Dimensional Analysis
at the Port of Long Beach
Lesson five
Students will be able to use dimensional
analysis to convert units used at the Port of
Long Beach.
Grade 7 Measurement and
Geometry
7.1.3: Use measures expressed
as rates and measures
expressed as person-days to
solve problems; check the
units of the solutions; and use
dimensional analysis to check
the reasonableness of the
answer
Materials
1. Dimensional Analysis
PowerPoint
2. Whiteboard
Time Required
1 class
Dimensional Analysis at the Port of Long Beach
| 45
Dimensional Analysis at the Port of Long Beach Lesson 5
Content Standard
Reference:
Terminal Objective
Introduction of Lesson
Anticipatory Set:
Ask students where they have seen containers in
the city of Long Beach. They may have seen them
on campus where they are used to store earthquake
supplies or on the back of a truck driving along the
freeway.
Student Objective:
Students will be able to use dimensional analysis to
convert units used at the Port of Long Beach.
Purpose:
Dimensional Analysis at the Port of Long Beach Lesson 5
Dimensional analysis is useful to convert units that
are not common.
Lesson
Keyword
1. Dimensional
analysis using unit analysis to help
make conversions from one
unit to another.
Input
Dimensional anaylsis is using unit analysis to help
make conversions from one unit to another. Review
the five steps for dimensional analysis.
Modeling
1. Read the situation. Identify the original units.
2. Write the original units as a fraction.
3. Decide what is the conversion factor for the new
unit.
4. Be sure to set up the problem so the original units
will divide out.
5. Simplify the expression and divide out the
common units.
Check for Understanding
Have students work with a partner to make sure
they have the five steps written correctly in their
notes.
46 | Dimensional Analysis at the Port of Long Beach
Lesson cont’d
Input
Review converting simple units using dimensional
analysis.
Modeling
Example 1:
5 feet = ? inches
1. What information is given? 5 feet
2. Write all information as fractions.
Number of yards = 5/1
Dimensional Analysis at the Port of Long Beach Lesson 5
3. What units do you want? inches
What conversion rate can be used?
1 foot = 12 inches
4. S
et up the expression so the original units
divide out.
5 feet 12 inches
1 ×
1 foot = 60 inches
5. Simplify
Check for Understanding
How do you write a fraction of one for the
conversion factor? Answer: 1/1
Modeling
Example 2:
5 feet = ? meters
1. What information is given? 5 feet
2. Write all information as fractions.
Number of meters = 5/1
Dimensional Analysis at the Port of Long Beach
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Lesson cont’d
3. What units do you want? meters
4. What conversion rate can be used?
1 foot = 0.3 meters
5 feet .3 meters
1 ×
1 foot
= 1.5 meters
Dimensional Analysis at the Port of Long Beach Lesson 5
Guided Practice
A ship from China is measured in meters but the
Port of Long Beach berths are measured in linear
feet. The ship is 300 meters long. How many
linear feet are needed at the Port of Long Beach
pier?
Conversion Factor:
One meter is approximately 3.3 feet
Have students put their expressions on white
boards. On the count of three, check the
expressions.
300 meters
1
×
3.3 feet
1 meter
Solve the expression.
300 meters
3.3 feet
1
× 1 meter
= 990 feet
300 × 3.3 = 990 feet
Input
Select a student randomly to explain the
expression.
Guided Practice
The Neptune Amber, a cargo ship, is 231 meters
long. Is the expression below correct to change the
length to feet?
48 | Dimensional Analysis at the Port of Long Beach
Lesson cont’d
231 meters
1 meters
1
× 3.3 feet
Tell your partner if the expression is correct or not.
Explain what is wrong if it is not correct.
Answer: No - It is not correct.
Students should identify that the original
units did not divide out, so the reciprocal of the
conversion factor should be used.
Input
Dimensional Analysis at the Port of Long Beach Lesson 5
Oil is sold in barrels. One barrel of oil is 42
gallons. How many barrels are in a tanker truck
that holds 11,000 gallons of oil?
1 barrel=42 gallons
Modeling
Have students set up the expression to convert the
units to barrels.
Check for Understanding
Have students put the expressions on their white
boards. On the count of three, check to see if the
expressions are correct.
11,000 gallons
1
x
1 barrel
42 gallons
Dimensional Analysis at the Port of Long Beach
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Lesson cont’d
Guided Practice
Write the expression to find out how many barrels
of oil are on an oil tanker that holds 1.3 million
gallons of oil.
1,300,000 gallons
1
x
1 barrel
42 gallons
Input
Cargo containers are measured in TEUs, or twentyfoot equivalent units.
Dimensional Analysis at the Port of Long Beach Lesson 5
1 TEU = 1 Twenty-foot Equivalent Unit
Modeling
Review the different sizes of cargo containers from
the introductory lesson, including an explanation
of 1 TEU (20-foot container) and 2 TEUs (40-footcontainer).
Check for Understanding
Tell your neighbor:
1. What does TEU stand for? Answer: Twenty-foot
Equivalent Unit
2. What size are the containers you normally see on
the back of semi trucks? Answer: 2 TEUs. They
are 40 feet long.
Input
Let’s convert 50 forty-foot containers to TEUs.
Modeling
How many TEUs are in 50 forty-foot containers?
50 forty-foot x
2 TEUs
= 100 TEUs
1
1 forty-foot
50 × 2 = 100 TEUs
50 | Dimensional Analysis at the Port of Long Beach
Lesson cont’d
Input
Convert a 45-foot container to TEUs.
Modeling
How many TEUs are in a 45-foot container?
45 ft x 1 TEU =2.25 TEU
1
20 ft
45 9
= = 2.25 TEU
20 4
Input
Dimensional Analysis at the Port of Long Beach Lesson 5
Convert a 20-foot container to meters. One meter
is approximately 3.3 feet.
Modeling
20 ft x 1 m =6 m
1
3.3 ft
Input
A train has 50 cars that hold forty-foot containers.
How many TEUs are on the train?
(1 forty-foot container = 2 TEUs)
Modeling
50 forty-foot x
2 TEUs
= 100 TEUs
1
1 forty-foot
50 × 2 = 100 TEUs
Guided Practice
A train has 100 cars that hold forty-foot
containers. How many TEUs are on the train?
100 forty-foot . 2 TEUs
= 200 TEUs
1
1 forty-foot
100 × 2 = 200 TEUs
Dimensional Analysis at the Port of Long Beach
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Lesson cont’d
Guided Practice
The Hanjin Amsterdam cargo ship holds 5,618
TEUs. How many forty-foot containers are on the
ship?
5,618 TEUs . 1 forty-foot
1
2 TEUs
= 2,809 forty-foots
Dimensional Analysis at the Port of Long Beach Lesson 5
Closure
Fill in the Blank:
The most important thing to remember when
using dimensional analysis is if you want to
eliminate unit from the numerator, you need to
put the same unit in the ________ of the conversion
fraction.
Answer: Denominator
Have students complete the Dimensional Analysis
and Dockage Charges worksheets.
52 | Dimensional Analysis at the Port of Long Beach
Worksheet
Lesson five
Dimensional Analysis Worksheet
Directions
Use dimensional analysis to convert the following units. Use the
Dimensional Analysis at the Port of Long Beach Lesson 5
conversion chart to find the conversion factors.
Conversion Chart
1 foot is approximately 0.3 meters
1 meter is approximately 3.3 feet
1 barrel of oil = 42 gallons of oil
1 twenty- foot container = 1 TEU
1 forty-foot container = 2 TEUs
1. 350 feet = ______ meters
2. 600 feet = _______ meters
3. 400 meters = ______ feet
4. 520 meters = ______ feet
5. 60 barrels = ______ gallons of oil
6. 550 barrels = ______ gallons of oil
7. 840 gallons of oil = ______ barrels
8. 210 gallons of oil = _______ barrels
9. 500 forty-ft containers = _____ TEUs
10. 500 forty-five ft containers = _____ TEUs
11. 250 TEUs = ______ forty-ft containers
12. 600 TEUs = ______ forty-ft containers
Dimensional Analysis at the Port of Long Beach
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Worksheet Solutions
Lesson five
Dimensional Analysis Worksheet
Answers
Use dimensional analysis to convert the following units. Use the
Dimensional Analysis at the Port of Long Beach Lesson 5
conversion chart to find the conversion factors.
Conversion Chart
1 foot is approximately 0.3 meters
1 meter is approximately 3.3 feet
1 barrel of oil = 42 gallons of oil
1 twenty- foot container = 1 TEU
1 forty-foot container = 2 TEUs
1. 350 feet = 105 meters
2. 600 feet = 180 meters
3. 400 meters = 1320feet
4. 520 meters = 1716 feet
5. 60 barrels = 2520 gallons of oil
6. 550 barrels = 23,100 gallons of oil
7. 840 gallons of oil = 20 barrels
8. 210 gallons of oil = 5 barrels
9. 500 forty-ft containers = 1000 TEUs
10. 500 forty-five ft containers = 1125 TEUs
11. 250 TEUs = 125 forty-ft containers
12. 600 TEUs = 300 forty-ft containers
Dimensional Analysis at the Port of Long Beach
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Dockage Charges
Handout
Lesson five
Directions
ship in feet and meters.
Ship
Dimensional Analysis at the Port of Long Beach Lesson 5
The Port of Long Beach berths are measured in linear feet, so all ship
lengths must be calculated in feet to determine at which berth a ship can
dock. The Port also charges dockage fees based on the length of the ship in
meters. Therefore all ship lengths must be calculated in meters and feet.
Use dimensional analysis to complete the chart to give the length of each
Chart A
Complete the following chart using dimensional analysis.
Length in Meters
Hanjin Amsterdam
Neptune Amber
Zim Atlantic
279
15.
231
Length in Feet
13.
14.
823 feet
Dockage Charges
Use the information in Chart A to determine the dockage charge for each ship.
Length Range in Meters
24-hour Charge per Day
226 – 240
$3899
256- 270
$5066
210 – 225
$3371
241 – 255
$4463
271 – 285
Ship
$6379
24-hour Charge per day
Hanjin Amsterdam
16.
17.
Neptune Amber
18.
19.
Zim Atlantic
20.
Five Day Charge
21.
Dimensional Analysis at the Port of Long Beach
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Dockage Charges
Answers
Lesson five
Directions
Chart A
Length in Meters
Hanjin Amsterdam
Neptune Amber
Zim Atlantic
279
15.
231
Length in Feet
13.
920.7
14.
246.9
Dimensional Analysis at the Port of Long Beach Lesson 5
Ship
Complete the following chart using dimensional analysis.
762.3
823 feet
Dockage Charges
Use the information in Chart A to determine the dockage charge for each ship.
Length Range in Meters
24-hour Charge per Day
226 – 240
$3899
256- 270
$5066
210 – 225
$3371
241 – 255
$4463
271 – 285
Ship
$6379
24-hour Charge per day
Hanjin Amsterdam
16.
$6379
17.
Neptune Amber
18.
$3899
19.
Zim Atlantic
20.
$4463
21.
Five Day Charge
$31,895
$19,495
$22315
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