Marveling At The Historical

Math Oldies But Goodies

  • About This Blog

    This blog is mostly about math procedures in textbooks dated from about 1825-1900. I’m writing about them because some of the procedures are exquisite and much more powerful, and simpler, than some of the procedures in current text books. Really!

    I update this blog as frequently as possible ... every 2-3 days. And, if you are a lover of old texts and unique procedures, you might want to talk to me about them, at I’m not an antiquarian; the books I have are dusty, musty, brown-paged scribbled-in texts written by authors with insights into how math works. Unfortunately, most of their procedures have vanished. They’ve been overcome by more traditional perspectives, but you have to realize that at that time, they were teaching the traditional methods.

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Percent Problems from 1868

Posted by mark schwartz on June 28, 2016


After presenting percent and having students work many problems from the text, I decided to give them a set of problems from 1868. I did this for several reasons: first, I gave this as an in-class quiz in which I allowed the entire class to discuss strategies, compare answers, and work with others. I roamed the room to watch things happen. Second, I gave these problems because they all had fractions in them as well as related information that they had to decide where it fit in the problem. Problems like these are rare in today’s texts. It was a real challenge for the class but some of the students actually said it was fun! The story begins with a copy of what I handed to them. I’d like to note that I taught a visual percent proportion method only (no formulae, no short cuts) – Percent Proportion – which you can see in this blog. It’s a slower procedure but gives students a better understanding of percent. They said so.

The Story

Here’s the assignment I gave the class …

The 5 problems below are from The Progressive Practical Arithmetic by Daniel Fish. (Ivison, Phinney, Blakeman & Co, Chicago, 1868, pg. 228). There are some minor punctuation and word changes.

Please show all your setups and solutions. Consider carefully how to handle the fractions in the problems. Consider that only non-repeating decimals will give you a precise and accurate answer, so you may have to use improper fractions in your calculations, or use the “fraction” key if your calculator has one. Feel free to work with anyone (or everyone) in the class. Be careful handling dollars, cents and decimal points, and fractional answers. ALL ANSWERS ARE MONEY – DOLLARS AND CENTS.

Before you start, any questions?

  1. A miller bought 500 bushels of wheat at $1.15 a bushel, and he sold the flour at % advance (profit) on the cost of the wheat. What was his gain?

2. A grocer bought 3 barrels of sugar, each containing 230 pounds, at cents a pound, and sold it at percent profit. What was his whole gain?

3. A sloop, freighted with 3840 bushels of corn, encountered a storm, when it was found necessary to throw percent of her cargo overboard. What was the loss, at cents a bushel?

4. A gentleman bought a store and contents for $4720. He sold the same for percent less that he gave, and then lost 15 percent of the selling price in bad debts. What was his entire loss?

5. A man commenced business with $3000 capital. The first year he gained percent which he added to his capital. The second year he gained 30 percent on the whole sum, which gain he also put into his business. The third year he lost percent of his entire capital. How much did he make in the 3 years?


Roaming the room and hearing the discussions and debates was a lot of fun. I occasionally answered questions with questions on how to handle the values and the relationships. As it turned out, when the work was turned in, everybody got it! And, of course, the class wanted this format for all future quizzes, but I noted to them that I had other formats in mind. Someone pointed out how valuable this learning experience was and why would I not want to repeat it? Ah, logic, but as it turned out the other quiz formats turned out to be good learning experiences too.

Below are the answers if you want to play with these 5 problems.

  1.    $95.83 &1/3 (I accepted $95.83; our money system stops with pennies)
  2.    $10.35
  3.    $900
  4.    $1209.50
  5.    $981.25

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