Some Outdoor Mathematics Topicsfor the Elementary School

Robert Sovchik

College of EducationUniversity ofAkronAkron, Ohio 44325

Mathematics is rich in applications to physical phenomena. Thebeauty of nature illustrates many mathematical patterns and serves as amarvelous source of application activities. For example, the famousFibonacci sequence is found in many plants exhibiting a spiral leaf-growth pattern. This sequence 1,1,2,3,5,8,13,21,34, ... is produced bystarting with 1 and adding the preceding two numbers to arrive at thenext number. The daisy’s spiral ratio of 21:34 and the pine cone’s ratioof 5:8 correspond to two adjacent Fibonacci numbers.

In the elementary school, the outdoors can serve as a focus point forobserving mathematical patterns. Students can also apply computationalskills and problem solving strategies in a real world setting. Finally, anappreciation and awareness of nature can be cultivated by exposing stu-dents to the natural environment.

This article is designed to present specific activities which elementaryschool teachers can use for an outdoor mathematics experience. The ac-tivities are classified in two categories: primary (K-3) and intermediate(4-6).

PRIMARY OUTDOOR MATHEMATICS ACTIVITIES

1. Preformal Mathematics.

Fundamental meanings of terms like near, far, short, long and be-tween can be developed in an outdoor context. Pupils can find a shorttwig, a long twig, and a twig whose length is between that of the long andshort twigs. Pupils can estimate which tree is highest in a group of trees;which rock is heaviest in a group of rocks; which leaf is smallest in agroup of leaves.

2. Acquiring the meaning of numerals.

Pupils can gather leaves to make a bulletin board by placing one leafby the numeral 1, two leaves with the numeral 2, three leaves with thenumeral 3, and so on.

3. Using natural objects as measuring instruments.

Students can go outside to select natural objects as measuring instru-ments. For example, they could select a blade of grass, a twig, or even a

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flat rock. After naming the measuring unit (with creative names) theycan perform the following measurements:

a. height to the top of the headb. length of pacec. arm span (arms stretched out at the side)d. width of hand or fingere. height of upward reachf. length of one arm

4. Developing a metric track meet.

Students can use centimeter and meter rulers to measure distancesduring a metric track meet. The following activities can be performed:

a. run a 30 meter raceb. jump horizontally from a standing positionc. throw a softball as far as you cand. jump vertically into the aire. run a 200 meter relay

5. Using shadows to illustrate geometric concepts.

Bruni and Silverman (1976) have developed some creative activities forworking with geometric objects and their shadows. The basic idea is toconstruct from cardboard different kinds and sizes of triangles, squares,rectangles, parallelograms, trapezoids and so on. A light source like sun-light or, if indoors, from an overhead projector, is projected onto thecardboard figures. The difference between the shape and size of theoriginal figure and its shadow is then compared. For example, what kindof shapes can be projected when using an isoceles triangle? Can youmake a square? A right triangle? An obtuse triangle? A scalene triangle?A rectangle?When outside, children can also measure their heights and their shad-

ow lengths. Perhaps a table can be developed which lists the results ofthis activity. Other questions that can be mathematically valuable arethese: Who has the longest shadow? Who has the shortest shadow? Howshort can you make your shadow? How tall can you make your shadow?

Interested readers are urged to read the original article by Bruni andSilverman. The article contains many useful ideas for working with^shadow mathematics."

6. Comparing height with armspread

Children can measure their heights and compare this value to themeasurement value obtained when their hands are stretched out at theirsides. A table can then be developed which shows each child’s height andarmspread measurement. What do you think children will discover whenthey study this table?

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INTERMEDIATE OUTDOOR MATHEMATICS ACTIVITIES

1. Using insects to illustrate mathematical concepts.

Meiring (1976) has provided some interesting facts about insects whichcan be developed during an outdoor mathematics experience. For ex-ample, when the temperature is between 20°C and 35 °C, a cricket canhelp children to estimate the temperature. The number of times thecricket chirps in ten seconds is approximately equal to the temperature inCelsius units.

Also, children can measure the distance a large ant travels during ashort period of time. After capturing the ant, they can measure its lengthand determine how many body lengths were represented by the distancethe ant covered. They can also determine the ant’s speed in kilometersper hour or miles per hour.

2. Making and using a clinometer.

A simple device for measuring angles of elevation can be made from aprotractor and a piece of thread with a weight on one end (see figure 1).

Suppose that children want to use this device to measure the steepnessof a hill. Pick two children of approximately equal height. One childshould hold the clinometer at the bottom of the hill. The second childshould climb to the top of the hill. The child holding the clinometer canthen sight the other child’s eye level by tilting the clinometer upward (seefigure 2).

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The number of degrees that the string moves will indicate the degree ofelevation of the hill. For our example, the hill shows a steepness of 45°.It is important to emphasize that the child using the clinometer mustsight from his eye level to the eye level of the student standing at the topof the hill. Also, children sometimes get confused when reading the pro-tractor because there are often two numerals for each marking point.Therefore, emphasize the degree shift from 90°.

3. Using similar triangles to make indirect measurements.

When two triangles are similar the ratios of corresponding sides areequal. We can use this fact to find the height of a tree, flag pole or build-ing. Take a ruler and place it perpendicular to the ground (see figure 3).

Then measure the length of the shadow. Notice that we have a right tri-angle formed. Now measure the shadow of the object which has an un-known height. For purposes of illustration, we will find the height of aflagpole (see figure).

We now have two similar triangles which exhibit this relationship:

length of the ruler length of the ruler’s shadow

length of the flagpolelength of the flagpole’s shadow

Outdoor Mathematics Topics 645

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Specifically, suppose the ruler’s length is one meter and its shadow is70 centimeters. If the length of the flagpole’s shadow is 8 meters, then wecan substitute these values and obtain the following solution for x, the

height of the flag pole:-1- = �;8 = .7x; 11.43 = x.x 8

For our example the height of the flagpole is 11.43 meters.

4. Determining a student’s walking rate.

Students can compute their comfortable walking rate (in miles perhour or kilometer per hour) by completing the following activities:

a. The number of steps per minute is ____.b.The distance traveled (measured in feet or meters) is

.

c.The walking rate (in feet or meters per minute) is_

d.The walking rate (in feet or meters per hour) is.e.The walking rate (in miles per hour) is ____.f.The walking rate (in kilometers per hour) is __

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5. Determining water speed in a stream.

Meiring (1976) suggested that a useful activity for children is tomeasure the speed of a stream. Students can float an object in themoving water and measure the distance it travels in one minute. Then,the speed of the stream in kilometers per hour is calculated. The experi-ment can be repeated at different places along the stream and ondifferent days, particularly after a heavy rainfall.6. Gathering data about automobiles.

Students can collect data on the school grounds regarding the auto-mobile. Going to the school parking lot can yield interesting data. Somepossible questions are these:

a. How many cars are there?b. What manufacturers are observed?c. How many cars of each manufacturer are located?d. How many of the cars have four cylinders?e. How many of the cars have six cylinders?f. How many of the cars have eight cylinders?

If the situation permits, it may be possible to extend this activity to thesurrounding community by asking the same questions when observingtraffic patterns. Also, the information collected may be portrayed ingraphical form. For example, a bar graph may be drawn depicting thenumber of Chevrolets, Fords, etc. found in the school parking lot.

In closing, these are just some of the many activities that can be devel-oped for an outdoor education experience in the elementary school. Theycan be a welcome change from ordinary classroom procedures.

REFERENCES1. BRUNI, J. V. and SILVERMAN, H. J. From shadows to mathematics. The Arithmetic Tea-

cher, 23, 1976,232-239.2. MEIRING, S. "Outdoor Activities in Mathematics", Columbus, 1976. (mimeographed)

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