# 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 2:

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Purpose:
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The second lesson of this unit is designed to get students acquainted with relevant background and to lay the groundwork for the connection between the real-world situation and the mathematics. Students will develop an initial sense of what the current state of the Arctic is, one of the economic changes occurring in the region, and some of the challenges and opportunities associated with this change.

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Objective:
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a. Students will summarize the key economic changes brought about by a warming Arctic b. Students will use principles of trigonometry and basic measurement to map out the path of a large freighter through the Arctic region

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Relevant Mathematical Skills:
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1. Direct measurement of distances with a ruler 2. Calculation of real-world distances using a map scale 3. Calculations involving rate, time, and/or distance

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Background Information:
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a. While it is difficult to see on a normal 2D map, passage through the Arctic region is often the quickest route between two points on the globe. b. Melting sea-ice is making it possible for more ships to travel directly across the Arctic ocean rather than make lengthy and costly detours. c. This type of shipping is expected to become more and more common in the future and may lead to some international disputes about who owns the shipping lanes, how they should be used, and whether they harm the environment in some way.

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Lesson Design:
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1. Students will be placed in groups of two. Each group will be assigned a ruler, protractor, and map of the Arctic region (with scale). Additionally, students will be assigned a shipping route. Each group will use the tools provided to measure the shipping route's distance (kilometers) if the ship is a) allowed to pass unimpeded through the Arctic region and b) required to avoid the Arctic circle. 2. Students will draw the shipping routes on the map and calculate distances. 3. This will be followed by a whole-class discussion in which students share results, discuss which shipping route would be most shortened by passage through the Arctic circle, and what the potential consequences of such travel could be. 4. Lastly, students will create a "report" for their shipping route in which they summarize the results of their mathematical analysis. Specifically, they will address: a. The difference in total distance between the two calculated shipping routes b. The difference in total travel time between the two calculated shipping routes (students will assume that a tanker travelling their route will have a constant speed of 17 mph) c. The difference in total cost between the two calculated shipping routes. Students will use the fact that an average supertanker travelling at 17 mph will require 41 gallons of fuel to travel its own length. The price of fuel can be set by the teacher.