Hundred-Year-Old Rural Math Problems

18-year-old Helena Muffly wrote exactly 100 years ago today: 

Wednesday, October 15, 1913:

10/13 – 10/17: Nothing worth writing about for these days. Don’t go any place or do anything of much importance.

Source: Rural Arithmetic (1913)

Source: Rural Arithmetic (1913)

Her middle-aged granddaughter’s comments 100 years later:

I’m still fascinated by the 1913 textbook I found called Rural Arithmetic by John E. Calfee that I mentioned the previous two days. Since Grandma didn’t write anything specific for this date a hundred years ago, I am going to share a few more problems today.

Here are the problems:

1.  If a cord of wood for cooking purposes lasts a family 3 weeks, how much does the family pay out in the course of a year for cook-stove wood when wood is $2 per cord? . . . when wood is $3 per cord?

2. If a quail, in the course of a year, eats 25¢ worth of grain, and destroys $2 worth of harmful insects and weed seed, how much has a farmer injured himself by killing 3 pairs of quails if a pair raise a brood of 12 each year?

3. If the water running from a piece of land that has been planted with corn contained 1 pound of sediment for every 250 gallons of water, how much soil was carried away from a 40-acre corn field after a 2-inch rainfall, with 1/4 of the water running off?

4. If a team travels 16 1/2 miles a day with a breaking plow, how many days work can a man save in plowing 30 acres (110 rod by 43 7/11 rod) by using a 16-inch instead of a 12-inch plow?

5. A county store on a gravel road pays 1¢ a mile for each 100 pounds of freight hauled from the railroad station.; a county seat of the same road 24 miles from the railroad, 18 miles of which are not gravel, pays 2¢ a miles for hauling 100 pounds of freight. What is the annual bad-road tax paid by this county seat upon 300,000 pounds of freight?

rural.arithmetic.p. 86

rural.arithmetic.p. 87

It’s amazing how much you can learn about routine activities (as well as issues and challenges) a hundred years ago from word problems.

It’s also intriguing to think about how pedagogical experts a hundred years ago must have believed that it was important to have textbooks with problems that were designed specifically for the rural context that the students experienced in their day-to-day lives.

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1913 Math Problems Designed to Motivate Students to Get an Education

18-year-old Helena Muffly wrote exactly 100 years ago today: 

Tuesday, October 14, 1913:

10/13 – 10/17: Nothing worth writing about for these days. Don’t go any place or do anything of much importance.

Postcard with picture of Old Main at Penn State (postally used: 1908)

Postcard with picture of Old Main at Penn State (postmark: 1908)

Her middle-aged granddaughter’s comments 100 years later:

Since this is the second of five days that Grandma combined into one diary entry, I’m going to pick up where I left off yesterday.

Yesterday, I told you a little about a 1913 math textbook called Rural Arithmetic by John E. Calfee that included a section titled “Educated Labor.” That section included word problems apparently designed to motivate students to continue their education.

Here’s a couple problems from the book:

1.  Two classmates leave the country school, one for work for 75¢ a day with board; the other borrows $250 and goes away for 3 years to a trade school and learns a trade which pays him $1.75 a day with board. Counting each able to average 285 days a year, at the end of 10 years from the time they leave the country school which will have earned more money?

2. The average salary of the man who has completed a college course is about $1000 a year, and the average wages of the man who has completed the common-school studies [an 8th grade education] are almost $450. If it takes 1440 days to complete a high-school and college course, what is the average value of each day spent in taking such a course? (The college-trained man spends 8 years of the work period in school, and has an annual expense of $450 for college.)

Rural Arithmetic (1913)

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Capacity (Volume) Word Problems

17-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, January 16, 1913:  We had an examination in Geometry this morning. I think I will make a better mark than what I did the other time.

Source: Kimball's Commercial Arithmetic (1911)

Source: Kimball’s Commercial Arithmetic (1911)

Her middle-aged granddaughter’s comments 100 years later:

What was the Geometry test about—proofs? . . . angles? . . . shapes? . . . capacities?

The directions for doing capacity problems in a hundred-year-old textbook (I think it was called volume by the time I was in school. Is capacity the same thing as volume?) seem very different from what I remember doing when I was a student:

The method of finding the contents of any regular vessel in gallons, bushels, barrels, etc. is called gauging.

The capacity of tanks, cisterns, etc. is usually expressed in gallons or barrels. In every liquid gallon there are 231 cu. in.

To find the exact number of gallons in any vessel, divide the number of cubic inches in the vessel by 231.

To find the number of gallons in a cylindrical vessel, multiply the square of the diameter by the height, and this product by 5 7/8.

To find the approximate number of gallons in a cistern, multiply the number of cubic feet by 7 1/2 and from the product, subtract 1/400 of the product.

The capacity of bins, etc. is usually expressed in bushels. The standard bushel in the United States is a measure 8 inches deep, 18 1/2 inches in diameter, and contains 2150.42 cubic inches.  Hence, to find the number of bushels in any bin, divide the number of cubic inches in the bin by 2140.42.

Kimball’s Commercial Arithmetic (1911)

Got that?  Want to try some problems?

  1. Find the contents in gallons of a tank 4 ft. square and 5 ft. deep.

  2. The water in a cistern 8 ft. square is 2 ft. deep, how many gallons does it contain?

  3. A bin 8 ft. by 4 ft. by (?) contains 90 bushels of grain. Find the missing dimension.

  4. How many tons of water will fill a tank 11 ft. 8 in. by 3 ft. 6 in. by 2 ft. 3 in., if the weight of a cubic foot of water is 1,000 ounces?

Two Old Mental Math Tricks for Adding Fractions

17-year-old Helena Muffly wrote exactly 100 years ago today: 

Tuesday, September 24, 1912:  It is raining now. I guess or was. Had an exam in Geometry. Took up Arithmetic today. Didn’t have to but I chose to do so.

Her middle-aged granddaughter’s comments 100 years later:

High school courses apparently were only a month of so long a hundred years ago.

I wonder why Grandma decided to take Arithmetic if it wasn’t required. Maybe she enjoyed doing mental math.

Here are two mental math tricks for adding fractions that I found in a hundred year old textbook:

Example 1: Add two fractions whose numerators are 1.

Solution: Add the denominators, and place the sum over the product of the denominators.

Example 2: Add two fractions whose numerators are alike and greater than 1.

Solution: Add the denominators and multiply the sum by the numerator of either of the fractions, and write the product over the product of the denominators.

Source: Kimball’s Commercial Arithmetic (1911)

If you like  math, you might also enjoy these previous posts:

An Old Mental Math Trick

Odd, Unusual, and Strange Math Problems

More Odd, Unusual, and Strange Math Problems

Cube Root Word Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

Has the Math Curriculum Been Dumbed Down?

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Friday, January 5, 1912: It’s so cold now. How quickly the weather has changed. I didn’t mind it at all in school for the stove sent forth a regular shower of heat. Was rather freezy coming home and the wind a blowing. We’ve come to the extracting of the cube root in arithmetic and I can’t see very good the way it’s done. But suppose I can after I get some kind of an explanation from somebody and not from the book alone. We had these things several years ago, but my idea of them is now rather hazy.

Cube root example from Kimballs Commercial Arithmetic (1911). If you want to read the example, click on the picture to make larger.

Her middle-aged granddaughter’s comments 100 years later:

Whew, math has changed a lot over the years.

I never learned how to do cube roots when I took math in the 1960’s and 70’s, but I can remember struggling with square roots. My children can manually calculate neither square roots nor cube roots, but they do know how to calculate them using a calculator.

Has the curriculum been dumbed down over the years? . . . or has the tedium been removed so that students have time to grapple with more complex problems?

More Odd, Unusual, and Strange Math Problems

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Monday, October 16, 1911: Nothing new at school or at home. Read several stories after I had worked some problems. Still have some for tomorrow though.

Her middle-aged granddaughter’s comments 100 years later:

I wonder what type of problems Grandma was working on.  I enjoy looking at hundred-year-old math books. The problems are so different from the ones in today’s books.

I’ve previously shared some problems with you.  Here are some more odd, unusual, and strange problems from 1911:

1. If 44 cannons, firing 30 rounds an hour for 3 hours a day, consume 300 barrels of powder in 5 days, how long will 400 barrels last 66 cannons, firing 40 rounds an hour for 5 hours a day?

2. A ditch 80 yards long, 10 ft. deep, and 9 ft. wide was dug by 20 men in 12 1/2 days of 10 hours each; and a ditch 76 yards long and 12 ft. wide was dug by 30 men in 7 1/2 days of 9 1/2 hours each. How deep was the latter ditch?

3. A speculator bought 10 village lots, and gave a 4-months’ note in payment. This note was immediately discounted in the bank at 8%, and the bank discount was $192. What was the average price of the lots?

4. A druggist bought 6 pounds of quinine at $11 per pound, avoirdupois weight, and sold it in 2-grain capsules at 10 cents per dozen. What was his profit?

Kimball’s Commercial Arithmetic: Prepared for Use in Normal, Commercial and High Schools and the Higher Grades of the Common School (1911)

A hundred years ago prescriptions weren’t required and druggists made their own medicines, men actually dug ditches by hand, and labor laws about how many hours a day a person could work had not yet been enacted.

If you want to do the quinine problem–and, for some reason never had a math class that taught you the conversion factors for apothecaries and avoirdupois weights :) – here is the information you need:

Apothecaries Weight

20 grains = 1 scruple

3 scruples = 1 dram

8 drams = 1 ounce

12 ounces = 1 pound

Avoirdupois Weight

16 ounces = 1 pound

In case you missed the previous posts that contained math problems, here are the links:

Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

Old Math Problems

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Wednesday, September 6, 1911: Have to study in the evenings now, instead of sitting around, reading or doing nothing. I got stuck on an algebra problem this evening. Don’t know whether I’ll get it yet or not. I know how to work the problems of that kind but this is a bulky one.

Her middle-aged granddaughter’s comments 100 years later:

I suppose Grandma forgot some math over the summer.

Here are some problems in the first chapter of an algebra book that was published in 1911. Maybe the problems Grandma was struggling with were similar to these.

  1. A bicycle and suit cost $54. How much did each cost, if the bicycle cost twice as much as the suit?
  2. Two boys dug 160 clams. If one dig 3 times as many as the other, how many did each dig?
  3. The average length of a fox’s life is twice that of a rabbit’s. If the sum of these averages is 21 years, what is the average length of a rabbit’s life?
  4. The water and steam in a boiler occupied 120 cubic feet of space and the water occupied twice as much space as the steam. How many cubic feet did each occupy?
  5. Canada and Alaska together annually export furs worth 3 million dollars. If Canada exports 5 times as much as Alaska, find the value of Alaska’s export.
  6. The poultry and dairy products of this country amount to 520 million dollars a year, or 4 times the value of the potato crop. What is the value of the potato crop?

First Year Algebra (1911) by William J. Milne

For additional 1911 math problems see these previous posts:

Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

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