Ratios of
Perimeter and Area
Introduction Task Process Resources Evaluation Conclusion
Introduction
How are the perimeters, areas,
and side lengths of similar rectangles related? Will other polygons have
similarities as well? What about the
volumes?
Task
In this web quest, you will link to various sites
that contain special interactive lessons.
As you manipulate these programs, you will record the data and reach
conclusions from that data.
Process
1. Print out these instructions on a separate
piece of paper. Click on this site and scroll down to the box with the
blue and green rectangles. To change the size and shape of the green rectangle,
grab and drag one of the red vertices (corners). Notice that the blue and green
rectangles are and remain similar (congruent angles, proportional sides). Notice the scale factor of 1.5. What does that mean? Change the size of the blue rectangle by
adjusting the scale factor. Observe the changes in the measurements.
2. Now click on Graphs. Again adjust the shape of the green
rectangle and the size of the blue rectangle and observe the changes in the
measurements and the graphs. What is being shown in the graphs?
3. As you observe and interpret the changes in the perimeter and
area, you should look at what happens for scale factors that are whole numbers.
What mathematical relationship is being depicted in the "Ratio of
Perimeters" graph? What mathematical relationship is being depicted in the
"Ratio of Areas" graph?
4. Focus on why the relationship between the scale factor and the
ratio of perimeters of similar rectangles is linear,
whereas the relationship between the scale factor and the ratio of areas of
similar rectangles is nonlinear. Why does the graph depicting the relationship
between scale factor and perimeter have a different shape from the graph depicting
the relationship between scale factor and area? Compare the ratio of the perimeters with the ratio of the areas
for rectangles with various scale factors. What is the relationship between
those two ratios?
5. Organize their data in a table using various scale factors, record side lengths,
perimeter, and area.
6.
Prepare a 5 –10 minute presentation about your project. Teach the class some of the basics of what
you have learned and design a quick problem for a volunteer to practice (Don’t
pick a goof ball). DO NOT READ BORING
PARAGRAPHS TO THE CLASS! Discuss it
like you know what you are talking about!
Use several visual aids to help the class understand the topic.
Resources
Evaluation
Web Quest Evaluation Rubric
Conclusion
Now that your quest is complete, you should have a better understanding of the importance of the ratios of perimeters and areas of polygons. These can be time saving tips for on the job applications in several fields.