Thursday, May 6, 2010

Math problems of the week: middle school 1900's math vs. Core Plus Math

I. From Hamilton's Essentials of Arithmetic, Volume II (published in 1919), first four word problems involving rate (intended for students in "year 7"), p. 253:

How much will 30 dozen eggs cost when 70 dozen cost 42?

When Irish potatoes are 5 lb for 17 cets, how much should a bushel of 60 lb. cost?

If 25 men can build a bridge in 18 days, how long, at the same rate, will it take 15 men to build it. (Notice that fewer men require more time. 15: 25 = 18: ?).

It is estimated that 90 men are necessary to grade a certain street in 45 days. If only 81 men are hired to do the work, how long will it take them?

II. From the Core-Plus Mathematics ("a four-year curriculum that replaces the traditional Algebra-Geometry-Advanced Algebra/Trigonometry-Precalculus sequence") Course 1 Student Study Guide, first four word problems involving rate, p. 30:

Which is the better deal? $18 for 3 bracelets; $30 for 5 bracelets

Which has the fewer calories per serving? 120 calories in 2 servings; 360 calories in 6 servings

Which is the better pay? 4 hours worked for $12; 7 hours worked for $28

Which is the better deal? 15 blank CDs for $5; 45 blank CDs for $15

III. Extra Credit
Comment on the following:

Numerical calculations in the pre-calculator age.

Everyday math problems before "Everyday Math."

Rote patterns in word problems before and after the age of aversion to rote learning.

1 comment:

Alex Francis said...

Argh! Three of the four problems in the Core-Plus book have the same non-answer. Not only is the correct answer confusing (it's unfair to ask "which" when the answer is "they are the same"), but once students have figured out the answer to one of them there's not even anything to discuss with respect to the answers to the other two.