Acer saccharum (Sugar Maple) Sap & Freezing This may or may not be the appropriate scientific discipline to ask this question of, but I'll give it a shot. I'll happily invite chemists to chime in as well.
It's time to tap sugar maples in the North East USA once again. What we essentially pull from the trees via taps is a sugar solution that, using reverse osmosis and evaporation, produces maple syrup. But there's a old tradition that's caused me a bit of concern. When buckets are hung (a dying method of collecting, usually big operations use tubing), sap is collected as the day warms up. At night, and especially on very cold nights, large portions of the sap freeze. I've noticed a lot of older sap producers toss out the ice, sometimes a substantial amount, saying that what is left is more concentrated sugar-water, and the ice is pure water.
But I'm not sure if I believe that. First of all, most sap is a 2% to 6% sugar solution, meaning that, at 2%, you'll need roughly 43 gallons of sap to produce 1 gallon of syrup. Syrup is defined as > or = 66% sugar (Sucrose). And I've seen sap run through reverse osmosis (which is then about 10% sugar), freezing up after an overnight below zero.
With that bloated introduction, my questions are as follows: Assuming you have 1 liter of pure water, vs 2% sap, vs 10% sap (solution I assume), at what temperatures will each solution start to freeze.
Secondly, when any of these solutions freeze, is it only pure water that is freezing initially? Or is the ice actually a mix of sucrose and pure water? And if it is separating pure water from sucrose, forming a more concentrated solution, at what temperature or time (again, assuming 1 liter and a constant atmospheric pressure) will the more concentrated solution start freezing?
Finally, many pails and the sap have lots of particles in it. This can range from bugs to wood chips to bits of dust, dirt, and corrosion. Although it might seem a separate topic, this may also influence freezing rates and should be taken into consideration when trying to answer this question.
The point is this: We don't want to throw away the valuable sucrose the tree is providing, but we want to be more efficient in removing water from the solution to form syrup. Is tossing out ice that forms in the buckets overnight helping with that efficiency, or are we actually throwing out valuable sucrose that could be made into syrup?
 A: 
Is tossing out ice that forms in the buckets overnight helping with that efficiency, or are we actually throwing out valuable sucrose that could be made into syrup.

There's an easy way to test: take a sample of the discarded ice, melt it, measure the volume $V$, evaporate it until only solids remain, weigh the solids, and compute the percent dissolved solid, $X=m/V$.
This will give you a more straightforward (and more accurate) measure of exactly how much you're throwing away than theoretical calculations, and it's syrup-tapping season, so it should be very convenient to conduct the experiment.
I suspect that there is some sugar that is adhering to the ice (either on the surface or trapped in interstitial pockets that form during freezing due to solute precipitation), and this sugar will be lost in the process. However, whether it is cost-competitive with the additional energy expenditure that would otherwise be required to evaporate the ice that is discarded will crucially depend on the total dissolved solids content $X$, and the market price of maple syrup.
If you get a number after evaporating a sample of the ice, feel free to post it; it would be easy to calculate whether it is a cost-positive or cost-negative process.
A: Each mole of sucrose in a kilogram of water would depress the freezing point of water by 1.85 degrees C, according to Blagden's law (which is more valid at low concentrations). 
The molecular weight of sucrose is 342 grams/mole. 
So 2% sucrose should freeze around -0.1 C and 10% sucrose -0.5 C. 
Fractional freezing of grapes increases sugar concentration in the production of eisvien (ice wine). It is likely similar for maple syrup.  Certainly you would loss some sugar content when you throw out the ice.  The ice isn't pure water, it just has a lower concentration of sugar than the liquid phase.  
A: I have measured this with a refractometer.  This year my sugar level has been around 3% for sap.  I have isolated the ice and measured its sugar content and it is definitely lower (around 2%), so there is still a good amount of sugar in the ice.
An interesting anecdote is that this is how the Native Americans made their maple syrup, by skimming off the ice every morning to purify.
