# TeeJaw

Are you as smart as a 1912-era Bullitt County, Kentucky 8th grader?

• Jack Harvey

WIth a college degree, a graduate degree and a professional degree I think I would be happy to get a D- on this one:-(

• TeeJaw

This question appears under the heading, “Arithmetic”.

8. How long a rope is required to reach from the top of a building 40 feet high to the ground 30 feet from the base of the building?

I don’t think there is any way to solve this problem with arithmetic alone because it’s really a geometry problem, unless the Pythagorean Theorem is part of arithmetic. From the application of geometry one can see that these dimensions describe a right triangle with the length of the rope as the hypotenuse. With that you know that the relationship of 30 squared plus 40 squared equals the square of the length of the rope. In other words, 900 plus 1600 equals 2500 and the length of the rope equals the square root of 2500, or 50 feet.

You actually don’t need to do that calculation because it is obvious that the question describes a 3-4-5 right triangle and thus a 50 foot rope is required. Anyone with a semester of plane geometry would quickly solve it that way, but I wonder how many 8th graders today could do it.

The ship and anchor problem in the Pages section of this blog is from my 8th grade class at Carey Junior High in Cheyenne, WY in 1958. I wonder if such a sophisticated problem appears in any 8th grade class in America in 2013.

• Sean

The rope question is technically geometry, BUT, back in the day – I went to elementary school in the 1970’s – from about 4th grade on, part of the arithmetic curriculum touched on some basic geometric principles: things like the Pythagorean triples 3-4-5, 6-8-10, 5-12-13, 7-24-25, 8-15-17 right triangles. Critics of these types of test will scream “Well, that’s just memorization.” These critics need to understand that virtually ALL triangle questions on the SSAT, PSAT, SAT, ACT, GMAT and GRE involve those very Pythagorean triangles. Having a solid foundation – including some memorization – makes application of the principles all the easier.

• TeeJaw

I agree. Some things should be memorized because they will stay with you and help you later, especially if you memorized them as a kid. Just because one memorized something doesn’t mean he doesn’t understand it, as the memorization critics seem to think. Ability to commit something to memory and keep it there may also be related to overall cognitive ability.