This is how they're teaching fractions?

The BBQ Pit
1

I just subbed for a 7[sup]th[/sup] grade math teacher today. All her classes took tests, on fractions. Although most of the answers were multiple-choice :rolleyes: , a few answers were ones they actually had to figure out. I noticed that very few – about 15% – got this particular problem right. Here is the basic question.

Mary wants to make 2 1/2 batches of cookies. Each batch need 1 3/4 cups of sugar. How much sugar is she going to use?

My solution: multiply. So:

2 1/2 x 1 3/4 = 5/2 x 7/4 = 35/8 = 4 3/8

Like I said, only 15% got the answer right. And of those, several had denominators of 16 or 64. Some of the closer student answers also had those denominators. I was mystified.

Then for the last period of the day, I was working in the Content Mastery room. A teacher/paraprofessional was guiding several students through retaking the same test. When she helped them work through this problem, she did the following steps:
2 1/2 x 1 3/4
5/2 x 7/4

Then she found a common denominator (???), asking for a least common multiple, but insisting 8 was it. She change the fractions to:

20/8 x 14/8
280/64

then dividing:
4 24/64 = 4 3/8

Ok, they got to the right answer, but with a couple of unnecessary steps. She did the same process for two other fraction multiplications. (Don’t ask what she did for division.) I asked another teacher watching about why she was converting to a common denominator, and that teacher asked her. The tutoring teacher said that this method is what was dictated by the school district’s “Central Office”.

It then made sense why my students had such varied answers: they had difficulty with the 64 denominator, not reducing it as far as possible, or other errors that accrued due to the unnecessary steps.

It leaves me wondering what math-dead administrator thought up this extra step (which I’ve never heard of) for multiplication (and division) for fractions. It clearly is a process that just confuses the poor students.

2

C’mon AWB. Get 7/8 of a life.

*Hooray for new math,
New-hoo-hoo-math,
It won’t do you a bit of good to review math.
It’s so simple,
So very simple,
That only a child can do it!

Come back tomorrow night. We’re gonna do fractions.*

  • Tom Lehrer
3

The only thing I can think of is for consistency. For subtraction, addition, and division* you are required to get the common denominator, so maybe as to not confuse students they tell them to do it for multiplication as well?

*I am aware the easier method for division of fractions is take the reciprocal and multiply, but many children have problems with understanding why that works so I think some schools have moved to getting common denominators and dividing the numerators as the preferred method. I bet this school is one of them. Basically a lot of emphasis on math now is to get kids to understand why, not just how.

4

Someone confused the addition/subtraction rules (which require an LCD) with those of mult/division.

5

That’s my guess as well. I understand, for consistency’s sake, why you might just always want to get a common denominator, but that’s going to make their life in math land so much more complicated then it needs to be. Besides, half of math is about finding shortcuts.

Is there someone higher up you can mention this to? Just a quick “Hey, these students are multiplying fractions wrong. Is this the way they teach it now or is the teacher just not that good at math?” I know, for a fact, at some schools teachers are just tossed into whatever class they need someone for, regardless of how well they know the material. My aunt is currently teaching a grade school science class. I think she’s learning the materiel as she goes. Of course, she’s teaching at a really crappy school (but the pay is good).
You might find out that (for whatever reason) this is the way they teach this now. Or, you might get a response more like “Yeah, the math teacher quit three days before school started so the Social Studies teacher is covering for the year, maybe we need to see if the science teacher can take on an extra class”

6

.

Presuming the question was multiple choice from A,B,C&D, then randomised selection by monkeys would have got 25%.

That would indicate that there’s something systematically wrong.
How many questions had the correct answer as option C or D?

If you don’t know pick:
“C or D, or the longest answer”
“If given the option, never ‘None of the above’, always ‘All of above’”

7

Why the fuck are kids in 7th grade doing fractions? I hope that was the remedial class.

8

This was one of the questions where they had to figure the answer and write that answer in the blank. No multiple choice on that one. That’s why the denominators of 16 and 64 cropped up, doing 44 and 88.

9

Nah, instead let’s just confuse them about why common denominators are required for addition/subtraction, and maybe about what multiplication is and what fractions really are.

There are kids in college who don’t understand fractions.

10

Actually, it was a regular 7[sup]th[/sup] grade math class. From their good behavior, I would say they were the ones that just missed getting into AP.

I’ve been trying to find any online documentation that says to teach this method, but I couldn’t. It’s obviously something common, as two populations of students (my students and the ones in CM) were being taught this.

I know that teaching outside the method is frowned upon. I used to sub for a FOAF, until I covered one of her classes and supposedly taught a method not supported. (Dunno what it was; I just noticed I stopped getting calls to cover her classes.) She bad-mouthed me to the administration, and I haven’t subbed for her since. Other math teachers don’t have a problem with me there. Oh, well…

11

Oh, and to the OP: I weep at your story. That is the most 32/64-assed way of multiplying fractions I’ve ever heard of.

12

Jesus. I’m only 26 and did that stuff in 3rd or 4th grade. Normal public school.

13

I too did this stuff about 3rd or 4th grade. My daughter is doing them in 5th, and that’s considered GT.

One big problem I see is that lessons today have to be all touchy-feely, everybody-have-fun, nobody-gets-left-behind sorts of affairs. Going to stations around the room, having worksheet/puzzles that tell corny puns, give-them-multiple-choice-so-they’ll-have-a-25%-chance-of-getting-it-right. We had to memorize multiplication tables, unit circle chart (trig), and rules of fractions. Now, those things have to be posted on the walls somewhere for the students to refer to at any time.

Whenever a student complains about having to actually work out a math problem, I quip, “Math isn’t a multiple-choice topic.” If they complain further, I ask, “Would you drive across the Golden Gate Bridge if you knew the engineer did all his math via multiple-choice?”

14

What? There’s no such thing as AP 7th grade math.:confused:

15

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.

16

I teach math to liberal arts students at the college level. Let me just say that the math skills of my students are truly deplorable. Upon entering my class, most cannot add or multiply fractions, let alone solve an equation like 4b = 12.

Something is *very *seriously wrong with how mathematics is being taught at the elementary and HS levels.

17

What’s even funnier is that even if you needed to find lowest common denominator, it would have been 4, not 8!

18

This is what I was thinking. Even if you insisted on common denominators, why wouldn’t it be 5/2 x 7/4 = 10/4 x 7/4?
10/4 x 7/4 = 70/16 = 4 6/16 = 4 3/8. Much easier than 280/64.

19

Actually teaching what a fraction represents would have helped: it’s a multiplication and a division bundled together. A lot of kids I see just have not been taught this. Once you understand this, it’s far easier to understand how to multiply fractions, and it’s a small step from that to understanding how to divide 'em. Whoever decided that kids should be taught a method entailing finding common multiples should be spit-roasted, and not in a fun way, and whoever thinks that 8 is the LCM of 2 and 4 should go back to teaching three-year-olds to finger-paint.

20

I blame society.