TITLE : Where Has All the Ice Pack Gone

The Big Melt: Arctic Ice Caps

Teacher Background Information:

This exercise deals with statistics behind the amount of Arctic ice pack that has melted since 1979 (1980)

http://www.arctic.noaa.gov/reportcard/seaice.html

http://svs.gsfc.nasa.gov/vis/a000000/a003400/ a003456/index.html

Overview:

As written, this exercise could be used at a variety of levels to reinforce the idea of rate of change between different data, specifically linear vs. exponential. Students are asked to evaluate the rate of change in ice melt first through a linear interpretation of the data and then through an exponential interpretation. They are asked to explain the graphing results as well as to analyze the results and make their own predictions of ice melt.

Goals: To use research on ice cap melting to formulate an exponential decay equation.

Objectives: Students will…

· Compute the decline of the summer Arctic ice pack

· Formulate an equation that incorporates the variable as the exponent (exponential)

Procedure:

Optional warm-up activity:

· Have students get into groups of three

· Give each student group an aluminum baking pan filled half way with water

· Give each group a few stones.

· Explain that they are going to create a representation of the ocean and a continent. They can make believe it is any continent an ocean/sea that they like.

· Tell the students to place the stones in the water to represent landmasses.

· You can also place monopoly plastic houses on the stones to represent human population if you like.

· Ask the students if they have heard about global climate change and how it might cause the planets ocean/sea levels to rise?

· Explain that sometimes the science of this can be confusing so we have created a model to understand how this might happen.

· Explain that in many parts of the ocean there are icebergs floating around that could melt if the ocean temperatures rise.

· Put at least 5 ice cubes into each group’s pan.

· As you can see the majority of the mass of these icebergs is under the ocean.

· Have each group make a mark on the pan of where the water level is.

· Now have each group put their pan in a warm area of the classroom – in sunlight or near a heater.

· Explain to the students that the water level does not rise because the mass of the ice was the same as the water so icebergs, melting due to climate change will not cause the ocean/sea levels to rise.

· STOP HERE

· Play the following about the melting of polar ice caps

http://videos.howstuffworks.com/howstuffworks/344-how-polar-ice-caps-work-video.htm (This is a humorous, short video that shows interviews in which people are asked what would happen if all the polar ice melted. It then gives a brief explanation of the poles and the effect of the melt.)

· After some discussion from the video, allow the students to work through questions 1 – 6, supporting where needed. You might want to put the graph on an overhead or projected through a graphing program so that it can be compared to the upcoming graph.

· Move on to questions 7 – 14. Overlay the exponential graph on top of the linear to allow students to see the difference a simple interpretation of data can make. You can decide here if you want to introduce the concept of exponential decay or the fact that the equation will never completely go to 0.

· You might end the lesson with www.pbs.org/wnet/nature/episodes/arctic-bears/the-melting-arctics-impact-on-its-ecosystem/780/

The Big Melt: Arctic Melt Student Worksheet

Name:______Class period:______

Every year, the Arctic ice cap grows and shrinks according to the change of the seasons. Thus, its smallest surface area is in the month of September, at the end of the summer and before the cool of winter begins to refreeze surrounding water. The part of the cap that remains in September is called the perennial ice cap and has remained reasonably constant in size until the last few decades. Over the past few years, studies have come out with estimates of how fast the ice is melting, each leading to an estimate for when this perennial ice cap will no longer exist.

According to a study published by NASA scientists in 2003, this perennial ice cap has shrunk at an average rate of 10 percent per decade since 1980.

1. For this first question, imagine that “10 percent per decade” means that the amount lost each decade is 10% of the original amount. Without knowing how large the perennial ice cap was in 1980, could you still figure how many years it would be before the perennial ice cap is completely gone? Explain your thinking.

2. Given that the Arctic perennial ice cap in 1980 was approximately7.68 million square km, test your conjecture above by completing the chart below. Round to the nearest hundredth.

3. How do the results in the table compare with the estimation you made in #1. If there is a difference, what could account for the difference?

4. Write an equation that models the data above______Be sure to define your variables.

5. a) Now, graph the data either by using your equation or plotting the data points with the date as your input ( let 1980 be t = 0) and the resulting ice cap area as your output. Be sure to label your axes appropriately. of graph?

b) What kind of graph do you get? ______

c) What is it about the data that produces this kind of graph? ______

6. Use your equation or your graph to find the ice cap melt for 2032: ______

7. Now we are going to interpret the “10 percent per decade” a different way and the way that it was meant to be interpreted. This time you will be computing the 10% of the melting ice cap for each year, instead of the original size. Before completing the chart below, make a new estimate on what year you think the Arctic ice will melt completely. : ______Does knowing the amount of the original ice cap make a difference in your estimate?

8. Now, given that the Arctic ice cap was approximately 7.68 million square km in 1980, complete the chart below to check your estimation.

9. a) How does this data compare with those found in our first table?

b) How does this data coincide with the estimation you made in #7?

10. Construct a graph below using the date ( let 1980 be t = 0) as your input value ( x) and the resulting size of the ice cap ( column 4) as your output values (y). Be sure to label your axes appropriately.

11. Does this graph make a straight line? What is it about the data that gives the graph its shape?

12. Now, can you figure out a faster way to compute the amount of ice cap left for 2010? (Hint: compare your answers in column 2 with the answer in column 4. What is the relationship between them? ) Explain.

13. Write an equation to model what you discovered in #12. ______

14. Use your equation to determine the ice cap area in 3000. ______How many decades would it take for the ice cap to completely disappear? ______.

15. The graph below gives a visual representation of the yearly Arctic ice activity since 1980. Note that the perennial data discussed above comes from the Sept readings. The chart below approximates the values from that graph for the perennial ice cap.

Year / Perennial area in square km in millions
2000 -2004 / 6.5
2005 / 5.75
2007 / 4.0
2008 / 4.25

16. What are some observations you made from this data? Be specific using numbers to support your comments.

17. Because of the data above, many new estimates for total Arctic perennial ice cap melt have been proposed ranging from 2015 to 2080. Looking at the data, has your estimate changed from the estimate you made earlier? Explain your thinking.

18. In your warm up activity you discovered that the melting floating ice such as that of the Arctic does not raise sea levels. However, the reduction of the Arctic ice does contribute to the following:

· Reduction of polar bear habitat

· Reduction of solar reflection: the white ice is a natural coolant for the earth as it sends sunrays back into the atmosphere. A reduction of ice means more water to absorb the rays and, therefore, increase global warming trends.

The Big Melt : Arctic Melt-

Teacher Answer Key

Name:______Class period:______

According to a study published by NASA scientists in 2003, this perennial ice cap has shrunk at an average rate of 10 percent per decade since 1980.

2. Given that the Arctic perennial ice cap in 1980 was approximately7.68 million square km, test your conjecture above by completing the chart below.

Year / Square miles (in millions from previous year) / Change in square km ( in millions)
- (7.75 x .10 ) / Resulting size of ice cap ( in millions) for current year
1980 / 7.68
1990 / 7.68 / -.768 / 6.912
2000 / 6.912 / -.768 / 6.144
2010 / 6.144 / -.768 / 5.376
2020 / 5.376 / -.768 / 4.608
2030 / 4.608 / -.768 / 3.84
2040 / 3.84 / -.768 / 3.072
2050 / 3.072 / -.768 / 2.304
2060 / 2.304 / -.768 / 1.536
2070 / 1.536 / -.768 / .768
2080 / .768 / -.768 / 0

3. How do the results in the table compare with the estimation you made in #1. If there is a difference, what could account for the difference?

Answers will vary

4. Write an equation that models the data above__y= -.768x + 7.68 Be sure to define your variables.

x is the number of decades since 1980, y is the size of the ice cap that year in millions km2

b) What kind of graph do you get? ____linear______

c) What is it about the data that produces this kind of graph?

Decreasing by the constant rate of -.768______

6. Use your equation to find the ice cap melt for 2032:

3.6864 mill. km2

y = -.768x + 7.68 2032 is 5.2 decades so -.768 (5.2) + 7.68 = 3.6864 million km2

7. Now we are going to interpret the “10 percent per decade” a different way and the way that it was meant to be interpreted. This time you will be computing the 10% of the melting ice pack for each year, instead of the original size. Before completing the chart below, make a new estimate on what year you think the Arctic ice will melt completely. : __Answers vary__ Does knowing the amount of the original ice cap make a difference in your estimate?

8. Now, given that the Arctic ice cap was approximately 7.68 million square km in 1980, complete the chart below to check your estimation.

Year / Square km of previous year
(in millions) / Change in square km (Sq. km. x .10) / Resulting size of ice cap in sq. km (sq. km - column 3)
1980 / 7.68
1990 / 7.68 / -.768 / 6.912
2000 / 6.912 / -.6912 / 6.221
2010 / 6.221 / -.6221 / 5.599
2020 / 5.599 / -.5599 / 5.039
2030 / 5.039 / -.5039 / 4.535
2040 / 4.535 / -.4535 / 4.082
2050 / 4.082 / -.4082 / 3.674
2060 / 3.674 / -.3674 / 3.307
2070 / 3.307 / -.3307 / 2.976
2080 / 2.976 / -.2976 / 2.678

9. a) How does this data compare with those found in our first table?

There is a different amount subtracted each time and I did not end up at 0

a. How does this data coincide with the estimation you made in #7?

Answers vary

(Note that students will have plotted this by hand, not through the equation.)

11. Does this graph make a straight line? What is it about the data that gives the graph its shape?

The graph is not a straight line because the rate of change is not the same from decade to decade. I am not taking 10% of the same number each time