Firewood (Cordwood) Math Problems

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

Monday, July 13, 1914:  I remember now what I did today, which wasn’t anything unusual.

Source: Wikimedia Commons

Source: Wikimedia Commons

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

Grandma—You remembered. . . so please tell us. . . WHAT did you do?

Did you work in the fields? . . . weed the garden? . . . can green beans? . . . stack fire wood for next winter? (Oh, never mind. . . Maybe this is the wrong time of year for stacking wood.)

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Several days ago a reader commented that he’d enjoy a post about stacking firewood. Well, here goes-

I haven’t seen any old articles about how to stack firewood, but I have seen cordwood problems in a hundred-year-old arithmetic book:

Cordwood

Cordwood is 4 ft. long.

A cord of wood is a pile 8 ft. long and 4 ft. high.

A cord of stove wood is a pile of wood 8 ft. long, 4 ft. high, and of any length that will fit a stove.

Rule: To find the number of cords of wood in a pile, multiply the length of the pile by the height in feet and divide by 32.

Problems

1. How many cords of wood are there in a pile 18 ft. long and 4 ft. high?

2. At $6 per cord, what is the value of a pile of oak cordwood 40 ft. long and 6 ft. high?

3. Which is cheaper for a man living in town: to buy stove wood 16 in. long at $3 per cord, or to pay $6 per cord for cordwood and give a man $2 to saw and split it into stove wood?

4. How many cords of wood 16 in. long can be placed cross-wise in a wagon bed 10 ft. long, 3 ft. wide, and 14 in. deep?

5. Make an estimate of the number of cords of wood in the fallen trees that are wasting on your father’s farm. What is the value of this wood at $2 per cord?

Rural Arithmetic (1913) by John E. Calfee

You may also enjoy these previous posts with other hundred-year-old math problems:

Hundred-Year-Old Rural Math Problems

Unusual, Odd, and Strange Math Problems

More Unusual, Odd, and Strange Math Problems

Old Math Problems

Cube Root Word Problems

1911 Algebra Problems: The Lusitania and Molasses

A Hundred Years Ago Chicago Schools Had a Female Superintendent!

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

Monday, July 6, 1914:  Nothing doing

Ella Flagg YoungPhoto caption: Probably the most distinguished and influential superintendent of schools in this country, and especially revered in the West—Mrs. Ella Flagg Young, pictured in the electric runabout in which she goes from school to school. Married teachers are not discriminated against in Chicago, and the records in Mrs. Young’s office show that their efficiency marks are as high as those of unmarried teachers. (Source: Good Housekeeping. January, 1914)

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

Since Grandma didn’t write much a hundred years ago today, I thought you might enjoy this photo and caption that I found in an 1914 issue of Good Housekeeping.

Until I saw it I didn’t know that there were any female school superintendents back then—though I’m appalled that Chicago Schools considered it necessary to analyze whether married teachers were as efficient as unmarried ones. Thank goodness it turned out that they were.

(An aside: I wonder how they measured teacher effectiveness back then. Hmm. . . . maybe I’ll have to research that for a future post.)

The Goop Directory

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

Thursday, October 16, 1913:

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

Goop.3

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

This is the fourth of five days that Grandma combined into one entry. Since she didn’t write anything specific for this date I’m sharing several pages from a fun children’s book published in 1913 that I found.

The book is called The Goop Directory and contains short scenarios of children who were naughty—or, using the terminology in the book, “Goops.”

title page

title page

Goop.1

Goop.2

The book that I have was well-loved—perhaps that isn’t exactly the right term—and some pages have coloring on them.

Other pages have remnants of names written in pencil that were later erased.  I can just picture a child going through the book and identifying which of their playmates were like each of the characters in the book. Obviously a Goop once owned this book!

Goop.5

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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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The Problem with Tests and Exams a Hundred Years Ago

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

Tuesday, April 15, 1913:  Tomorrow witnesses the beginnings of our final examinations. I do hope that I’ll pass.

Source: Wikimedia Commons

Source: Wikimedia Commons

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

Hang in there Grandma—you’re almost there. Your graduation invitations have been mailed. You’ll navigate your way through this final hurdle.

The way students are tested today is controversial. I was amazed to discover that people also had concerns about exams a hundred years ago.

Here is an excerpt from an article in the October 1912 issue of Ladies Home Journal called “The Black Beast in Every Child’s School Life”:

No evil in the present American public-school system is, to my mind so great and so manifestly unjust to the pupil as what may very aptly be called “the black beast of every child’s school life”: examinations, as they for the most part now are conducted. .

Examinations, as they are now almost universally conducted in our schools, are a memory extortion pure and simple. An examination is supposed to be a final twist which will forever fix in the memory as a whole the items that have been put into it one at a time.

Why should we longer put our children to these terrible strains as we do now? I have tried to think out a good reason and I am unable to do so.

The dictionary is always at hand when the pupil is studying his lesson, and so can be referred to at will. Besides this the grammar is always accessible, to explain new an unusual forms and phrases that appear in it.

But when examination day s comes every one of these rightful and useful helps in his work is taken away from him, and arm’s length of memory alone if he is asked to translate, give forms of words and account for constructions, without any assistance from the tools that he ordinarily has been permitted to use.

Memory-test examinations must be abolished. Time was when the word “scholar” meant a wailing dictionary. There are too many words now, and knowledge has too vast a reach, to be compressed into any one single head. Besides, what’s the use? Dictionaries are cheap. The missions can have cyclopedias now; and things are so much easier to get at, so much more reliable withal so much more liable to keep in any climate when preserved for ruse in this way.

Did Students Memorize Dates in History a Hundred Years Ago?

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

Tuesday, February 4, 1913: We had an exam in General History this morning. It was a review of all we had gone over this year. I was so afraid I’d make a sorry mark, so I began to review but I didn’t get over it all. I got some things wrong, but then I know I got more right. At least I think so.

Picture on page 155 of the hundred-year-old textbook

Roman Fleet (Source: Outlines of General History by V.A. Renouf)

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

Did Grandma need to memorize dates for the exam?

Here’s what the Suggestions for Teachers section of a hundred-year-old text-book had to say about memorizing dates:

In conclusion, I will touch on the question of learning dates. These should be memorized by all students. It is well to bring as many events as possible into relation with a memorized date. The few students who have a ready memory for dates can be encouraged to remember most or all of them; but the majority of the class should not be burdened with more than are necessary for a correct general perspective of the centuries.

Outlines of General History (1909)  by V.A Renouf

Would a history teacher today agree or disagree with this suggestion?

The book also included some sample questions that teachers might use. I did a previous post that included a few of the sample questions:

History Test Questions a Hundred Years Ago

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