Trust me...the box will not work.
You are doomed to failure.

Here is a link to a video on growing potatoes and there are many many others on the same subject on YouTube. Google "growing potatoes" or search potatoes on this forum and you will get more info than you can process. (this is called "Using the Internet 101)

http://www.youtube.com/watch?v=i79tuAEbh1Y

Here is a link that might be useful: Pot Video

If they're certified seed potatoes, don't worry about the fuzz, they should be okay. Leave them in a warm, sunny place before you plant, and the eyes should start growing, which is a good thing.

Potatoes are fairly heavy feeders, so you may need some organic fertilizer to boost your natural soil. Without enough nutrition, they won't produce much.

Try some in your box, but don't crowd them or you won't get much. Each potato piece should have at least one foot of free space all around it.

Mix some of your natural soil with some organic fertilizer (and hopefully some compost) and put it in your box 6" deep or more. Set down your potato piece(s) and cover with 2 more inches of the fertilized soil.

Put in full sun and wait until you seed leaves coming up. When the leaves are about 6" tall, add a couple more inches of soil. As the plants grow, add more soil until you've got 8" to 12" of soil over the seed potatoes.

If you want to do the straw method, still cover the potatoes with the first 2" of fertilized soil (for nutrition), then add loose straw as the potatoes get taller. DON'T bury the potatoes under a foot of straw right off, add it gradually as they grow until you've reached the top of the box (should be covered with a foot of straw).

The potatoes will grow between the top of the seed potato and where the leaves start.

If you're growing in the ground, make rows about 3 or 4 feet apart so you'll have plenty of soil for hilling. Dig a shallow trench about 2 or 3" deep. If you need to add some organic fertilizer, scratch-mix it into the soil in the bottom of the trench. Add your potato pieces, planting from 12" to 16" apart in the row, and cover them to ground level, then hoe up another 2" of soil. Wait for the potatoes to grow about 6" tall, then hoe up more soil from the path between the rows. You shouldn't need to do it more than three times from the time you dropped the potatoes in the ground.

Don't water them until you see leaves -- too much moisture will help them rot.

The advantage of planting the potatoes in shallow trenches (esp in heavier soils, or with rocks) is that as the potatoes grow and the tubers expand, the soil in the hill gives enough to let them expand. My soil is heavy sand with rock (glacial), and it just never stays light and fluffy for long. If you have light, loamy soil, you could plant them deeper, but that's also deeper that you have to dig when you harvest.

And if you're looking for a big crop, don't pull small 'new' potatoes off the plant -- let them grow. If you haven't got a field full of growing potato plants, harvesting new potatoes will cut into your overall crop.

I just looked it up... For regular potatoes, a good crop is about ten times the weight of the potatoes you planted (6 lbs of seed potatoes should be good for a 60# harvest). For the fingerling types, you could get up to 20 times the planting rate.

Good luck! And don't mind lonmower, he seems to be in a pissy mood today.

Sue

@lonmower: Thanks. I have seen that video many times over. It still is like a foreign language to me.

Very sad to hear the box does not work.

Yes I know Internet 101, but my appeal to blogs is for direct experience of posters.

@belgianpup: Thanks for your uplifting comments and reviews. Just the info I needed. Also the top on lonmower

Sue, I appreciate your post too. I've been reading up before planting my first potatoes, and I was specifically wondering about the fuzzy stuff on the (rather long) eyes on some of my seed potatoes too. That whole answer was very helpful.

I think people expect too much from potato boxes, potato bags, etc. They think the box will be totally filled with tubers, top to bottom, and the more stuff you dump on top of the plants, the more the tubers will grow right to the top of it. So lonmower is right, not gonna happen.

People should have reasonable expectations and learn what an average good yield is before they get started.

"I planted last year and tried to HILL them but it did not work and I only got about 7 potatoes each plant. UGH."
Seven potatoes each plant assuming they got to a reasonable size is actually a good yield.

Last spring was a wet one and I decided to plant my seed potatoes in boxes, one existing 4X16X16in. tall. and I built 2 new ones 4X6. I grew in the 2 new boxes exactally as Sue explained.(very good post, Sue.)I planted the larger existing raised bed by pushing the seed potatoes into thesoil about 12 in. deep. I was very happy with the results. I plan to do the same this year along with those planted in the ground. Keep trying and enjoy those spuds.

Ages ago (dating myself) Sunset featured growing potatoes in black garbage bags, 2 thick, poke holes in the bottom. I did it and it worked and I know I got more than 7 large potatoes (was zone 9 Sunset 14 - so a perfect and long growing season). Since you're building your box - the main thing is potatoes don't like it too hot - a narrower tall box will heat quickly in hte sun, a wider box will not. My new zone 7 has weeks of 100, so I'll put my potatoes in afternoon shade.
Since I'd changed zones, I'd re-read up on potatoes as I know I have ot adjust my timing and methods. Article linked below.

Here is a link that might be useful: U.C.Davis Home Potato Growing

I am most concerned about 2 things: your statement that you cut the potatoes into pieces with only one eye each--and also that "they have some fur/fuzz on them." This sounds like mold to me, and while belgianpup says not to worry about it...well, I think I would. If the sprouts were long as mentioned by one of the other posters then the "fuzz" could be root hairs--but since you said "eyes" and not "sprouts" I wonder... If the sprout molds & dies, you will not have a plant from that piece.

I always have left golfball-sized potatoes whole and cut larger ones in such a way that each piece has several eyes since the sprouts are what will grow leaves and help feed the roots. I fugure, the more roots, the stronger the plant will be and the more tubers it is likely to produce. Just my thought. The experts say that one eye is fine, and if you buy them by mail order, pre-cut with one eye each may be how they will come. University of MN has a good article at http://www.extension.umn.edu/distribution/horticulture/m1257.html and the one I have linked below compares 7 different planting options.

Now I am going out to plant mine; I cut them 2 days ago. (OSU says to plant right away after cutting, not to let them dry. Seems there's never JUST ONE WAY to do anything in the garden!! LOL)

Here is a link that might be useful: 7 ways to plant potatoes