Usually when it gives two weights like that and says one is dry and one is prepared, that means the first measurement is out of the box (e.g. 2 oz uncooked) and the 2nd measurement is prepared as directed (1 cup prepared).
So for example, the pasta I cooked tonight was 2 oz or 1 cup cooked - I measured out 2 oz of dry pasta and by the time it was done cooking it was a little over 1 cup in volume.
As far as whether you weigh or measure, that's up to you. I prefer to weigh, since it's more accurate, but I'm compulsive (as you know by the great popcorn quest)!
There are some things that it doesn't make a difference in, and some things I've noticed it does. For example, I always weigh my peanut butter now, since it's easier to be exact. But I always measure out 1/4 cup of oats - since it's easier and faster and a few grams either way won't make that much of a caloric difference.
As for the muffins - unfortunately muffins are some of the most calorie laden "healthy" things you can eat. Flax is somewhat oily and has quite a few calories. And if the muffins were made with sugar (even cane sugar or honey or whatever), and had eggs in them ... plus the glaze, which would be practically solid sugar ... ! Add to that, you said they were big muffins, which means a 1/2 of a big muffin could still be the equivalent of 1.5 or 2 regular servings.
Even so, it's just hard to know w/out knowing exactly what went into them. I would say around 300 cals would be a good estimate for 1/2 a muffin.
One thing though, you said at the end of the day, you had extra calories left over, so with the muffin, that puts you at 1200 - that's not enough calories for you to be eating including your dinner!
That means that you only ate 900 healthy calories today and that fully 1/3 of your calories (and we're assuming the muffin clocks in at around 300) is a sugary glazed muffin.
If it's a once in a while thing, that's ok. But if you're regularly finding yourself below 1000 calories after dinner with room for a sugary snack, you need to add more healthy calories throughout the day. Ideally you shoudl never go below 1200 calories unless you're following a medically directed diet plan.
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