# This is how they're teaching fractions? **URL:** \ **Category:** The BBQ Pit\ **Created:** [November 11, 2010, 2:12am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264 "2010-11-11T02:12:25Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [November 11, 2010, 11:05pm UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/41 "2010-11-11T23:05:34Z")
> [@Bosstone](#): > > I can’t stand all this division! ☹ This discussion of fractions is tearing us apart! Seriously, seventh graders reviewing fractions? When I was that age I drew a Rubik’s Cube! In Logo! On an Apple IIe! Unrelated, I know, but my prouder school math moments didn’t come until a few years later, when I worked out an angle trisection method using a compass and ruler. It was wrong, but it took my math teacher a solid ten minutes of thinking to prove it. Later still was my inductive proof that: [2n(n+1)][sup]2[/sup] + (2n+1)[sup]2[/sup] = [2n(n+1) + 1][sup]2[/sup] …thus proving an infinite number of Pythagorean triples. I didn’t date in high school. Maybe this half-assed method of teaching is an attempt to let students develop better social skills by stifling the nerd within. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 11, 2010, 11:09pm UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/42 "2010-11-11T23:09:36Z")
> [@friedo](#): > > Why _do_ they insist on deradicalizing the denominator, anyway? I had an algebra teacher once with a big stick up her ass about that, and I never saw the point. x = 3/sqrt(5) is just as good an answer as x = 3( sqrt(5)/5 ). Easier to type, too. On the other hand, 10/sqrt(5) doesn’t look quite as elegant as 2 sqrt(5). So **sometimes** “rationalizing the denominator” really does simplify things. In some situations, there is **no** advantage to rationalizing the denominator. In some other situations, there is an advantage, based on the idea that it’s best to keep your denominators as simple as possible. But **some** of **those** situations are artifacts of the old, pre-calculator days. If you didn’t have a calculator (but you did have a table where you could look up the square root of 5 to several decimal places), you could more easily calculate 3(sqrt(5)/5) by hand than 3/sqrt(5), because it’s easier to divide an ugly decimal by an integer than vice versa. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [November 11, 2010, 11:55pm UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/43 "2010-11-11T23:55:07Z")
Yeah?! What if pi is in the denominator? Huh? Huh? What then, bigshot?! ---
**Author:** ![Rachellelogram](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rachellelogram/32/8689_2.png) [@Rachellelogram](https://boards.straightdope.com/u/Rachellelogram)\ **Post date:** [November 12, 2010, 12:43am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/44 "2010-11-12T00:43:39Z")
Seventh graders are not old enough to be taking shortcuts yet. Their method sucks, but teaching them shortcuts to the method they’re learning is just going to cause confusion. Most of the process of math for me was learning how to do things the long hard way and then learning why/the shortcut later. I wouldn’t find this method confusing, but I was also G/T in math starting around 2nd grade. Being realistic, you’re just a sub at this school and have no power to change their curriculum (although complaining about it is cathartic). If you don’t like it, don’t sub for math. Or sub at another school. ---
**Author:** ![Jorge\_Burrito](https://avatars.discourse-cdn.com/v4/letter/j/e9bcb4/32.png) [@Jorge\_Burrito](https://boards.straightdope.com/u/Jorge_Burrito)\ **Post date:** [November 12, 2010, 1:07am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/45 "2010-11-12T01:07:08Z")
> [@Nava](#): > > I never was taught to take the reciprocal and multiply; we were taught that “division of fractions is crossed multiplication” before being taught what the reciprocal was. I was one of those students who are always asking “why” (I eventually learned to shut my trap about it, but have never stopped wondering why) and in this case the reason why was “it evidently works”. Crossed multiplication is one single step, you’re talking about two and this other method with the LCD is even longer. Cross multiplication is taking the recipricol and multiplying, you just didn’t realize it :p. They are trying to teach the kids “why” which you said yourself you always wondered. It is by far easier to teach kids the why of how finding the common denominator and then dividing the numerator works versus trying to explain the why of how cross multiplication works. As you said though it is definitely more steps, and when the kids are actually doing problems they really should be using any shortcuts available to them. Knowing why is great, but for all intents and purposes all that really matters for most of the math these kids will end up doing is that they get the correct answer. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 12, 2010, 1:11am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/46 "2010-11-12T01:11:18Z")
> [@rachelellogram](#): > > Their method sucks, but teaching them shortcuts to the method they’re learning is just going to cause confusion. This isn’t about shortcuts. The way the students learned wasn’t just “the long way”; it was a way involving a long, dangerous, and unnecessary detour. It’s a way that (a) led, on the OP’s evidence, to more mistakes and fewer correct answers, and (b) is totally nonstandard, and probably could only have originated from someone who didn’t understand what the fuck they were doing. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [November 12, 2010, 1:17am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/47 "2010-11-12T01:17:57Z")
This is only a shortcut in the sense of believing a proper appendectomy requires performing a manicure. ---
**Author:** ![etv78](https://avatars.discourse-cdn.com/v4/letter/e/d78d45/32.png) [@etv78](https://boards.straightdope.com/u/etv78)\ **Post date:** [November 12, 2010, 1:18am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/48 "2010-11-12T01:18:50Z")
[QUOTE=Indistinguishable;13130964}. (Not quite the same topic, but coming to mind nonetheless in discussing reducing to lowest terms, it annoys me to no end when (college) students of mine run screaming away from having square roots in denominators; “But we have to move them to the numerator!” “No, you don’t.” “But… but…” “You’ve been trained to always put things into a certain standardized form, but there’s nothing to be gained by this except when you have some need for that standardization”. Showing that it’s perfectly fine to treat multiple representations of the same number on equal footing early and often would perhaps help avoid this kind of thinking.).[/QUOTE] That’s what I was always taught. ---
**Author:** ![etv78](https://avatars.discourse-cdn.com/v4/letter/e/d78d45/32.png) [@etv78](https://boards.straightdope.com/u/etv78)\ **Post date:** [November 12, 2010, 1:24am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/49 "2010-11-12T01:24:14Z")
[QUOTE=Bryan Ekers;13132098! Unrelated, I know, but my prouder school math moments didn’t come until a few years later, when I worked out an angle trisection method using a compass and ruler. It was wrong, but it took my math teacher a solid ten minutes of thinking to prove it. Later still was my inductive proof that: [2n(n+1)] [sup]2[/sup] + (2n+1)[sup]2[/sup] = [2n(n+1) + 1][sup]2[/sup] …thus proving an infinite number of Pythagorean triples. . [/QUOTE] Maybe it’s the same equation, but in HS, I figured out that: if X+(x+1)=Y, then x, x+1 and square root of Y are a Pythagorean triple. ---
**Author:** ![Jas09](https://avatars.discourse-cdn.com/v4/letter/j/d07c76/32.png) [@Jas09](https://boards.straightdope.com/u/Jas09)\ **Post date:** [November 12, 2010, 1:46am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/50 "2010-11-12T01:46:34Z")
> [@Giles](#): > > I blame the snake in the Garden of Eden – it was an adder, so it couldn’t multiply fractions. It should have eaten off a stump in the garden. With a log table, even adders can multiply! Finally that joke from my HS math teacher comes in handy… ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 12, 2010, 2:30am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/51 "2010-11-12T02:30:58Z")
> [@etv78](#): > > Maybe it’s the same equation, but in HS, I figured out that: if X+(x+1)=Y, then x, x+1 and square root of Y are a Pythagorean triple. I don’t think you’ve phrased that correctly… Do you mean Pythagorean triple in the same sense I’m interpreting it as (numbers A, B, and C such that A^2 + B^2 = C^2)? ---
**Author:** ![Zsofia](https://avatars.discourse-cdn.com/v4/letter/z/7bcc69/32.png) [@Zsofia](https://boards.straightdope.com/u/Zsofia)\ **Post date:** [November 12, 2010, 2:39am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/52 "2010-11-12T02:39:48Z")
> [@rachelellogram](#): > > Seventh graders are not old enough to be taking shortcuts yet. Um, these are _seventh graders_, some of whom are _shaving_. If they can’t master the finer points of _multiplying fractions_, we got bigger problems. ---
**Author:** ![marshmallow](https://avatars.discourse-cdn.com/v4/letter/m/df705f/32.png) [@marshmallow](https://boards.straightdope.com/u/marshmallow)\ **Post date:** [November 12, 2010, 2:51am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/53 "2010-11-12T02:51:41Z")
Fractions in middle school? By 7th grade they should be waist deep in algebra. I think that’s where we started to FOIL it up. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [November 12, 2010, 2:51am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/54 "2010-11-12T02:51:43Z")
> [@Indistinguishable](#): > > I don’t think you’ve phrased that correctly… Actually, I can see how etv’s formulation works. Using my formula to generate the numbers for A, B and C: 0[sup]2[/sup] + 1[sup]2[/sup] = 1[sup]2[/sup] 4[sup]2[/sup] + 3[sup]2[/sup] = 5[sup]2[/sup] 12[sup]2[/sup] + 5[sup]2[/sup] = 13[sup]2[/sup] 24[sup]2[/sup] + 7[sup]2[/sup] = 25[sup]2[/sup] And using etv’s to pick the two terms out of each equation that have a difference of one (in this case, A and C) and comparing them to the square of B: 0 + 1 = 1[sup]2[/sup] 4 + 5 = 3[sup]2[/sup] 12 + 13 = 5[sup]2[/sup] 24 + 25 = 7[sup]2[/sup] etv’s version likely works for triples other than the ones that can be found by my formula. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 12, 2010, 2:55am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/55 "2010-11-12T02:55:00Z")
Oh, I see. That does indeed always work, taking A = x, B = sqrt(y), and C = x + 1. I was just taking them in the wrong order. ---
**Author:** ![Jas09](https://avatars.discourse-cdn.com/v4/letter/j/d07c76/32.png) [@Jas09](https://boards.straightdope.com/u/Jas09)\ **Post date:** [November 12, 2010, 3:32am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/56 "2010-11-12T03:32:29Z")
> [@marshmallow](#): > > Fractions in middle school? By 7th grade they should be waist deep in algebra. I think that’s where we started to FOIL it up. Algebra? They should be on calculus! Seriously, however, 7th grade honors courses, in the early 90s at least, were pre-algebra. 8th grade was algebra. 9th geometery. Then algebra II/trig, pre-calc, and calc to finish out HS. This was the honors/AP track, and caused no difficulty in college admissions or getting both engineering and math degrees. ---
**Author:** ![Rachellelogram](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rachellelogram/32/8689_2.png) [@Rachellelogram](https://boards.straightdope.com/u/Rachellelogram)\ **Post date:** [November 12, 2010, 3:41am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/57 "2010-11-12T03:41:01Z")
> [@Jas09](#): > > Algebra? They should be on calculus! > > Seriously, however, 7th grade honors courses, in the early 90s at least, were pre-algebra. 8th grade was algebra. 9th geometery. Then algebra II/trig, pre-calc, and calc to finish out HS. This was the honors/AP track, and caused no difficulty in college admissions or getting both engineering and math degrees. Just to add in another perspective: In the late '90s/early '00s (specifically for my class of 2003), 9th grade was honors algebra. 10th grade was honors geometry. 11th grade was trig and pre-calc–half a year of one, 2 quarters of another. And 12th grade was AP calculus. ---
**Author:** ![Zsofia](https://avatars.discourse-cdn.com/v4/letter/z/7bcc69/32.png) [@Zsofia](https://boards.straightdope.com/u/Zsofia)\ **Post date:** [November 12, 2010, 3:51am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/58 "2010-11-12T03:51:46Z")
However, I did take AP calc and make a 5 on the AP exam and can tell you nothing about calculus except that if you take the derivative you get a point on the exam. I didn’t even really get what calculus was _for_ until I was an adult reading about the history of science. Probably because, I dunno, all the problems I did in calculus were along the lines of “There is a hill which is a parabola which can be described as…” If a hill is a perfect parabola we got bigger problems, okay? Plus now the hill is two dimensional? If higher math had ever been taught to me in a realistic manner (I had a great calculus teacher, don’t get me wrong, but the one time the class clown asked a real question: “what is this for?” she lost her shit at him) I might have learned it for real. Of course, I was also kind of asleep in eighth grade algebra the day they taught factors, so I never learned how to factor a quadratic equation and faked it all through high school. I was kind of a dumbass, looking back. Ms. Murphy could have taught me in ten minutes if I’d just asked. ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [November 12, 2010, 3:53am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/59 "2010-11-12T03:53:29Z")
> [@AWB](#): > > Mary wants to make 2 1/2 batches of cookies. Each batch needs 1 3/4 cups of sugar. How much sugar is she going to use? > > My solution: multiply. So: Before looking at your answer, I just did it in my head, like this: 2 1/2 times 1 3/4…take the 2 times first…2 times 1 is easy, 2 times 3/4 is obviously 1 1/2, so that much adds up to 3 1/2. Now take one half of 1 3/4. Easy-peasy…half of 1 is 1/2, and half of 3/4 is 3/8. 3/8 plus 1/2 is 7/8. Now add 3 1/2 and 7/8 to get 4 3/8 (7/8 is 1/8 short of 1, so 3 1/2 plus 1 is 4 1/2, take away 1/8 to make 4 3/8.) Somehow I don’t think this problem needs to be written down or formalized. It’s too easy. Besides, why is Mary making a half batch of cookies? Doesn’t she know that the dough will be eaten before it gets to the oven? And is it white sugar or brown? Make 5 batches, like Og intended! ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 12, 2010, 4:11am UTC](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264/60 "2010-11-12T04:11:50Z")
> [@Zsofia](#): > > I didn’t even really get what calculus was _for_ until I was an adult reading about the history of science. Do you remember what, specifically, you were reading that made you get it? [Previous page](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264.md?page=2) [Next page](https://boards.straightdope.com/t/this-is-how-theyre-teaching-fractions/560264.md?page=4)