Pebble
Power: Investigating Stone Shapes
One of the
habits my children had when young was to collect
rocks wherever we went.
We often filled
our pockets and carted them (often bags full) home. To my kids,
the
rocks had qualities I could not begin to understand.
Their
collections include a variety of colors, designs, and shapes--the more
unusual
the better!
I know my children's
affection for rock collection is shared by many other kids, much to the
exasperation of their teachers and parents.
I
am pleased I have finally found a mathematical connection
by which we can "organize" and discuss their collection without getting
into
intensive geological discussions.
A geologist acquaintance told me about a
method to classify rocks according to calculations made regarding their
dimensions.
Rocks are placed into
one of four categories by making three measurements and computing two
simple
ratios.
In short, the measurements
are the three longest diameters of the rock that are perpendicular to
each
other.
Figure
1
Measurements
of a stone
Use calipers,
if possible, to do the measurements.
They can even be made from a ruler and sticks or you can
substitute a
drawing compass.
A standard ruler
can be used for the measurements after students understand how to avoid
parallax error by getting close to the ruler and looking perpendicular
to its
surface.
The greatest distance
between any two points on the rock is the "largest diameter." Call this
distance
a.
The measurement is done by moving the caliper around the
rock until it shows the greatest span.
Record a. Note the endpoints of a with pencil marks or by returning the
caliper to the
rock. Measure b, the next greatest diameter of the rock
that is
perpendicular to the segment that made a. Record b. Try to
visualize a plane made up by the intersection of segments a and b. Measure c as the largest diameter perpendicular to
that
plane. Record c.
Divide, preferably by calculator, to find the ratios c:b and b:a. Place the rock on the graph according
to its coordinates (c:b, b:a) where you go across the first value then
up the
second value. Identify the rock's
type by its placement on the graph.
The table in Figure 1 shows how data can be organized and offers
a few
examples. The measurements are in
millimeters.
Figure
2
Rock
a
b
c
c:b
b:a
Rock
Type
1
63
44
16
.36
.70
disk
2
109
64
41
.64
.59
roller
3
4
5
etc.
Sample
Data Table
Draw a large
graph like the one in Figure 2 on the classroom floor.
Students will begin to make connections
between a rock's dimensions and its properties.
Rock #1 would make a good "skipping stone" but rock #2 will
not.
Students will notice patterns
in the shapes as the rocks are distributed across the graph.
Students also volunteer why the names
given the groups are descriptive and why the ratios never exceed 1.
Students also see interesting
relationships as they explore the reasons why some rocks are placed on
the
boundaries between categories, why overall size is unrelated to a
rock's
classification, and how certain characteristics change as one moves
from the
extremes of one category to another.
Figure 3
Graph
of rock types
This activity
can be done easily and cheaply with students of virtually any age.
All they need is a basic understanding
of how to measure and what division means.
The
activity enhances discussions of stone tool use, the
forces and products of Nature, and why we pick up the rocks we choose
to
collect.
Rocks seem to
provide a compelling interest to kids.
I believe this activity provides a new dimension to something
they
already like and provides a way of connecting mathematics to the "real
world"
while kids practice skills and develop understanding.
Richard
T.
Edgerton, Ph.D.
Seattle
Public
Schools
rtedgerton@seattleschools.org
