Technology objective: After an introduction to Geometer's Sketch Pad, students can expand their knowledge by exploring area and perimeter in rectangles using the software.
Lesson: Students should be given the introduction to the Geometer's Sketch Pad and feel comfortable using the software. After this, have them go to NEW SKETCH. Ask the students to create what they think to be a rectangle. How can they be sure it is a rectangle? Have students observe other students sketches to see how the rectangles compare.
Have the students go to NEW SKETCH again. They will need to just create a quadrilateral first by connecting four line segments. Now is the time to have students define, in their own words, classifies a quadrilateral as being a rectangle. Have them label all the vertices.
Next, have them measure each angle (which they have been taught to do in introduction). In the discussion, the students should have decided a rectangle has to have four right angles. Have them create a quadrilateral with four right angles. Discuss with the class is that the only qualification for being a rectangle. Does anyone have a quadrilateral with four right angles that is not a rectangle? Maybe have them create a quadrilateral with those conditions.
It should now be obvious to the class that in order for a quadrilateral to be classified as a rectangle opposite sides must be equal. Ask the class how we could check to see if opposite sides are equal. I even let them explore the menus to see if they can find a way to measure the sides.
Now is the time to discuss how to measure a line segment. Have them highlight the line segment they wish to measure. Once they have highlighted one line segment, have them go to the MEASURE menu and drag down to LENGTH. This will tell them the length of the line segment. Have them repeat this procedure for the remaining sides of the rectangle. Ask the class if they had a true rectangle. If they did not, have them move their quadrilateral around until opposite sides are equal.
You may want to spend some time having students compare their neighbors "sketches." How do they compare? Are the measurements the same? It may be helpful to show the class how to change the precision of the measurements and how to change the unit of measurement. This can be done by going to the DISPLAY menu and dragging down to PREFERENCES. Have the class change each precision to tenths and the measurement to centimeters.
Next, have the students highlight each vertex of their rectangle. Have them go to the CONSTRUCT menu and drag down to POLYGON INTERIOR. This will cause the whole rectangle to be highlighted. Now have the students go to the MEASURE menu to find the area and perimeter. Ask the students to look at the results and see if they can remember how to find the area of a rectangle and how to find the perimeter of a rectangle. Have the class change the size of the rectangle and look at the resulting area and perimeter. Have the students record the measurements of the sides of the rectangle and the resulting area and perimeters of those rectangles in their journals - about five different rectangles.
Reinforcement: Have the students explain in their own words how to find the area of a rectangle and the perimeter of a rectangle in their journals. Also have them discuss some real life situations where they would use area and perimeter.
Assignment: Students can work on the exploration in their textbook on page 109 (1-6). This assignment will have the students find a given area and create the greatest possible perimeter for each rectangle.