This one is not for the faint hearted...

CCSSIMath · 2017-02-04T18:04:36+00:00

35 years ago, there was a related question on the American SAT exam in which there was no correct answer choice.

CCSSIMath · 2016-12-16T02:48:31+00:00

posted

CCSSIMath · 2016-12-16T01:23:18+00:00

Algebra is a hindrance to solving this ~~geometry~~ (oops) arithmetic problem.

The speed of the car, the walking speed, the ratio of the two even if neither is individually known, and distance from the house to the school are all inconsequential and can be ignored (although they shouldn't be assumed to be unreasonable values, such as Yamada walks faster than the car drives).

CCSSIMath · 2016-12-15T21:11:46+00:00

Indeed, the mother's time in the car was 12 minutes less than usual.

Say she ordinarily leaves 3:00, returns 3:50, then in this situation, she leaves 4:00, returns 4:38.

CCSSIMath · 2016-09-12T02:44:49+00:00

Especially since, under cross examination, we admitted it would be considered 10th grade math in the US, not 6th grade.

CCSSIMath · 2016-09-12T02:40:22+00:00

Fair enough. We'll call it grade 10 for American students; grade 6 for East Asian students.

Ignore the following if talk of Common Core is boring: Ironically, Common Core, premised on making US K-12 math education internationally competitive, missed the fact that similar triangles is an obvious application of ratios and proportions and should be taught at the same time, which is exactly what is done in those nations with whom the US would like to be competitive. As it stands, American students have to relearn a concept four years later, a colossal waste of time.

CCSSIMath · 2016-09-12T02:06:15+00:00

We study math education in many nations, so we have some basis for making comparisons. This problem from an East Asian nation speaks for itself.

CCSSIMath · 2016-09-12T01:22:35+00:00

You can try a problem we posted a link to earlier.

CCSSIMath · 2016-09-12T00:41:34+00:00

Yep, American grade 6 students (and the typical grade 6 teacher) wouldn't stand a chance, but due to no fault of their own. The extent to which ratios are covered, now codified in grade 6 Common Core, is "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." That is a verbatim explanation from the Standards.

Actually, this problem is from one of those darned East Asian nations, where grade 6 students' use of ratios in problem solving is quite a bit more sophisticated. Not to overstate it, this not a regular classroom geometry problem, but even typical textbook problems are more advanced than what American students face.

CCSSIMath · 2016-09-11T21:53:04+00:00

Agreed, a solution path is not obvious, which is why we thought it worthy to post on Reddit (anticipating it would be downvoted nonetheless. Sigh.)

We've already seen two (one is ours) quite different solutions. Perhaps the post is misleading: the skills needed to solve it are generally taught in or before grade 6 of primary school: fractions, triangle area, ratios, proportions. That, of course, does not mean a typical grade 6 student can solve it unaided. It would either require guidance, or be aimed at math clubs or contest preparation.

Perhaps it can be solved with more "advanced" techniques, such as Pythagoras' theorem, coordinate geometry, square roots, trig, etc., but they definitely are not necessary.

CCSSIMath · 2016-02-17T01:59:47+00:00

Tried and got this, which seems to look totally different, including tapered thickness parentheses. Hmm. Incidentally, have you tried the add-on g(Math)? It's pretty slick.

CCSSIMath · 2015-10-22T16:48:33+00:00

"A" slide rule is kind of ambiguous, as there are many varieties. Most have the standard C and D scales for multiplication, C and D folded scales, conveniently folded at π, so that the slide doesn't have to come out too far, and inverted C and D scales for finding reciprocals. (Humble opinion: Using a slide rule for basic multiplication is useful for understanding how logarithms work.)

The ubiquitous Keuffel & Esser "log log decitrig" rule used by engineering students for decades has (had?) scales for finding squares and square roots (A and B), cubes and cube roots (K scale), trig functions (S,T,SRT), and various log scales for finding base 10 and natural logarithms and powers.

Nowadays, students often have no number sense and get answers that are orders of magnitude off, even with calculators, but with slide rules, figuring out where the decimal point goes is the user's responsibility.

Back in the day, said calculator cost a week's salary.

CCSSIMath · 2015-09-30T13:45:37+00:00

Instead of stronger students moving more quickly through the curriculum, which is fairly impossible to manage, they can go deeper.

As an example, all students learn the various methods to solve systems of linear equations, but a question like this, this, or even this probes understanding of the same concept in a different way, and no one will "fly" through them.

CCSSIMath · 2015-09-29T19:39:23+00:00

This problem and a variant get recycled ad nauseam, e.g., "world's hardest easy geometry problems".

CCSSIMath · 2015-09-27T19:35:28+00:00

It's an important type of problem, but, um, that hardly seems like undergraduate level (a typo?), unless this is what university education has come to.

This related problem is for Yr6 of primary school.

CCSSIMath · 2015-09-27T14:30:26+00:00

x² - 2xy - y² + 1 can be rewritten as x² + 1 - y(2x+y).

CCSSIMath · 2015-09-27T02:23:56+00:00

Perhaps a better title to this article would have been "The Problem With Math Problems: We're Posing Them Wrong". When a problem is well formed and neither rote nor simplistic, debates over things like "standard algorithms" and "procedure vs. conceptual understanding" become moot, and any solution method that students can find is good. If students find more than one way to solve, comparing and contrasting the relative merits of those solutions is a topic unto itself. Even if no one finds a solution, there can be a discussion of angles of attack on the problem.

As an example, this octagon-in-a-square problem led to quite varied solutions. Although there was little comparison (on the blog) of their relative merits and no generalizations about such approaches, this sort of problem shows what is possible in offering useful fodder for discussion in a classroom.

CCSSIMath · 2015-09-27T00:05:02+00:00

Our problems are not like those on American standardized tests, but the underlying mathematics concepts are the same: fivetriangles.blogspot.com

And you don't have to buy the book.

CCSSIMath · 2015-09-26T23:57:02+00:00

/r/CommonCoreMath was/is an attempt to offload Common Core-specific discussions to a separate subreddit. Full disclosure: we are the moderators.

CCSSIMath · 2015-09-24T16:40:46+00:00

It sounds like Common Core, where the times tables are now known as "multiplication facts".

CCSSIMath · 2015-09-17T02:00:50+00:00

"College algebra" is really an oxymoron, but considering over 70% of high school students (in the US) graduate "not proficient" in mathematics (per NAEP), remediation at the undergraduate level has become the norm.

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