On Funny Math (Updated)

You know, I thought the math on Dr. C.'s 28 calorie recipe was a little weird, but math has never been my strong suit, so I just figured I was just a dumb blonde and she was the smart doctor, so I should just do what I was told. Um, I'm not actually blonde, but go with me on this one, okay? I mean, the thought had occurred to me to run the math by my pharmacist husband, but see... I never have a lot of faith in that either... I always think this sort of thing is some secret, highly complex code that even my super-smart husband can't possibly crack and I don't want to burden him with the embarrassment of straining his intellect. I mean, it would be a horrible blow to his ego, right? And I wouldn't want to be the cause of his mid-life crisis at such a young age (he and I just had birthdays, so I'm a bit sensitive about his age since I'm catching up to him). And so, I simply followed the doctor's directions, knowing that I could never possibly understand the highly complex calculus involved in mixing 28-calorie food for my under-fed daughter. After all, I am a mere mortal, and Dr. C... well, SHE went to medical school.

Ahem.

And then Lea Bea... Dear, sweet Lea Bea, was avoiding schoolwork, so she tried out the math for me. Because, really, apparently, schoolwork avoidance=too much damn time on your hands (see, some math isn't too difficult for me!). And apparently, this math is pretty damn simple. The piece I was missing was that I didn't know how many calories were in a scoop of formula, because I'm a total moron. See, I know that formula contains 20 calories per ounce. And I know that you mix one scoop of formula with 2 ounces of water when you're just making regular formula for a baby. So it would make SENSE that one scoop of formula has... YOU GUESSED IT... 40 calories! But I am tres stupid, so it never occurred to me that it was that simple.

Dr. C's directions were VERY clear. "1 scoop formula + add breastmilk until total volume = 5 oz" Now this is the exact opposite of how you make formula. When you're mixing formula for a baby, you pour water in a bottle to the desired volume, THEN add the powder (or so I'm told... I've never actually made formula). If you put the powder in first, and THEN add the liquid to 5 oz total volume, you only need to add about 4-4.5 ounces of liquid before you get to that 5oz mark. If you add liquid first to the 5oz mark and then add powder and then shake it all up, you end up with 5.25 oz of final volume. Go figure (I'm not really sure why this works this way, and I really don't WANT to know). I remember very specifically clarifying Dr. C's instructions, because it was the exact opposite of how I'd been taught to make formula, and she was very specific that she meant to put the powder in the bottle first and THEN add the liquid. So if you do it her way, here's the math, courtesy of Lea Bea:

1 scoop formula = 40cal
4 oz breast milk = 80cal
Total = 120 cal in 5oz bottle
divided by 5 oz = 24cal/oz.

Gah! So all this time*, I've allowed Dr. C. to make me feel guilty for hanging on to breastfeeding my daughter, despite the fact that it's making her fall short of her calories because she's only getting 4, 3-oz 28-calorie-per-ounce bottles per day, plus 2 breastfeeding sessions per day (approximately 3 oz of intake per session at 20 calories per ounce)... for an estimated total of... 456 calories per day (if I've done my math correctly, but remember I've already admitted math isn't my strong suit). Ellie's supposed to be getting a MINIMUM of 480 calories per day. However, if these are really 24-calories-per-ounce bottles, she's ACTUALLY been getting an estimated 408 calories per day, which is an even greater shortfall than I thought. And that's because of Dr. C's lousy math.

According to dear, sweet Lea Bea, however, if I added the powder to 5oz of milk, I'd get closer to 27 calories per ounce, which is a lot closer to what I wanted in the first place. And I trust Lea Bea's math more than Dr. C's at this point (plus, um, my husband concurred, because apparently it's insulting that I didn't trust him to be able to do the math in the first place). But honestly, I'm not making any changes until we see our regular pediatrician tomorrow. She's barely tolerating the fortified bottles as it is. But she IS definitely gaining some weight. Her cheeks have filled out a little bit and she's more alert than she was. And she's definitely getting more calories than she had been before, so anything's an improvement.

It's just... so frustrating! There's this doctor who already frustrated me with her recommendation to stop breastfeeding all together, but I could at least understand her logic. But then I thought there was a reasonable compromised reached which I assumed wouldn't pose any serious problems for Ellie since she'd still be getting pretty darned close to her calorie requirements, when it turned out that a problem in Dr. C's math was going to cause a pretty significant shortfall! Gah!

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*Okay, to be fair, "all this time" is really only a week, but still! This is a tiny baby we're messing with!

Update:
I hate that blogger doesn't do threaded comments. Anyway, a couple comments I've gotten about the math:

It's a question of total calories vs. calories-per-ounce.
If you have 5 oz of milk and a scoop of formula, you'll have more total calories but fewer calories-per-ounce.
If you have 4 oz of milk and a scoop of formula, you'll have fewer total calories but more calories-per-ounce. It will be more concentrated.
So it's actually more a question of which is works better, filling her belly fuller with a lot of milk, or having her try to tolerate the more concentrated stuff. It also depends on how much she'll actually eat!
Hope that makes sense!!

It does make sense. However, since Ellie only drinks 3-ounce bottles (she throws up if we give her more than that), what actually matters is the calories-per-ounce. Obviously, I mix up more than I will use, and then just pour out 3 ounces worth into the bottle that I'm feeding her from.

The calculation of one scoop at 40 calories plus 5 ounces of EBM at 100 calories totalling 140 calories divided by 5 ounces comes out to 28 calories per ounce. The problem apparently is that the powder isn't volumeless. You need to use the full 5 ounces of EBM, and then each fifth of the mixture -- each 1.05 ounce -- will contain 28 calories.

This is quite correct. HOWEVER, this is only correct if this had been what Dr. C's instructions had been. Her instructions were NOT to add powder TO milk, but rather to add milk TO powder. Which meant I was adding only about 4 oz of milk to one scoop of powder. My issue isn't with how to do the math at this point. My issue is that Dr. C's math was faulty and, frankly, after her attitude last week, I have little patience for sloppy math.