Chapter 9 Project
Use these Internet links for more information to help you complete the Chapter Project.
Go to b4ubuild.com to find residential construction information.
Ask Dr. Math for a review of evaluating expressions.
You can also visit Ask Dr. Math for a review of cylinders.
Beginning the Chapter Project
Many schools celebrate Arbor Day by planting young trees to replenish our ecosystem. Trees use carbon dioxide that
humans and animals exhale to make oxygen. Trees anchor the soil and prevent erosion. They also produce fruit. Wood
from trees is used for the construction of everything from pencils to houses.
As you work through the activities, you will learn more about the uses of trees. You will use formulas to analyze data and
predict the production of wood and fruit. Then you will decide how to organize and display your results.
List of Materials
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Calculator
Graph paper
Activities
Activity 1: Researching
A board foot is a linear measure of lumber equal to a square foot of wood 1 in. thick.
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What can you make from 10 board feet? 100 board feet? 1000 board feet? How is the size of a house related to the amount
of wood used to build it?
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What different types of wood are needed for cabinets, floors, and roofs? What tools do carpenters use to make these items?
Activity 2: Calculating
You can use the expression 0.0655l(1 – p)(d – s)2 to find the number of useable board feet in a log.
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Estimate the useable board feet in a 35-ft log if its diameter is 20 in. Assume the log loses 10% of its volume from the saw
cuts and a total of 2 in. is trimmed off the log.
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The diameter of a log is 25 in. A total of 2 in. is trimmed off the log. The estimated volume loss due to saw cuts is 10%.
How long must the log be to yield 600 board feet of lumber?
Activity 3: Calculating
With aerial photography, you can study a forest of ponderosa pines without ever walking through it. To find the diameter
in inches of trees in the forest, use the expression 3.76 + (1.35 × 10 –2)hv – (2.45 × 10–6)hv2 + (2.44 × 10–10)hv3. The variable
h is the height of the tree in feet, and v is the crown diameter visible in feet (from a photograph). Determine the diameter
of a 100-ft tree that has a visible crown diameter of 20 ft.
Activity 4: Graphing
You can use the function b = –0.01t2 + 0.8t to find the number of bushels b of walnuts produced on an acre of land. The
variable t represents the number of trees per acre.
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Use your graphing calculator to graph this function. Include an accurate graph in your notebook. You may wish to
investigate the TABLE feature on your calculator. Use the maximum feature under the CALC menu to determine the
number of trees per acre that gives the greatest yield.
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How many walnut trees would you advise a farmer to plant on 5 acres of land? Explain your reasoning.
Finishing the Project
The answers to the four activities should help you complete your project. Assemble all the parts of your project in a folder.
Add a summary telling what you have learned about the uses of trees.
Reflect and Revise
Ask a classmate to review your project folder with you. Together, check that your graph is clearly labeled and accurate.
Check that you have used formulas correctly and that your calculations are accurate. Make any revisions necessary to
improve your work.
Extending the Project
Trees have many uses that you could investigate. You can begin your research by contacting the United States Department
of Agriculture Forest Service or a local, state, or national park. You can also get more information by using the Internet.
Chapter Project Checklist
Have you done all of the following?
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Measured wooden objects to help you estimate.
Used the given formula.
Had someone check your solution.
Selected an appropriate viewing window.
Scoring Guide
3
Thorough research techniques are demonstrated with many different sources of information used. Calculations are
correct. The graph is neat, accurate, and has an appropriate scale. Explanations are complete and well thought out.
2
Good research techniques are evident. Calculations are mostly correct, but have minor errors. The graph is neat and
mostly accurate with minor errors in scale.
1
Needed information is located with some help. Calculations contain both minor and major errors. The graph could be
more accurate.
0
Major elements of the project are incomplete or missing.