The potato plants have really started growing in all three buckets now. These are the second round of 5 gallon bucket potatoes that I planted. I used the cut up and cured potato seeds in these buckets.
I added more of the soil mix that I have been using to each bucket last night. When I checked the buckets I noticed that in bucket #1 the plants had grown about 4 inches taller in the last couple of days.

I added enough soil to bucket #1 to almost cover the entire plant. It is supposed to rain today so I expect this bucket will continue to grow pretty rapidly.
The plants in bucket #2 had grown about 2 inches over the last couple of days/ I added enough soil to almost cover these plants as well.

The last bucket of potatoes is the one that is growing the slowest so far. It has finally sprouted multiple plants. They each grew between 1 and 2 inches so far this week. Since I was adding soil to the other buckets and I know it is going to rain today I decided to go ahead and add additional soil to this bucket.

I will continue to monitor the growth on these plants so that I can compare it to the growth on the first round of buckets where I used whole potato seeds instead of cut seeds.