Thursday, December 16, 2010

Math problems of the week: 4th grade Investigations vs. 1920's Math

"Real-world" measurement problems:

I. A page from the "Measures of Length or Distance" section of the 4th grade chapters of Hamilton's Essentials of Arithmetic (published in 1919), p. 167:

1. A foot = ____ inches.
2. A yard  = ___ feet.
3. What measure should you use to measure the length of your book? of your desk? the width of your schoolroom? the length of the blackboard?
4. Measure 5 1/2 yards or 16 1/2 feet along the street or on the school ground. Call it one rod.
5. With a tape measure 5 1/2 yards long, measure the length and width of your school grounds in yards and feet.
6. With a pole or a tape a rod in length, measure the distance in rods and feet around of square or a field.
7. 20 city blocks, each 16 rods in length, are 320 rods long. This is called one mile.  1 miles = 320 rods.
8. There are 5280 feet in one mile. How many feet are there in 3 miles.
9. Memorize this table:
12 inches (in.) =  1 foot (ft.)
3 feet  = 1 yard (yd.)
5 1/2 yards, or 16 1/2 feet = 1 rod (rd.)
320 rods = 1 miles (mi.)
5280 feet = 1 mile

II. A page from Sessions 1.1 and 1.2 of the "Size, Shape and Symmetry" unit of the 4th grade Investigations (TERC) curriculum:

When and How Do You Measure Length?

Ask an adult to tell you about at least four situations in which he or she measures. Write each situation in one of the boxes. Answer the following questions about each situation.

* Did you need to measure exactly or estimate?
* If you estimated, how did you estimate?
* What tools did you use?

Situation 1: [Box 1]
Situation 2: [Box 2]
Situation 3: [Box 3]
Situation 4: [Box 4]

III. Extra Credit:
Discuss how the "real world" has changed in the course of the last century.


sean said...

Well, in most of the real world, we don't use arcane measurements like "feet," "yards," and "miles" - and don't even get me started on "rods!"

Barry Garelick said...

Fabrics are still sold by the yard in this country, and last time I checked, we still haven't converted over to the metric system. Pints, quarts and gallons are still used as measurements. And feet and miles are still used. The advantage of teaching such "arcane" measurements is because math problems involving conversion of units provides an avenue for mastery of dimensional analysis which is pretty handy in science courses and the field in general. Solving problems what time was it 2 hrs and 35 minutes earlier than 6:30 AM is a good way to re-emphasize how place value works.

You're correct that "rods" aren't used any more.