Turn the plastic tub upside down and drill 10 to 15 small holes in the bottom in a random pattern.
Place four concrete blocks in a square on top of the grass. Set the tub on top of the blocks and use a level to ensure that it is level. Once the tub is full of soil, water and sweet potato vines, it will be too heavy to move.
Fill the tub with equal parts potting soil and compost. Mix well, and add water until the planting mix is moist.
Dig a 5- to 6-inch-deep hole in the middle of the tub. Insert one sweet potato slip into the hole and cover it with the planting soil. Tamp the soil gently and water thoroughly.
Add 3 inches of mulch to the tub, pulling the mulch away from a 6-inch circle in the center of the tub, over the slip. Mulch inhibits weed growth and helps the soil retain water.
Water twice a week unless the weather is extremely hot. Test the soil by pushing a finger down into the soil. If it is dry, water. If it is moist, wait another day or two before watering again.
Fertilize with 5-10-10 fertilizer according to the manufacturer's instructions. Too much nitrogen will encourage leaf and vine growth and skinny roots.
Harvest the sweet potatoes in 90 to 170 days, depending on the variety.