I don't know if a cup would be the wisest thing to do a freeze precip in just because if it has a narrow mouth, it may be difficult to scrape up. I've also found additional surface area from tupperware to be helpful in getting everything to freeze precip evenly and quickly. Perhaps the tek calls for multiple jars because of this surface area issue? I only use one piece of tupperware and it works fine.
"Science without religion is lame. Religion without science is blind" - Albert Einstein
"The Mighty One appears, the horizon shines. Atum appears on the smell of his censing, the Sunshine- god has risen in the sky, the Mansion of the pyramidion is in joy and all its inmates are assembled, a voice calls out within the shrine, shouting reverberates around the Netherworld." - Egyptian Book of the Dead
"Man fears time, but time fears the Pyramids" - 9th century Arab proverb