|Photo from the United States Department of Agriculture |
Natural Resource Conservation Service
Students will develop and understanding of area,the size of an acre and spatial relationships as well as learn different strategies for determining land area of irregular polygons in this lesson designed for students in grades 6 and up (adaptations for younger students are included at the end of this lesson).
The assignment revolves around this scenario:
Mr. & Mrs. Rice recently sold their dairy her and want to convert their former pasture land into a tree farm. They have a map of their property that shows the pasture land. Literature from the Massachusetts Cooperative Extension agent about growing evergreen trees suggests that trees can be successfully grown in a 6' x 6' arrangement with trees planted 6' apart in rows that are 6' apart. With this arrangement, 1,200 trees can be planted per acre of pasture land. An acre is a surface are of 43,560 feet.
Side note: I love the name Rice used in the scenario above! The land where our OARDC campus is located originally belonged to the Frederick Rice family. Frederick was a veteran of the Revolutionary War and eventually divided the farm between his two sons Simon and Barnhardt.
Question for students to answer: How many trees can the Rice family plant in their former cow pasture? A map of the property is included in The Annual Cycle of the Tree Farmer package.
Suggestions for teaching:
- Take the students outside and measure an acre on your school or personal property to help them understand how large an acre actually is. Before going outside, explain that since the square footage of an acre is 43,560 feet, the easiest way to measure out an acre is to create a square or rectangle with an area this size (Area = Length x Width, and in this case the area would be 43,560). Have students experiment in the classroom with calculators to find what combination yields a product of 43,560. Just a few of the possible solutions include: 208.47 x 208.47, 10 x 4,356, 100 x 435.6, 150 x 290.4, etc. Students should discover that the width will always equal the area (43,560 feet) divided by whatever length they choose. The students can then be divided into groups of 4 to go outside, measure and stake out the bounds of their acre using different dimensions for each group. This will help them understand that several different polygons can have the same area (in this case, 1 acre).
- Divide the students into groups of 3-4 and distribute the maps of the farm showing the pasture land that is to be planted to trees. Focus on 1 pasture and show it on an overhead. Give students 5 minute to discuss with their group possible ways to find the square footage of this pasture, then present their solutions. If using the map included with the Annual Life Cycle of a Tree Farmer, the lengths on that map have been converted to actual lengths using the map scale, where 1 inch = 100 feet. If you don't have the Annual Life Cycle of a Tree Farmer, you can create your own map selecting pasture shapes appropriate to the age level of your students. Perhaps the pasture shape is a trapezoid (calculate the area by dividing it into 2 triangles and a rectangle, then add the areas together) or a series of different shaped rectangles
These are fun, hands-on ways to help students learn about basic mathematical concepts and real-life problem solving. Which is always a good idea when it comes to minimizing the "But why do I have to learn my math?" questions!