types of functions that they have looked at so far. If possible, have them open up some of their old GSP work. Now ask them what would happen if you placed a vertical line somewhere on the graph. Would there be any geometric shapes created? Ask that they put down one, two, or three vertical lines on one of their graphs, and ask they they look to see how many shapes they can discover. The shapes the students will be looking for are those bounded by the function, the vertical lines the students place, and the x-axis. They are likely to find some combination of triangles, rectangles, and trapezoids. Have them color in the shapes that they find.
See the figure.
After giving them a few minutes to color in their polygons, ask them to see if they can find the area!
Description: Now, have the students recall how to find areas of shapes. Are they able to find the areas of some of the shapes that they made on their graph? Assist the students who are having a hard time getting started. (Note that this subject is addressed in our introductory video)
Post-Activity: Have the class discuss their what seemed to cause each type of shape to occur and the class’s methods for solving the polygons they made in their graphs. For example, rectangles only occur in constant functions. Three types of shapes should have come up, triangles, trapezoids and squares. A discussion of the different ways to look at finding the area of the trapezoid might come up.