Section 11.7, Approximating area of Irregular Shapes and 11.8: Relating the Perimeter and Area of a Shape
Imagine that one of your students comes to class very excited. She tells you that she has figured out a theory that you never told the class. She explains that she has discovered that as the perimeter of a closed figure increases, the area also increases. She shows you this picture to prove what she is doing:
How would you respond to this student?
Take a few moments to think about your answer, and then send it using the form below. Please start your answer with 11.7- to make them easier for me to sort and read, thanks!
Now, check out this article to see how US and Chinese teachers responded to this scenario.
Read Section 11.8 in your book, and respond to the following question in the form below. Explain your answer: (Hint, if you get stuck, look at the practice problem for section 11.8 in the book.) Please start your answer with 11.8- to make them easier for me to organize. Thanks!
True/False: You can determine the area of a figure if you know its perimeter.
True/False: You can determine the perimeter of a figure if you know its area.
Read 11.7 and 11.8, pages 619-627.
Complete problem number 1 on page 623.
[1. Suppose that you have a map with a scale 1 inch= 100 miles. You trace a state on the map onto 1/4 inch graph paper. (The grid lines are spaced 1/4 inch apart.) You count that the state takes up about 80 squares of graph paper. Approximately what is the area of the state? Explain.]
Complete problem number 5 in your book, on page 627.
[5a. Draw 4 different rectangles, all of which have a perimeter of 8 inches. At least two of your rectangles should have side lengths that are not whole numbers (in inches). Label your rectangles with their lengths and widths.
b. Determine the areas of each of your 4 rectangles in part (a) without using a calculator. Show your calculations, or explain briefly how you determined the areas. Then label your rectangles A,B,C, and D in decreasing order of their areas, so that A has the largest area and D has the smallest area among your rectangles.
c. Qualitatively, how do the larger-area rectangles you drew in part (a) look different from the smaller-area rectangles? Describe how the shapes of the rectangles change as you go from the rectangle of the largest area to the rectangle of the smallest area.]