Cordwood Dilemma. Cordwood Dilemma. 1 of 12. Copyright 2007, Exemplars, Inc. All rights reserved.

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1 I ordered 2 cords of wood that were just delivered. I finally got it stacked, and I am wondering if I really received 2 cords of wood or if the company cheated me. A cord is defined as wood stacked 4 feet by 4 feet by 8 feet. I measured my 2 stacks of wood. One is 72 inches by 167 inches by 16 inches. The other is 65 inches by 266 inches by 16 inches. Did I get about 2 cords of wood? 1 of 12

2 Suggested Grade Span 6 8 Task I ordered 2 cords of wood that were just delivered. I finally got it stacked, and I am wondering if I really received 2 cords of wood or if the company cheated me. A cord is defined as wood stacked 4 feet by 4 feet by 8 feet. I measured my 2 stacks of wood. One is 72 inches by 167 inches by 16 inches. The other is 65 inches by 266 inches by 16 inches. Did I get about 2 cords of wood? Alternative Versions of Task More Accessible Version I ordered 2 cords of wood that were just delivered. I finally got it stacked, and I am wondering if I really received 2 cords of wood or if the company cheated me. A cord is defined as wood stacked 48 inches by 48 inches by 96 inches. I measured my 2 stacks of wood. One is 72 inches by 167 inches by 16 inches. The other is 65 inches by 266 inches by 16 inches. Did I get about 2 cords of wood? More Challenging Version During the American occupation of Fort Crown Point on Lake Champlain in New York, troops were required to each cut 12 cords of wood for the winter. If the troops were to stack the wood they were required to cut, end to end, in stacks that were 4 feet high by 4 feet wide by 8 feet long (the approximate equivalent of 1 cord of wood), how many troops would be needed to create a length of wood equal to 1 mile? How many cubic yards of wood would there be in all? Context My sixth-grade math classes had just finished learning about density in their science class. I wanted to see if they could make the connection between this problem and density problems they were doing in science. We have not studied volume this year in math class, but we live in Vermont and all of the students have seen wood stacked as firewood. 2 of 12

3 What This Task Accomplishes This task has students working with measurement. Since some of the information in the task is given in inches and some in feet, the students will have to decide which to convert. Using a calculator and measurement is always a learning experience. Many students think that 3.4 feet is the same as 3 feet 4 inches. This task will also allow the teacher to see which students understand the concept of volume. What the Student Will Do Most students decided to convert to one measure. It was interesting to see which students chose to convert to inches, which converted to feet, and how they dealt with the decimal measure. Time Required for Task This task took sixth graders one 45-minute period to complete, but many took their papers home to finalize as homework. Interdisciplinary Links The most direct link this task has is to science and the study of density. Density is defined as mass per volume (grams/cubic centimeters), thus the class had to study volume in order to find the density of certain materials. A social studies unit on colonial life and how colonists heated their homes with wood would also be a link to the volume of cordwood. Students could also estimate how many cords of wood a colonial family would need to heat their home for the winter. Teaching Tips If you do not live in an area that uses cordwood for heat, you may want to find a picture of stacked wood to share with your class. In my presentation of the problem, I made sure students understood that the wood was dumped in my driveway in one big pile, that I had to stack the wood myself, and I couldn t tell if I had received two cords of wood. Suggested Materials Provide students with calculators. 3 of 12

4 Possible Solutions A cord of wood has a volume of 128 cubic feet (4 feet x 4 feet x 8 feet) or 221,184 cubic inches (48 inches x 48 inches x 96 inches). My stacks have a volume of 192,384 cubic inches (72 inches x 167 inches x 16 inches) or about cubic feet (6 feet x 13.9 feet x 1.3 feet). and 276,640 cubic inches (65 inches x 266 inches x 16 inches) or about cubic feet (5.4 feet x 22.2 feet x 1.3 feet). I asked for 128 feet x 2 feet or 256 cubic feet and got about cubic feet, so I got about 8 cubic feet more wood than I ordered. More Accessible Version Solution See the solution to the original version. More Challenging Version Solution 5,280 feet in a mile 8 feet long (the length of one cord) = cords = 55 troops needed 5,280 x 4 x 4 = 84,480 cubic feet 27 = approximately 3,129 cubic yards Task-Specific Assessment Notes Novice A Novice will not recognize this as a volume problem and will have a difficult time getting started. Even if the Novice manages to convert the measurements, s/he will not know how to proceed. A Novice might also want to add the measurements of each stack and compare the totals. Apprentice An Apprentice will recognize the task as a volume problem. However, the Apprentice may use a calculator to convert the measurements and may equate 1.3 feet as 1 feet 3 inches. An Apprentice may also make calculation errors that result in an incorrect solution. Some Apprentices might find the volume of each stack in cubic yards and then divide by 12 to incorrectly convert to cubic feet. 4 of 12

5 Practitioner The Practitioner will recognize this as a volume task. The Practitioner will decide that I received more than two cords of wood. The solution will be easy to follow and the reasoning evident. The Practitioner will work either in inches or in feet. Expert I would expect an Expert to convert to cubic feet. Even though cubic inches will give you a more exact answer, I would expect an Expert to realize that stacking cordwood is not an exact science and that rounding would not jeopardize the solution while giving a more efficient and understandable answer. An Expert will have all measurements labeled correctly, so it is clear the student has an understanding of cubic measurement. The Expert should also make mathematically relevant comments or observations. The Expert may, for instance, go beyond merely answering the problem to tell how much more wood was received than ordered. 5 of 12

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