Summary:
Students estimate the perimeter of a pond using a chance method of estimation and then compare that measurement to one using standard units.
Main Curriculum Tie:
Recognize, describe, and determine surface area and volume of threedimensional shapes.
Materials:
 Single hole punch
 Blank piece of paper
 String
 Meter stick
 Markers
 Map, aerial photo, or drawing of a pond photocopied onto grid paper. You may want to use a printout of the virtual pond for your classroom.
Background For Teachers:
In this activity students will measure the curvilinear perimeter of a pond. An easy way to measure nonlinear distance is to place a string along the curved perimeter, mark the ending point and then by holding it taut measure the length of the string against a measuring stick (a meter stick is recommended for students working with the concept of tenths).
If your pond has a large perimeter you may wish to assign sections of the perimeter to different groups. Later you can combine the group measures to find the total shoreline of the pond.
If possible visit a real pond at some point in this lesson. Using a map for both methods of estimation obscures the point about the role that chance plays in the first method. If you must use a map of a pond for both methods, select a map with a scale appropriate to the mathematical ability of your students.
Intended Learning Outcomes:
Students will make and use estimates of measurement. Students will multiply numbers with digits in the tenths place.
Instructional Procedures:
The value of lake side property is often determined by the length of shoreline on the property. Mathematicians refer to the entire shoreline as perimeter. Real Estate agents would refer to segments of the shoreline as 'water frontage'. Pond frontage is less valuable in real estate sales, but it is very important in determining the amount of aquatic life a pond will support. In class today we will use two methods of measuring the shoreline of a pond and then compare those two results in a graph.
Divide the students into groups of at least three members. Explain that the groups will estimate the perimeter of the pond using a chance method of estimation and then compare that measurement to one using standard units.
Estimating the Shoreline Using a Chance Method 
Using the single hole punch create ten paper circles from the blank piece of paper. Blindfold one member of your group and have them drop the paper circles onto the map until one of the paper circles hits a grid square containing pond water. Measure the length of shoreline inside the grid square as best you can.
Estimating Shoreline using Chance Method continued 
Convert the map measurement into standard units by multiplying by the scale of your map (if you are using the virtual pond, each grid square represents a 0.5 m by 0.5 m strip of land. On the author's printout, the grid squares measure 0.5 cm by 0.5 cm producing a scale of 1 cm = 1 m. Hence if the shoreline in the grid square measured 0.3 cm it would represent 0.3 meters of shoreline).
Estimating Shoreline using Chance Methods continued 
Repeat dropping the paper circles until two more grid squares containing 'pond water' are selected. Measure the shoreline within those two grid squares and calculate the real world equivalent in meters.
Estimating the Shoreline using Chance Method continued 
Average the three shoreline lengths and then multiply by the number of grid squares containing shoreline on your map (if you are using a map of the virtual pond the number of shoreline squares is about 52 grid squares). Record this answer for the graphing activity that follows.
Measure the Shoreline in Standard Units 
Visit the pond site (or display an overhead of the pond map).
Scan the shoreline for any problem areas that might interfere with measuring the shoreline (creeks, holes, swamps, moose, etc.).
Assign each group a section of the shoreline to measure.
Provide each group with a ball of string. Encourage the students to keep the string dry (unless measuring the virutal pond) as some string expands when wet giving an incorrect representation of shoreline length.
Measuring the Shoreline in Standard Units continued 
Return to the classroom and convert the string lengths to standard units (see the background section above).
Record the group measurements and then ask the students to calculate the total shoreline.
Graph the Two Measurements 
Create a bar graph comparing the shoreline estimate from the Chance Method section with the measurement of the shoreline in standard units.
Extensions:
Many states publish the length of their shoreline to attract tourists to their state. Every state has a perimeter and using a map of your state your students could calculate the state's perimeter. Many large cities construct freeway systems that include a 'belt loop'. A belt loop is a section of freeway that circles the urban area. Challenge the students to estimate the length of a belt loop from a map.
Assessment Plan:
Students may keep a math journal of their experiment with chance methods and standard measurement. Their calculations are accurately recorded in their journals. Their bar graphs accurately display the comparison of perimeter measurements.
Created Date :
Mar 19 1999 13:38 PM
