# Engineering in the K-12 Classroom: Math and Science Education for the 21st-Century Workforce

## CONTENTS OF CURRICULUM UNIT 12.04.05

## The Mathematics of a Warming Arctic

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## Lesson 3

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Purpose:
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This lesson continues students' investigation of the economic opportunities and challenges brought about by a warming Arctic. Students will analyze the extraction of liquid and gaseous natural gas

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Objective:
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Students will use principles of volume, area, and unit conversions to analyze the collection and transport of oil and natural gas (both liquid and gaseous).

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Relevant Mathematical Skills:
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1. Calculations involving the area of circles and the volume of cylinders.

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Background Information:
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a. The Arctic is thought to have a large supply of natural resources, especially natural gas. Extracting these resources would have a large economic impact on the region and even on the world in general. b. Extracting resources is not easy; it requires the construction and maintenance of a huge amount of complex infrastructure, as well as the employment of a large number of people and machines. c. Geometry can be used to understand how these resources are extracted and transported.

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Lesson Design:
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1. Working again in pairs, students will analyze the flow of oil in a pipe and its storage aboard a tanker. Each pair will receive the dimensions of a pipe and information about the flow rate. Using this information, they will be responsible for determining how much oil is released into an awaiting tanker per unit of time. For the sake of simplicity, the pipe will be treated as a cylinder.

Guiding/extension questions:

- i. What would happen if more oil were pumped through the pipe over the same period of time?
- ii. What real-world consequences might there be for trying to pump oil more quickly through the pipe? This will be an intuitive/conceptual discussion, as most geometry students will not be at the point to study work and its dependence on flow rate / pipe diameter. The teacher is encouraged to ask the following:
- What effect will making the pipe more narrow have on the oil's flow speed? (imagine a garden hose that gets squeezed. What happens to the water's speed?)
- iii. What consequences - for both the environment and the flow of oil in the pipe - if there were a leak in the pipe?

2. After students have completed their analysis of the oil flow, they will turn their attention to the transport ship. They will determine how long it would take to fill the tankers (whose tanks will be treated as cylinders - students will be given the measurements of these tanks). Next, using data about the density of oil, they will calculate the amount by which the ship has increased in weight.

3. Lastly, students will calculate the market value of the collected crude using current data about world oil prices. Students will also use data about the cost of oil transport by tanker to generate some cursory calculations about the cost of transporting the crude oil to various refineries (e.g. those in Alaska, Washington State, and Russian cities along the Pacific coast).