Home > Examples > Tasks & Rubrics > Mathematics

Task

You are a volcanologist. You are studying three 10-kilogram buckets of rock collected from different locations on a volcano. Each bucket (labeled A, B, C) contains rocks collected from a different type of deposit. You have brought the buckets back to the lab and now together with your two teammates you must analyze the contents.

The contents of each bucket are sorted separately. You use a series of sieves that allow you to divide the rocks into size groups. Then you weigh the rocks in each size range. You repeat the process for each bucket. This is your data:

Sample A has the following distribution of rock sizes:

1) <0.1 cm = 0.5 kg
2) 0.1 - 0.5 cm = 0.2 kg
3) 0.5 - 1 cm = 8.3 kg
4) 1 - 10 cm = 0.5 kg
5) >10 cm = 0.5 kg

Sample B has the following distribution of rock sizes:

1) <0.1 cm = 1.4 kg
2) 0.1 - 0.5 cm = 1.1 kg
3) 0.5 - 1 cm = 5.4 kg
4) 1 - 10 cm = 1.8 kg
5) >10 cm = 0.3 kg

Sample C has the following distribution of rock sizes:

1) <0.1 cm = 1.0 kg
2) 0.1 - 0.5 cm = 2.3 kg
3) 0.5 - 1 cm = 2.1 kg
4) 1 - 10 cm = 2.9 kg
5) >10 cm = 1.7 kg

Make a graph by plotting particle size (X axis) versus cumulative mass of the sample (Y axis) to determine what type of event formed each deposit.

Interpret those plots. Does your plot indicate that the sample was collected from an airfall deposit from a volcanic eruption? Or was it a sample taken from a pyroclastic flow site? Or did the rocks arrive at the sample site in an avalanche?

Make an analysis of each plot. Answer the question: "What type of deposit is it?" for each sample. Justify answer using graphical analysis and the definitions given below.

• Pyroclastic flow deposits form when the gas and rock column from an erupting volcano gets too heavy and part of the column collapses. They have fairly well sorted rocks, but not nearly as well-sorted as an airfall deposit.
• Airfall deposits are formed of rock fragments and pumice (solidified lava that is full of airpockets) that are shot out of the mouth of the volcano and then fall to the ground. Most of the rocks are about the same size.
• Avalanche deposits can be caused by earthquakes associated with volcanic eruptions, or they can form from earthquakes not associated with volcanic eruptions. Since volcanoes are typically very steep, avalanches commonly occur on the slopes. Thus, avalanche deposits are commonly found at volcanoes. They contain rocks of all sizes.

Rubric

Copyright 2008, Jon Mueller. Professor of Psychology, North Central College, Naperville, IL. Comments, questions or suggestions about this website should be sent to the author, Jon Mueller, at jfmueller@noctrl.edu.