What Does Declension Mean?

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

Wednesday, January 10, 1912: There is sleighing now, but all the same, I haven’t got a ride yet. Began with our monthly exams today. I had a hard declension down pat in Latin, but it happened to be excluded in the number of questions.

Rachel and Al were down this evening. I wish I knew all about the questions tomorrow.

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

I learned a new word today. Declension means the change of form in some languages that nouns, pronouns, and adjectives undergo to indicate distinctions such as gender, number, person, and tense.

Rachel Oakes was a friend of Grandma and her sister Ruth. Al was Rachel’s brother. They lived on a nearby farm.

How to Find the Temperature on Any Date in Any City in US

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

Tuesday, January 9, 1912: I believe a fellow could freeze his ears off on a day like this. You certainly don’t have to use paint on your cheeks on such a morning as we had today. Pa took me to school. Jimmie didn’t go. Got my face blackened at school today and burnt in the bargain.

Weather data sheet for Williamsport PA (January, 1912).

For the complete January 1912 data sheet, click on Williamsport.

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

In nearby Williamsport the low on January 9, 1912 was 7 degrees and the high was 32 degrees. It was a cold morning, but not as cold as the previous day. On January 8 the low was –1 and the high was 16.

I found the weather data on the National Climatic Data Center website. Several people have asked me how to find old data on that site.

Here are the directions for finding weather data for a city on a certain date:

On the page that the link goes to, scroll down to “Global Historical Climatology Network-Daily” and click.

Then scroll down to “Individual Station Original” and click

Select the state that you are interested in. The names of lots of weather stations in the state will appear. Scroll down to the city you are interested in. Some cities are listed several times because there are different weather data series for that city.

For example, Williamsport PA is listed three times. I wanted the series that included 1912, so I selected the one that said, “Williamsport 1895-02 -1977-09.” This means that there is weather data from February (02), 1895 through September (09), 1977.  Williamsport had two data series for this time period–one with river levels on the West Branch of the Susquehanna River; the other temperatures.

 

Cube Root Word Problems

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

Monday, January 8, 1912: A regular snow storm set in this afternoon. How beautiful the snowflakes looked as they descended to ground. Am now able to extract the cube root without difficulty. Pa came for Jimmie and me this evening.

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

The teacher must have clarified how to do cube roots. Grandma was struggling with cube roots the previous Friday.

As a parent who had strong opinions during the “math wars” of the 1990’s about what should be included in (and, perhaps more importantly, what should be excluded from) the math curriculum, I’m fascinated by early 20th century math text books.

In textbooks from a hundred years ago, there was more focus on calculation than there is today but they also contained some cool word problems. Cube roots are a great example of this.

Here are some cube root word problems from a 1911 textbook called Kimball’s Commercial Arithmetic:

1. If a cubical block contains 21,952 cubic inches, how many square feet of paper will be required to cover the entire surface?

2. The entire surface of a cubic block is 384 square feet. How many 1-foot cubes can be cut from the block, allowing nothing for waste?

3. A cubical cistern holds 400 bbl. of water. How deep is it?

4. What are the dimensions of a cube that has the same volume as a box 2 ft. 8 in. long, 2 ft. 3 in. wide, and 1 ft. 4 in. deep?

The texts also contained lots of “tricks” and principles.

Principles

1. The cube of a number cannot have more than three times as many figures as its root, nor but two less.

2. If a number is separated into periods of three figures each beginning at the units’ place, the number of figures in the cube root will be the same as the number of periods.

I thought of several easy cube roots (100 is the cube root of 1,000,000. and 5 is the cube root of 125.), and decided that the principles are correct. (Of course they were correct—but somehow I felt better after I thought of a few problems to confirm it.)

If you’re a math geek, here are some previous posts that explored the math curriculum and problems from a hundred years ago.

Odd, Unusual, and Strange Math Problems

More Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

An Old Mental Math Trick

Lowest Common Multiples and Highest Common Factors

Fractions in 1911 Algebra Book

Hundred-Year-Old Recipe for Caramel Corn (Sugared Popcorn)

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

Sunday, January 7, 1912: Walked to Sunday School this morning though the new fallen snow. I wore my old hat because I didn’t want to get snow on my new one. Miss Carrie was over this afternoon, and we had popcorn by the way of refreshments. By so doing I broke the third commandment for I was the one who did the popping.

Caramel Corn (Sugared Popcorn)

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

Miss Carrie was Grandmas’ friend Carrie Stout. She lived on a nearby farm. I believe that the third commandment refers to “Remember the Sabbath day to keep it holy.” Today that is generally the fourth commandment, but I believe that some denominations number the commandments differently.

The popcorn that Grandma popped was raised on the Muffly farm. In May 1911 she wrote about planting popcorn. In the fall it would have been harvested and hung to dry. When the corn had just the right amount of moisture for popping, the family would have shelled it and stored it in a glass jar until they were ready to pop it.

Grandma probably popped the corn in a cast iron skillet. I bet that she sometimes “dressed it up” and made Caramel Corn.

Here’s a great hundred-year-old recipe for Caramel Corn  that was in the 1912 Boston Cooking School Cook Book by Fannie Farmer. (It is called Sugared Popcorn in the book.)

Sugared Popcorn (Caramel Corn)

2 quarts popped corn

2 tablespoons butter

2 cups brown sugar

1/2 cup water

Put butter in saucepan, and when melted add sugar and water. Bring to boiling point, and let boil for sixteen minutes. Pour over corn, and stir until every kernel is well coated with sugar.

I salted the popped corn before mixing with the syrup. This recipe is a keeper. The Caramel Corn turned out perfectly.

New Mexico Becomes the 47th State

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

Saturday, January 6, 1912: Oh you lonesome Saturdays. It’s just about the same every week-end when you have to stay at home.  Ruth went to Turbotville today and forgot to ask me to go along. When she came home she thought I ought to have done her milking but I didn’t.

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

Since today’s diary entry is fairly self-explanatory I’ll share an interesting piece of trivia—

A hundred years ago today New Mexico became the 47th US state.

New Mexico is highlighted in red. (Map Source: Wikipedia)

(Arizona would become the 48th state on February 14, 1912. Alaska and Hawaii won’t be admitted until 1959.)

A hundred years ago New Mexico was still considered part of the wild west. It’s amazing how much the state has grown.  The population of New Mexico was about 327,000 in 1912; today it’s about 2.1 million. In 1912 Albuquerque had only about 11,000 residents; it now has 550,000. Santa Fe, the capital, had 6,000 residents in 1912; today it has about 68,000 people.

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?

1912 Dresses That Could be Made for One Dollar

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

Thursday, January 4, 1912: Such a time as we had this morning. Ma was going to Milton and oh she had to make her train. Thought I might possibly be late to school with all her flying around, but I got there in plenty of time. I must be one of these early birds that you don’t like to hear so much about. I thought maybe she’d get me a nice surprise, but she didn’t.

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

What was Grandma was hoping that her mother would bring her? Might it have been a dress pattern and fabric to make it?

A 1912 Ladies Home Journal article showed examples of dresses that could be made for one dollar. (Yes, you read that right! $1. Money was worth a lot more a hundred years ago.)

Well-chosen material, neat sewing, and the careful adjustment of a dress are more to be desired than expensive material badly made up and carelessly adjusted.

This is easily demonstrated in the simple dress of blue dimity above, and you can readily duplicate it for one dollar. Pattern No. 6624, which is ten cents, requires in size 16 years five yards of 36-inch material at fifteen cents a yard, and buttons at fifteen cents. The lawn bow at the neck is not included in the cost, as every girl usually has such an accessory or can make one from fine lawn or net or from scraps of lace or embroidery in her scrap-bag. . .

“Would You Believe These Cost Only One Dollar?” (Ladies Home Journal, February 1912)