# 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 1:

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Purpose:
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This lesson has students examining some of the environmental impacts of the warming Arctic by performing some relevant calculations of temperature and the melting of sea-ice.

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Objectives:
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Students will use algebraic and geometric skills to calculate Arctic warming. Students will also write down their own ideas about how mathematics could be used to make sense of a variety of real-world challenges brought about by rising temperatures.

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Relevant Mathematical Skills:
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1. Calculation of percentage increase and decrease 2. Estimation of future data points through extrapolation of a trend. 3. Graphical analysis of student-generated data 4. Analysis of area and volume

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Background:
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a. The Arctic is undergoing a number of dramatic changes. Warming temperatures have been observed for the past few decades and, while some temperature variation is a natural occurrence in regional climates, it is generally accepted by the scientific community that human beings are having an accelerating - perhaps even causative - effect on this process. b. One of the most visible consequences of this increase in temperature is the melting of Arctic sea-ice. It is thought that within a decade, sizeable portions of the Arctic Ocean will be entirely ice-free during the summer months. Since the 1980's Sea-ice has generally been decreasing in area by 7% per decade. Average depth of sea-ice could change from roughly 3 meters today to around 1 meter by the end of the 21st century.

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Lesson Design:
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1. Following an overview of the current state of the Arctic, students will be asked to consider each and hypothesize about what geometric/general mathematical concepts could be useful in describing/analyzing it. This will be a whole-class discussion. 2. Next, students will analyze the area of the Arctic. Using the observation that sea-ice has been decreasing by 7% in area per decade, students will create a graph comparing time and sea-ice area. Students will be responsible for labeling the axis and then answering the following questions on the back of their graph: a. In what year will the area of sea-ice be half of what it is today? b. In what year will the area be one quarter of what it is today? c. Compared to the sea-ice area today, what percent will there be in 20 years? 3. Students will then complete a very rough calculation of the volume of sea-ice at present and in the future by using the facts about the average depth of sea-ice.