Unless otherwise noted, information contained in each edition of the Kansas School Naturalist reflects the knowledge of the subject as of the original date of publication.

Volume 6, Number 2 - December 1959

Conservation Arithmetic

KSN - Vol 6, No 2 - Conservation Arithmetic

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Published by The Kansas State Teachers College of Emporia

Prepared and Issued by The Department of Biology, with the cooperation of the Division of Education

Editor: John Breukelman Department of Biology

Editorial Committee: Ina M. Borman, Robert F. Clarke, Helen M. Douglass, Gilbert A. Leisman, David Parmelee, Dixon Smith

The Kansas School Naturalist is sent upon request, free of charge, to Kansas teachers and others interested in nature education. Back numbers are sent freg' as long as the supply lasts, except Vol. 5, No.3, Poisonous Snakes of Kansas. Copies of this issue may be obtained for 25 cents each postpaid. Send orders to The Kansas School Naturalist, Department of Biology, State Teachers College, Emporia, Kansas.

The Kansas School Naturalist is published in October, December, February, and April of each year by The Kansas State Teachers College, Twelfth Avenue and Commercial Street, Emporia, Kansas. Second-class mail privileges authorized at Emporia, Kansas.

Conservation Arithmetic

Many elementary teachers regularly include conservation in their teaching plans and have been successful in interesting their pupils in conservation. These teachers know that learning to use resources wisely involves more than reading books about conservation, going on conservation field trips, making conservation posters, and, seeing conservation slides and films. Conservation is both something we know about and something we do. The doing need not all occur in science or social studies classes, or under the heading of conservation. Activities which are conservation-oriented and center pupils' attention on resource use may take place in classes in language, music, arithmetic, drawing, or in fact any school subject.

In this issue of The Kansas School Naturalist we present a group of arithmetic problems which may help to develop some knowledge of and interest in our resources and their use. The first planning for this issue came in the 1953 Workshop in Conservation, in which several of the participants made up a suggested list of conservation arithmetic problems. A number of these problems were tried out, during the 19.53-54 school year, by these teachers and by others who were interested. During the Workshops of 19,t)4, 1955, and 1956, the participants deleted and revised some of the problems, added some new ones, and tried out all or most of the problems in their own classes during the ensuing school years. The lists of problems were sent to a number of teachers who were not members of the Workshops. Many of these teachers sent in comments and criticisms.

The problems have not been allocated to grades, nor have they been listed in order of difficulty.. All of the problems here listed were used in more than one grade; some of them were used in all the grades in which arithmetic was taught.

The problems are of course not original; many of them occur in standard arithmetic books in nearly the same form in which they are presented here. While they deal with widespread aspects of resource use, most of them have been worded so that they have particular application to the conservation problems and practices of Kansas. We hope that these few examples will suggest many other conservation arithmetic problems to all readers who have occasion to teach arithmetic, either formally in school or informally at home, on field trips, in scout meetings, or anywhere else.

Many people had a hand in the collection, formulation, and testing of these problems. We do not even know who many of them are; with a few exceptions they were Kansas teachers at the time they were working with these problems. Even if we knew all of them, the list would be too long to publish. The Kansas School Naturalist takes this opportunity to thank all the Workshop participants and others who gave any kind of assistance to this issue.

A few specific acknowledgements are in order. Several of the problems were adapted from The Value of Soil Conservation,(1) by Alfred W. Philips, formerly in the Department of Mathematics at Kansas State Teachers College. R. P. Felkner, Work Unit Conservationist, Lyon County, revised the figures in several of the problems, to make them realistic in terms of present-day prices and conditions. The maps and sketches were drawn by Harold Willis, sophomore biology student at Kansas State Teachers College.

(1) Philips, Alfred W., 1949, The Value of Soil Conservation,
The University Publishing Co., Lincoln, Nebraska.


I. One acre-foot of water is defined as the amount of water that would cover one acre to a depth of one foot. One acre equals 43,560 square feet, and therefore one acre-foot equals 43,560 cubic feet.

1. One acre-foot equals how many gallons?

2. One million gallons equals how many acre-feet?

A certain lake which is used as a source of water by a nearby city has a capacity of 8000 acre-feet. The city uses an average of 4,400,000 of water per day.

3. How much water does the city use per year?

4. How many day's supply would the lake contain if all the water could be used?

5. If 30 % of the water is lost in evaporation, leakage, and other losses, how many days' needs will the lake actually supply?


II. One square mile equals 640 acres.

1. How many cubic feet of water fall on one square mile during a one-inch rain?

2. If 75% of this water soaks in and 25% runs off, how many cubic feet of water runs off?

3. This amount of runoff equals how many acre-feet of water?

4. This equals how many gallons of water?


III. A certain city in east central Kansas, with a population in 1940 of about 12,000 had an area of about 4.6 square miles. The average annual precipitation in this area (rain and snow) is about 28 inches of water.

1. About how much water falls on this city per year?

2. This equals how many gallons per person per year, based on the 1940 area and population?

3. This equals how many gallons per person per day, based on the 1940 area and population?

4. If the average daily water consumption is 200 gallons per person, what percentage of this amount falls on the city as rain or snow?

It is estimated that by 1970 the population of this city will have doubled, that the area will have increased to eight square miles, and that the average daily water consumption will be 240 gallons per person.

5. About how much water will fall on the city per year when its area has increased to eight square miles?

6. What percentage increase over the 1940 amount does this represent?

7. Recalculate the answers to (2), (3), and (4) above, using the 1970 estimates of the area and population of the city.


IV. The precipitation in Kansas, by the months of 1958, is shown in Table I. The figures include both rain and snow, with snowfall changed to its equivalent in rain. About 10 inches of snow equals one inch of rain; thus a station receiving 22 inches of rainfall and 20 inches of snow would record 24 inches of precipitation. Table I shows the 1958 precipitation by crop reporting districts, as shown in the map on page 11.

January .41 .44 .81 .62 .70 .80 1.49 1.43 1.13 .86
February 1.18 .74 .35 1.58 1.71 1.18 1.50 1.20 .93 1.11
March 2.73 4.00 2.56 3.68 3.57 3.62 2.04 3.54 5.62 3.54
April 1.66 1.78 1.22 1.46 1.59 1.54 1.70 2.26 3.24 1.83
May 3.37 4.00 4.06 4.28 4.06 3.65 4.35 3.12 3.93 3.86
June 2.78 2.52 3.35 2.80 3.66 5.27 6.40 6.86 5.31 4.30
July 5.05 6.95 6.54 6.45 7.36 7.26 13.02 10.06 9.46 7.86
August 2.89 3.02 3.06 3.29 2.65 1.72 1.96 3.02 2.01 2.62
September .92 .82 1.30 4.50 4.29 4.81 6.71 5.83 5.59 3.81
October .40 1.18 .10 .41 1.05 .29 1.51 1.03 .15 .51
November .63 1.12 .87 .72 .86 1.03 1.77 2.66 2.37 1.32
December .55 .29 .42 .23 .48 .63 .29 .76 .91 .52
Annual 22.57 25.86 24.64 30.02 31.98 31.80 42.74 41.77 40.65 32.14

From Farm Facts, 1958-59, A Report of the Kansas State Board of Agriculture, Topeka, Kansas.

1. What was the average monthly precipitation in Kansas in 1958?

2. What was the average monthly precipitation in your district?

3. What percent of the 1958 Kansas precipitation was the 1958 precipitation in your district?

4. a. In what district and what month did the largest monthly precipitation occur?

b. In what district and what month did the smallest monthly precipitation occur?

5. a. How many times the smallest precipitation was the largest?

b. What percent of the largest precipitation was the smallest?

The average Kansas precipitation over the period 1887 to 1957 was about 27 inches.

6. What percent of this average was the 1958 Kansas precipitation?



V. A certain city in Kansas, with a population of about 17,000, used 1,314,000,000 gallons of water during the year 1958. The total cost of pumping, purifying, storing, and piping the water to the consumers was $375,000.

1. How many gallons of water were used per day in the city?

2. How many gallons were used per person per day?

3. What was the cost per day to supply the city?

4. What was the cost per person per day?

5. What was the cost per thousand gallons of water?

6. What was the cost per person per year?

7. How much per thousand gallons would the city have to charge in order to 1nake a 10% profit?


VI. A farm boy collected one gallon of water from the muddy stream that came from a plowed field during a heavy rain. He evaporated away the water, and then put the remaining soil in the oven to dry,. He obtained from the gallon of muddy water 13 ounces of dry soil The amount of water from this and neighboring fields was enough to fill a pond with a capacity of 37 acre-feet. The total drainage area was 417 acres.

1. How many gallons of water drained into the pond?

2. How many ounces of soil were carried by this water?

a. This equals how many pounds of soil?

b. This equals how many tons of soil?

3. How many pounds of soil, on the average, were lost from each acre?

4. How many tons of soil, on the average, were lost from each acre?



VII. The population of the world is not distributed evenly; neither is all land equally capable of supporting people. Table II shows some of the variations on the amounts of land available to the peoples of the different parts of the world. Not all land is arable (suitable for cultivation); in fact there are many states and countries in which more than half of the land is occupied by deserts, mountains, swamps, or tundra, so that it cannot be farmed. The table also shows the number of acres of arable land per person. Some of the figures in the table are rather rough estimates because in many countries exact data have not been compiled.

1. Fill in the blank spaces in the table.

2. You can find out from the Soil Conservation Service how your county compares with Kansas and the United States. Calculate for your county:

a. the number of persons per square mile,

b. number of acres per person,

c. number of acres of amble land per person.



VIII. One acre equals 43,560 square feet. A certain one-acre homesite is in the form of a square.

1. How many feet long is each side of this one-acre square?

2. A rod equals 16 1/2 feet. How many rods of fence are required to enclose this site?

3. The topsoil on this site is 9 inches deep. How many cubic feet of topsoil are there?

4. A sample of this topsoil weighed 88.2 pounds per cubic foot. How many tons of topsoil are there?

5. Topsoil in this community sells for $4.50 per cubic yard. What is the value of the topsoil on this site?

6. At $4.50 per cubic yard, what is the cost per ton?



IX. It has been estimated that three billion tons of soil annually are carried away, by wind and water, from the fields, pastures, and other farm land of the United States. A railroad freight car, which can carry 50 tons, is 44 feet long.

1. If the engine is as long as four freight cars and the train has only one engine, how many cars would there be in a mile long?

2. How many tons of soil could this train carry?

3. Making two trips per day, how many tons of soil could this train carry in a year?

4. How many such trains would be required to carry three billion tons per year?



X. In the sketch on the following page the lengths of the terraces are shown in the feet.

1. What is the total length of all the terraces?

2. At 5 1/2 cents per foot, what will be the cost of constructing them?

3. If the government through the Agricultural Conservation Program, pays 70% of this cost and the farmer pays the remaining 30%, what will be the cost to the farmer?

see caption below

The above sketch was traced from the terrace and waterways plans drawn by soil conservation technicians, for a farm which occupies one square mile. The lengths of the terraces are shown in feet. Not counting the land occupied by buildings, woodlot, waterway, and meadow, or the land southeast of the creek, which was found to be so nearly level that terraces were not needed, the area to be terraced was 480 acres.

In Kansas, average farms require about one mile of terraces for each 20 acres of land; the above farm includes 560 acres to be terraced.

4. How much above or below average are the requirements for this farm?

a. In feet of terrace?

b. In percentage?


XI. Recently an agricultural experiment station reported findings of a long-time study of the effect of crop rotation on crop yield. The experiment, in which no fertilizers were used, was carried on for 32 years. Four adjacent plots, as nearly alike as possible were set aside for the study.

Plot I was planted to corn year after year. At first it produced as much as other corn land in the region. Gradually the yield decreased until after 29 crops were harvested this plot was turned to other use. For the 29 years the average yield on this plot was only 16.15 bushels per acre.

Plot II was planted to wheat for 32 years in succession. The average yield over this period was only 14.69 bushels per acre, far below what is normally expected in that part of the state.

Plot III was kept in alfalfa continuously for 22 years. The average crop per year for the whole time was 2,693 lbs. per acre, about 1 1/3 tons.

On Plot IV a rotation of alfalfa, corn and wheat was followed. Alfalfa is one of the best of the legumes, those plants including sweet clover, red clover, soybeans, and others, which are able to take nitrogen from the air and store it in the soil. Because alfalfa requires more than one year to reach full production and because it is a soil enricher as well as valuable feed for livestock, Plot IV was kept in alfalfa for the first four years of the test. The next twelve years were divided into four cycles of a year of corn followed by two years in wheat. The accompanying sketch shows how this 16-vear rotation of the three crops was carried out. The experiment was continued through two full 16 year cycles.

In Plot IV the 8 crops of corn raised in the 32 years averaged 26.6 bushels per acre. The 8 crops of wheat raised immediately after the 8 corn crops averaged 17.68 bushels per acre while the 8 wheat crops which immediately followed wheat crops averaged 20.70 bushels per acre. The alfalfa produced on Plot IV in the 8 years averaged 3,958 lbs. per acre per year.

16 year rotation chart

The rotation cycle used on Plot IV in Problem XI; as seen from the above, during each cycle, the land produced alfalfa for 4 years, corn for 4 years, and wheat for 8 years, or a total (for the two complete cycles) of 8 years each of alfalfa and corn and 16 years of wheat.

Some interesting comparisons can be drawn from these figures. To simplify the problems let us deal only with a 16 year period, the length of the main rotation cycle. To find the values of the various crops we may take approximate prices as follows: alfalfa, $20.00 per ton ; corn, $l.00 per bushel; wheat, $1..50 per bushel.

1. If corn had been raised continuously for 16 years and had produced an average of 16.15 bushels per acre as this experiment showed, what would have been the total value of the corn produced?

2. If instead, wheat had been raised each year for 16 years at the average rate of 14.69 bushels per acre, what would have been the total value of the wheat?

3. Compute the value of all the alfalfa, corn, and wheat raised on the 16-year rotation plan:

(a) Alfalfa, 4 crops at an average yield of 3,958 lbs., per acre each year. This is a total of how many tons per acre?

(b) Its value at $20.00 per ton?

(c) How many crops of corn were grown in the 16 years?

(d) What was the value per acre of the com at $1.00 per bushel if it averaged 26.6 bushels per acre?

(e) How many crops of wheat followed immediately a crop of corn?

(f) If these wheat crops averaged 17.68 bushels per acre what was their total acre value at $1.50 per bushel?

(g) How many crops of wheat followed immediately a crop of wheat?

(h) If these averaged 20.70 bushels per acre, what was their total acre value at $1.50 per bushel?

(i) What is the total value of all the crops raised on one acre under the alfalfa, corn, wheat rotation for 16 years?

4. Compare the total value of the 16 year production of one acre under the alfalfa, corn, wheat, rotation with the total acre value of the 16 successive corn crops. The difference in these totals is $___________ in favor of ___________.

5. Compare the total acre value of the alfalfa, corn, wheat, rotation crops with that of wheat raised continuously for the 16 years. The difference is $___________ in favor of ___________.



XII. The 1957 production of brome grass seed in each of the crop reporting districts of Kansas, as shown in the accompanying map, is shown in Table III.

see caption below

The Kansas State Board of Agriculture has divided the state into nine "crop reporting" districts, as shown in the above map. These are convenient for compiling and presenting data concerning precipitation, crops, livestock production, and many other statistics which vary by years or from area to area within the state. On this map you can look up your own county and know the district in which it is included, as in Tables I and III.

1. Calculate the yield in pounds per acre for each district and for the whole state.

2. Which district had the highest yield per acre? The lowest?

3. What per cent of the highest yield was the lowest?

4. a. What was the total production of your district?

b. What per cent of the total Kansas production was this?

5. a. What was the yield per acre in your district?

b. What per cent of the highest yield was this?


XIII. According to a recent estimate there were 460 million acres, or about 718,750 square miles of woodland and forest in the United States, not counting Alaska, and Hawaii, distributed as shown in Table IV.

1. Fill in the blank spaces in the table.

2. According to this estimate, what percentage of the total area of the area of the United States was forest? (See Table II for area of U.S.)

3. If Kansas had this same percentage of its area in forest, how many square miles of forest would there be in Kansas? (See Table II.)

4. How many acres of forest would there be in Kansas?

5. If your county had this same percentage of its area in forest, how many square miles of forest would there be in your county?

6. How many acres of forest would there be in your county?

(The soil conservation office in your county seat may have information of the actual acreage of forest in your county.)


see caption below

The above map shows the geographic sections of the United States, as used by the Bureau of the Census for population statistics. These divisions were also used by the Fish and Wildlife Service for the national survey of fishing and hunting. By referring to the map you can see that Kansas is in the West North Central section; you can also find out which section includes any other state in which you may be interested.


XIV. In 1955 the United States Fish and Wildlife Service made a survey(2) of hunting and fishing in the United States. About 300 interviewers called on more than 20,000 homes to get information about hunting and fishing and the amounts of money spent on these activities. It was found that about one third of all households visited had one or more fishermen or hunters, and that about 17.6 per cent of all persons 12 years old and older fished, and that about 10 per cent hunted.

The accompanying map shows the percentages of persons 12 and older who fished and hunted in each of the geographical sections of the United States. In each section the upper figure shows the percentage who fished and the lower figure the percentage who hunted. The total estimated number of persons 12 and older in each of the sections was as follows:

New England 7,919,000
Middle Atlantic  24,869,000
East North Central  25,733,000
West North Central  9,201,000
South Atlantic  14,336,000
East South Central  7,959,000
West South Central  10,250,000
Mountain  4,529,000
Pacific  13,570,000

1. Calculate the total number who fished and the total number who hunted, in each of the sections and in the entire United States.

The fishermen reported that they spent an average of $92.00 each per year on their fishing; the hunters said that they spent an average of $79.50 each per year on their hunting.

2. Calculate the total amounts spent for fishing and for hunting.

During the year, 13,737,000 fishing licenses were bought at a total cost of $37,240,000 and 9,951,000 hunting licenses were bought at a total cost of $39,935,000.00.

3. What was the average cost of a fishing license?

4. What was the average cost of a hunting license?


XV. According to the Kansas Forestry, Fish and Game Commission,(3) the following license revenue was received during the fiscal years ending June 30, 1957, and June 30, 1958.

1. Calculate the total cost, for the two years, of each of the following:

a. Resident hunting licenses
b. Non-resident hunting licenses
c. Resident fishing licenses
d. Non-resident fishing licenses, season
e. Non-resident fishing licenses, VE-day
f. Trapping licenses
g. Combination licenses
h. Quail stamps
i. All hunting licenses
i. All fishing licenses
k. All licenses and quail stamps

For those licenses of which the price is uniform, the cost per license is shown in Table V. Non-resident licenses vary in price, according to the state in which the hunter or the fisherman lives.

2. How many resident licenses of each type were sold?

3. What was the average cost of all resident licenses, including quail stamps?

(3) Seventeenth Biennial Report, Kansas Forestry, Fish and Game Commission, Pratt, Kansas, 1958.

XVI. Find out how many licenses of each type were bought in your county, and calculate the total amount paid in your county, for each type of license and for all types of licenses together.


XVII. The yield of fish from a pond depends on the fertility of the pond. Pond water which is low in fertility may be improved by the addition of certain types of fertilizer. The amount of fertilizer applied per acre of surface water varies because all ponds are not equally low in fertility and they are deficient in different ways. Fertilizers differ in percentage of active material. For example, a mixture containing chemicals equivalent to 5 per cent of nitrogen, 10 per cent of phosphoric acid, and 5 per cent of potassium is called a 5-10-5 fertilizer. Such mixtures are often used to increase the yield of fish from a pond. Table VI gives the fertilization data for a number of private ponds in a nearby state.

1. Calculate the total cost of fertilizing each of these ponds.

2. Calculate the cost per acre for each pond.

Pond B was fertilized over a five-year period, the first and second years at the rate of 80 pounds of 5-10-5 per acre, and the next three years at the rate of 60 pounds per acre.

3. What was the total cost of the program?



XVIII. In a lake or pond nearly all the animal life depends on the green plants growing in the water -algae, pondweeds, and the like. These plants contain chlorophyll and make their own food from nonliving (inorganic) materials, by a process known as photosynthesis. They are commonly known as producers. Animals, which live on these plants or on other animals, are known as consumers. Bacteria and other microscopic plants which lack chlorophyll and therefore do not manufacture food, are known as reducers. They carry on decay, by which they obtain their food from dead organic matter and in the process return to the water carbon dioxide and minerals necessary for growth of higher plants and animals.

The transfer of food energy through a series of organisms, beginning with the producers and ending with the final consumers, is known as a food chain. Most food chains have from two to five links. Thus a two-link chain is represented by the food chain: grass to cow. Grass to rabit to coyote represents a three-link chain. From algae to daphnids (microscopic or very small crustaceans) to minnows to bass is a chain of four links, and if man eats the bass the chain is lengthened to five links.

Each link in a food chain lowers the efficiency with which the food produced by the producer is used, because much energy is lost in each transfer. Thus in one experiment it was found that 25 ounces of algae were needed to produce only two ounces of daphnids. Some average values obtained in various research studies are shown below. In each case the ratio shows the number of ounces (or other unit) of food required to produce one ounce (or other unit) of the consumer.

Algae to daphnids 8 to 1
Algae to insect larvae 9 to 1
Algae to minnows 7 to 1
Algae to catfish  9 to 1
Daphnids to minnows 6 to 1
Insect larvae to sunfish  11 to 1
Minnows to bass  8 to 1
Sunfish to bass  7 to 1

1. According to the above averages, how many pounds of algae are needed to produce one pound of fish in each of the following food chains?

a. algae to catfish

b. algae to insect larvae to sunfish

c. algae to minnows to bass

d. algae to daphnids to minnows to bass

e. algae to insect larvae to sunfish to bass

2. In Pond A 1000 pounds are eaten by catfish; in Pond B 1000 pounds of algae are eaten as in food chain (e) above. How many pounds of fish are produced in each pond?

3. If it costs $12.00 to produce 1000 pounds of algae in each of the two ponds,

a. How much per pound do the catfish from Pond A cost?

b. How much per pound do the bass from Pond B cost?


1 gallon equals 231 cubic inches

1 cubic foot equals 7.48 gallons

1 cubic foot of water weighs 62.4 pounds

1 gallon of water weighs 8.34 pounds

1 square mile equals 640 acres


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