Then & Now

See how you’d’ test as a math student in 1863 and today.

Think you’re pretty bright, do you? Let’s see how you’d fare as a student in 1863—and a student today. The following math problems are taken from two different books. The first was taken from the Introduction to the National Arithmetic on the Inductive System by Benjamin Greenleaf, a book designed for students in common school (grades 1 to 8) in 1863. At the time, young scholars were taught not only addition, subtraction, and multiplication, but also banking, interest, and the assessment of taxes. The second set of problems were taken from Math Trailblazers, the 5th grade math textbook for the Bedford Central School District.

From 1863:

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1. The hindquarters of an ox weighed 375 pounds each, the forequarters 315 pounds each; the hide weighed 96 pounds, and the tallow 87 pounds. What was the whole weight of the ox?

2. A merchant bought five pieces of cloth. For the first, he gave 376 dollars, for the second 198 dollars, for the third 896 dollars, for the forth 691 dollars, and for the fifth 96 dollars. How much did he give for the whole?

3. A merchant bought five hogsheads of molasses for 375 dollars, and sold it so as to gain 25 dollars on each hogshead; for how much did he sell it?

4. John Smith’s farm is worth 7,896 dollars; he has bank stock valued at 369 dollars, and he has in cash 850 dollars. How much is he worth?

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5. Required: the number of inhabitants in the Middle States, including the District of Columbia. In 1850, there were in New York, 3,097,394; in New Jersey, 489,555; in Pennsylvania 2,311,786; in Delaware, 91,532; in Maryland, 583,034; and in the District of Columbia, 51,687.

From 2006:

1. A cheeseburger from a popular fast-food restaurant has 5.7 grams of saturated fat. If you eat 2½ cheeseburgers, how much saturated fat will you eat?

2. The contents of a bottle of liquid dishwasher detergent weigh 2.4 kilograms. How many kilograms do the contents of 4.5 bottles weigh?

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3. Mr. Moreno is buying sports equipment for the school. There are three basketball hoops on the playground. Mr. Moreno paid $19.79 each for basketballs so that every hoop can be used at the same time. How much money did he spend on basketballs?

4. In order for Mr. Moreno’s class to play softball, he needs 3 bats, 2 balls, and a set of bases. Each set of bases includes first, second, third, home plate, and a pitcher’s mound. The bats are $14.55 each. The balls are $4.55 each. Each of the bases costs $2.59. How much money will he spend on softball equipment?

5. A small order of onion rings can have as much as 67.5 milligrams of sodium (salt). How many milligrams of sodium can be in ½ serving?

Answers: 1863: 1) 1,563 pounds; 2) 2,257 dollars; 3) 500 dollars; 4) 9,115 dollars; 5) 6,624,988; 2006: 1) 14.25 grams; 2) 10.8 kilograms; 3) $59.37; 4) $65.70; 5) 33.75 milligrams.