Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 6, Part A:
Measuring Area

In This Part: Measuring a Surface | Areas of Irregular Shapes

 Trace your hand on a piece of paper. Think about how you might determine the area of your handprint. Problem A1 Will the amount of area covered differ if you trace your hand with your fingers close together or spread apart? Explain.

 Think about the activity you did with the tangram triangles in Session 1, Part C.    Close Tip Think about the activity you did with the tangram triangles in Session 1, Part C.

Units for measuring area must have the following properties:

 • The unit itself must be the interior of a simple closed shape. • The unit, when repeated, must completely cover the object of interest, with no holes or gaps (like a tessellation). Many polygons (e.g., rectangles, rhombuses, and trapezoids) and irregular shapes (e.g., L shapes) have this property and can thus be used as units of measurement.

Problem A2

 a. What units might you use to determine the area of your handprint? b. Why can't you use a small circle as the unit of measurement?

Problem A3

 a. One method for finding the area of an irregular shape is to count unit squares. Use centimeter grid paper (PDF - be sure to print this document full scale) to determine the area of your handprint. What are the disadvantages of this method? b. Another method is to subdivide your handprint into sections for which you can easily calculate the area. Find the area of your handprint using this method. Does using the two methods result in the same area?

 Up until now, you have been approximating the area of your handprint. In other words, your measurements were not exact.

 Problem A4 What can you do to make your approximation more accurate? Explain why this approach will lead to a better approximation.

 Another way to approximate the area of a handprint or any other irregular shape is to determine the number of squares that are completely covered and the number of squares that are partially covered. Average these two numbers to get an approximate area in the number of square units.

 Problem A5 Think about the following statement: If you repeatedly use a smaller and smaller unit to calculate the area of an irregular shape, you will get a closer and closer approximation and eventually find the exact area. What do you think of this line of reasoning? Explain.

 Problem A6 The palm of your hand is about one percent of your body's surface area. Doctors sometimes use this piece of information to estimate the percent of the body that is affected in burn victims. Use your data to approximate the amount of skin on your body.

 Session 6: Index | Notes | Solutions | Video