Applied Academics

Daunting Peaks

Volcanologist Applications of Mathematics 9

Lesson Idea by: Leanne Zorn, School District #23 (Central Okanagan)

Given the string of recent Hollywood movies, the study of volcanoes may seem like an extremely dangerous undertaking. While it is fascinating work, volcanologists agree that the greater part of their time is spent researching, rather than running from explosions of molten lava.

"Volcanologists use math everywhere," says Ben Edwards, a volcanologist with the Geological Survey of Canada. "It's in everything we do."

Volcanologists collect rock samples, then use math to analyse the results and learn more about how the volcano erupted. With the help of statistical analysis, photos and measurements, they can observe changes and determine what happened when a volcano erupted.

By studying what happened in the past, volcanologists can better determine what might happen during future volcanic eruptions. They can also apply their findings to look for valuable ores.

Get into groups of five or six people. Using a ruler, measuring tape or dressmaker's tape, measure and record the following data for each member of your group. (Hint: use centimetres for all measurements.)

i) arm span (arms outstretched from fingertip to fingertip) and height;
ii) foot length and mid-arm length (from wrist to elbow);
iii) circumference of head and circumference of calf;

Plot this raw data onto three separate graphs:
i) arm span (X axis) versus height (Y axis)
ii) foot length (X axis) versus mid-arm length (Y axis)
iii) head circumference (X axis) versus calf circumference (Y axis).

Create a line of best fit for each of these three graphs. Can you make any conclusions regarding the relationships of these three sets of data?

Part of the research Ben Edwards does involves measuring the size of rocks at volcano sites. He analyses the data to determine what type of volcanic (or non-volcanic) event brought the rock to the site. "There are many types of rock deposits found at young volcanoes," says Edwards. "Three of the most common types of deposits are pyroclastic flow deposits, airfall deposits and avalanche deposits." Each type of deposit can be characterized by the sizes of rocks in it. A volcanologist can tell what type of deposit occurred by looking at a graph showing the size of rocks in a sample.

• 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.

You are a volcanologist. You're studying three 10-kilogram buckets of rock collected from different locations on Mount Meager, northwest of Whistler and Pemberton, B.C. Each bucket (labelled A, B, C) contains rocks collected from a different type of deposit. You've brought the buckets back to the lab and now it's time to analyse 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 of the deposits.

Now 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 take 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.

Course/Grade: Applications of Mathematics 9
Curriculum Organizer: Number Operations, Patterns and Relations, Problem Solving	Curriculum Sub-organizer(s): Scatter plots
Prerequisites: Linear Equations, Graphing	Resources: · rulers or measuring tape

 

Student Activity Sheet - DAUNTING PEAKS

Group Members

 

Measurements
	Arm Span	Height	Foot	Mid-Arm	Head	Calf
1.
2.
3.
4.
5.
6.

 

Graphs:

i)Arm Span versus Height

ii) Foot Length versus Mid-Arm Length

iii) Circumference of Head versus Circumference of Calf

Solution to Learn To interpret your graphs, remember that an airfall deposit is characterized by having a well-sorted deposit of rock; a pyroclastic deposit is fairly well-sorted rock, but not nearly as well-sorted as an airfall deposit; and an avalanche deposit has rocks of all sizes in it. Judging from your graphs, Sample A is an airfall deposit, Sample B is a pyroclastic flow deposit and Sample C is an avalanche deposit.