Please note, links will be checked and updated soon. Thanks for your patience. 12/18/97

Here is a lesson using the data set of the number of earthquakes from 1900 to 1989 with a magnitude of 7 or greater. I found this after browsing the Internet at this location: United States Geological Survey (USGS), U.S. Department of the Interior. I clicked on Geologic Data, and then clicked on the National Earthquake Information Center. I found the data set after clicking on Earthquake Statistics.

**Grade level**: High School

**Instructional Goal**: To have students observe the number of earthquakes with a magnitude of 7 or greater from 1900 to 1989.

**Behavioral Objective**: After observing the curves, the students will determine the movement of the Earth's plates, and if there is a pattern to the frequency of strong earthquakes.

**Description of Materials**:

-Data set of earthquakes from 1900 to 1989 with a magnitude of 7 or greater.

-*Mathematica*

**How to Access**: To access this data set, use the software NCSA Mosaic at the Universal Resource Locator (URL)

address- http://info.er.usgs.gov/data/geologic/neic/lists/Number.html

**How to Use**: This data set can be used as enrichment materials for individual exploration/research. Using Mathematica , a least-square curve can be drawn that gives an approximate flow of the data points. The students can observe this curve and determine if these earthquakes follow a certain pattern or if they are unpredictable. The students can determine the movement of the Earth's plates (ie, if they move at a constant rate or not) from observing this curve.

**Assessment Activity**:

Here is the data of the number of earthquakes each year that were recorded as 7 or greater on the Richter scale from 1900 through 1989.

data =

{{1900,13}, {1930,13}, {1960,22},

{1901,14}, {1931,26}, {1961,18},

{1902,8}, {1932,13}, {1962,15},

{1903,10}, {1933,14}, {1963,20},

{1904,16}, {1934,22}, {1964,15},

{1905,26}, {1935,24}, {1965,22},

{1906,32}, {1936,21}, {1966,19},

{1907,27}, {1937,22}, {1967,16},

{1908,18}, {1938,26}, {1968,30},

{1909,32}, {1939,21}, {1969,27},

{1910,36}, {1940,23}, {1970,29},

{1911,24}, {1941,24}, {1971,23},

{1912,22}, {1942,27}, {1972,20},

{1913,23}, {1943,41}, {1973,16},

{1914,22}, {1944,31}, {1974,21},

{1915,18}, {1945,27}, {1975,21},

{1916,25}, {1946,35}, {1976,25},

{1917,21}, {1947,26}, {1977,16},

{1918,21}, {1948,28}, {1978,18},

{1919,14}, {1949,36}, {1979,15},

{1920,8}, {1950,39}, {1980,18},

{1921,11}, {1951,21}, {1981,14},

{1922,14}, {1952,17}, {1982,10},

{1923,23}, {1953,22}, {1983,15},

{1924,18}, {1954,17}, {1984,8},

{1925,17}, {1955,19}, {1985,15},

{1926,19}, {1956,15}, {1986,6},

{1927,20}, {1957,34}, {1987,11},

{1928,22}, {1958,10}, {1988,8},

{1929,19}, {1959,15}, {1989,7}};

Here is a plot of these data points.

It looks like we have a lot of points here. Let's take a look at the plot of the number of these strong earthquakes from 1900 to 1910.

Let's now take a look at a curve that describes the flow of these data points along with our points.

This curve gives a good approximation of the flow of these data points.

1. Explain the activity of the plates of the Earth over this period of ten years. What are some possible reasons for the rise in the number of strong earthquakes from 1930 to 1960?

Let's take a look at the next 10 years along with the first ten years.

As you can see this graph of the curve does not go through all the data points, but it does give an approximate description of the flow of the data points.

How are the plates of the Earth moving from 1900 to 1920?

Let's now see the data points from 1900 to 1950 and the curve that shows the general flow of this data.

Let's take a look at the curve without the data points.

From the curve shown, do the plates of the Earth move at a constant rate? Explain your answer.

What could account for the difference in the number of strong earthquakes through these fifty years?

Does this data curve contain a certain pattern?

Now we are going to predict what the curve will look like in the next 10 years. After observing the curve above, predict the numbers of strong earthquakes between 1950 and 1960 by placing your numbers in the data set titled "yourdata1". After you do that, execute the command and the curve of your data will show with the actual data from these ten years (your curve will be the thinner curve).

Here is example data input. If you want to use Mathematica, here is the code. You would have to change this text to "input" mode. From looking at this code you can determine how the code looked for the previous graphs.

yourdata1 = {{50,15},{51,37},{52,22},{53,25},{54,15}, {55,18},{56,22},{57,10},{58,26},{59,31}, {60,38}};

yourdataplot1 = ListPlot[yourdata1, PlotStyle->PointSize[.02], PlotRange->{0,40}, DisplayFunction->Identity];

yourfit1[x_] = Fit[yourdata1,{1,x,x^2,x^3,x^4,x^5,x^6,x^7},x];

yourplot1 = Plot[yourfit1[x],{x,50,60}, PlotRange->{0,40}, DisplayFunction->Identity];

data6 = {{50,39},{51,21},{52,17},{53,22},{54,17}, {55,19},{56,15},{57,34},{58,10},{59,15}, {60,22}};

dataplot6 = ListPlot[data6, PlotStyle->PointSize[.03], PlotRange->{0,40}, DisplayFunction->Identity];

polyfit6[x_] = Fit[data6,{1,x,x^2,x^3,x^4,x^5,x^6,x^7},x];

fitplot6 = Plot[polyfit6[x],{x,50,60}, PlotStyle->Thickness[.01], PlotRange->{0,40}, DisplayFunction->Identity];

Show[yourplot1,fitplot6, AxesLabel->{"1900's","# of quakes"}, DisplayFunction->$DisplayFunction]

Discuss why you predicted your points and what lead you to those predictions. How accurate were your predictions? If they were accurate, explain the reasons for your accuracy. If not, what are some possible reasons for the difference between your predictions and the actual data?

Here is the data curve from 1900 to 1960.

Make a prediction of the numbers of strong earthquakes between 1960 and 1970 and take a look at your data curve and the actual data curve (again, your curve is the thinner one).

Here is example data input. If you want to use Mathematica, here is the code. You would have to change this text to "input" mode. From looking at this code you can determine how the code looked for the previous graphs.

yourdata2 = {{60,15},{61,37},{62,22},{63,25},{64,15}, {65,18},{66,22},{67,10},{68,26},{69,31},{70,38}};

yourdataplot2 = ListPlot[yourdata2, PlotStyle->PointSize[.02], PlotRange->{0,40}, DisplayFunction->Identity];

yourfit2[x_] = Fit[yourdata2,{1,x,x^2,x^3,x^4,x^5,x^6,x^7},x];

yourplot2 = Plot[yourfit2[x],{x,60,70}, PlotRange->{0,40}, DisplayFunction->Identity];

data7 = {{60,22},{61,18},{62,15},{63,20},{64,15}, {65,22},{66,19},{67,16},{68,30},{69,27}, {70,29}};

dataplot7 = ListPlot[data7, PlotStyle->PointSize[.03], PlotRange->{0,40}, DisplayFunction->Identity];

polyfit7[x_] = Fit[data7,{1,x,x^2,x^3,x^4,x^5,x^6,x^7},x];

fitplot7 = Plot[polyfit7[x],{x,60,70}, PlotStyle->Thickness[.01], PlotRange->{0,40}, DisplayFunction->Identity];

Show[yourplot2,fitplot7, AxesLabel->{"1900's","# of quakes"}, DisplayFunction->$DisplayFunction]

Again, discuss why you predicted your points and what lead you to those predictions. How accurate were your predictions? If they were accurate, explain the reasons for your accuracy. If not, what are some possible reasons for the difference between your predictions and the actual data?

Now let's take a look at the data curve from 1900-1989.

Describe the movement of the plates of the Earth from 1900 to 1989. Do you see a certain pattern with this data? Are earthquakes predictable after observing this data curve? Explain your answer.