Comparing Fractions with Cross Multiplication

Today my 6th grader asked for with her math homework, specifically how to "cross multiply fractions with whole numbers". I wasn't quite sure what she was talking about, so I took a look at her homework. I saw that she had 10 problems to compare fractions with different denominators, some with whole numbers. I started to explain how to find a common denominator, etc... but she got really upset with me.

"Thats not how my teacher showed us", she said. "My teacher told us to cross multiply."

I still had no idea what she was talking about, so I went to check with my girlfriend, Shannon, to see if she knew what our daughter was talking about. But Shannon was as confused as I was.

Both of us being confused, we did a quick google and came across this explanation of the process from mathleague.com.

Comparing Fractions
1. To compare fractions with the same denominator, look at their numerators. The larger fraction is the one with the larger numerator.
2. To compare fractions with different denominators, take the cross product. The first cross-product is the product of the first numerator and the second denominator. The second cross-product is the product of the second numerator and the first denominator. Compare the cross products using the following rules:
a. If the cross-products are equal, the fractions are equivalent.
b. If the first cross product is larger, the first fraction is larger.
c. If the second cross product is larger, the second fraction is larger.

Example:
Compare the fractions 3/7 and 1/2.The first cross-product is the product of the first numerator and the second denominator: 3 × 2 = 6.
The second cross-product is the product of the second numerator and the first denominator: 7 × 1 = 7.
Since the second cross-product is larger, the second fraction is larger.

Example:
Compare the fractions 13/20 and 3/5.
The first cross-product is the product of the first numerator and the second denominator: 5 × 13 = 65.
The second cross-product is the product of the second numerator and the first denominator: 20 × 3 = 60.
Since the first cross-product is larger, the first fraction is larger.

Well, we figured it out and were able to help her finish her homework... her way, but we are rather conflicted about it.

Though the system works, we aren't quite sure what the purpose of it is. It almost seemed to us to be cheating. Though the system works, neither one of us could give a mathematical explanation of why. Finding a common denominator is relatively easy to explain, and is also an essential skill when it comes to adding unlike fractions. Is this new math, really really old math, or something in between?

Don't be a Hater!

Transform Education: What if KIPP "worked"?
Peter Campbell: dont be a hater, be a congratulator!

For all the kids that are not "lucky" enough to get a place at KIPP, it is not tolerable. For all the kids that do make it into KIPP but are not able to endure the 10-hour days and two hours of homework every night and who eventually drop out or are "counseled out," it is not tolerable. And even for those kids who do make it into KIPP and make it out of KIPP, their "success" is not tolerable because it comes at a price, a price that is too high to pay.

Ryan at Edspresso responds with a small bit of sarcasm:

So because school choice might harm others in some nebulous way, it should be withdrawn? And "success" in sneer quotes? Is this writer suggesting that said students are faking it, or that their academic achievements are somehow counterfeit?

but I wanted to add one more point. It's very hard to shake the feeling that there are some who truly wish for equality... equality of failure. I have used the argument in the past, but I will use it again. These are the sort of people who would let everyone drown on a sinking ship, because they couldn't save everybody. To them it's not about excellence, it's about equivalence. They have already given up on success, and now they just want to drag everyone down to the lowest level.

Is Teaching in the 408 going to bolt?

The first week back to work/school is always rough, but do I detect hints that Teaching in the 408 is about fed up.

told the POY I needed a new assignment, not the on-grade level kids necessarily, not the ones who'll do whatever I say and then ask if they can wash my car and go buy me Jamba Juice, but maybe some kids whose classroom existence alters the vast input vs. output imbalance just a little. Maybe some barely there Basic kids, and I'll make sure every one is proficient and redesignated by the end of the year. They don't need to utilize fluent English, or know how to write, or really know anything at all, but maybe they could possess a little bit longer runway for the skills I'm trying to land on their brains. Because I keep cracking my skull on all the crash-landings and aborted take-offs, and it hurts.

...

And the email says, you can dramatically impact student outcomes as the Director of various teacher-training programs in Oakland.