Algebra 1 Quarter Project
Part one
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
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 production of wood and fruit. Then you will
decide how to organize and display your results.
Activity 1
A board foot is a cubic measure of lumber equal to a square foot of wood 1in thick.
 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?
 What different types of wood are needed for cabinets, floors, and roofs?
 What tools do carpenters use to make the above items?
Activity 2
You can use the expression 0.0655𝑙(1 − 𝑝)(𝑑 − 𝑠)2 to find the number of useable
board feet in a log.
 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.
 The diameter of a log is 25in. A total of 2 in will be 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
With aerial photography, you can study a forest of ponderosa pines without even
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 )ℎ𝑣 2 + (2.44 × 10−10 )ℎ𝑣 3
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 diameter
of 20ft.
Activity 4
You can use the function 𝑏 = −0.01𝑡 2 + 0.8𝑡 to find the number of bushels b of
walnuts produced on an acre of land. The variable t represents the number of walnut trees
per acre.
 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.
 How many walnut trees would you advise a farmer to plant on 5 acres of land
to produce the most walnuts possible. Explain your reasoning.
Activity 5
 Investigate the many uses of trees and write a 1 page summary of your research.
 Complete a 1 page summary of what you have learned in part 1 of this project.
Part 2
What is a safe distance between cars traveling on the highway? After you apply
brakes to stop your car, how far will your car travel before coming to a full stop? How do
accident investigators determine whether cars involved in accidents were traveling at safe
speeds? There are many variables that affect how quickly a car can stop. These variables
include the car’s speed, the driver’s reaction time, the type of road, the weather
conditions, and of course, the effectiveness of the brakes.
As you work through the following activities, you will use formulas to estimate safe speeds
under various conditions. You will make a graph to illustrate the relationship between
speed and stopping distance.
Activity 1
To reduce the likelihood of an accident when driving, you should consider how far
your car will travel before safely coming to a stop for the speed at which you are traveling.
Assume you are traveling on a dry road and have an average reaction time the formula 𝑑 =
0.044𝑠 2 + 1.1𝑠 gives you a safe stopping distance d in feet, where s is your speed in mi/h.
Make a table of values for speeds of 10, 20, 30, 40, 50, and 60 mi/h. Then graph the
function.
Activity 2
Suppose a car left a skid mark d feet long. The formulas will estimate the speed s
in miles per hour at which the car was traveling when the brakes were applied.
 Use the formulas to complete the table. Round to the nearest mile per hour.
 Why do you think the estimates of speed do not double when the skid marks double
in length? Based on the results, what conclusions can you make about safe
distances between cars?
Activity 3
Suppose you are driving on a dry road with 150 ft (about 10 car lengths) between
your car and the car in front of you. Us the formula from Activity 1 to find the maximum
speed you should be traveling in order to leave a safe stopping distance.
Activity 4
Discuss your conclusions in a one page paper about safe driving speeds, stopping
distances, and road conditions.
Rubric
Activity
Points Available
Part 1
72 pts Total
Activity 1
16pts total




Question 1
Question 2
Question 3
Question 4
Activity 2
 Question 1
 Question 2
Activity 3
Activity 4
 Graph of function
 Prediction of trees/acre
 Number of suggested walnut
trees
 Explanation
Activity 5
 Paper
 Thoughtful research
 Understanding of
completed research
 Correct grammar
 Correct spelling
 Between 1-3 pages in
length
 Summary
 Provides summary of
what was learned in
project
 Uses supporting detail
from previous activities
 Correct grammar
 Correct spelling
 Between 1-3 pages in
length
4
4
4
4
8 pts total
4
4
4 pts
16 pts total
4
4
4
4
28 pts total
14 pts total
4
4
2
2
2
14pts total
4
4
2
2
2
Points Earned
Part 2
48pts total
Activity 1
8pts total
 Table of values
 Graph
Activity 2
 Completed table
 Question 1
 Conclusions
Activity 3
Activity 4
 Paper
 Thoughtful responses
based on previous
activities
 Understanding of
concepts covered in part
2
 Correct grammar
 Correct spelling
 Between 1 and 3 pages in
length
Presentation
 All activities are organized
 Everything is present
 Neat
Total points possible 120
Total points earned
Grade
4
4
13pts total
4
4
5
4pts
14pts total
4
4
2
2
2
9pts total
3
3
3