Q: How can students build jump work into their practice while at home? Should they wear tennis shoes and jump only on carpet?
A: Telling students to jump in tennis shoes isn't a bad idea, especially when you don't know what their flooring is like. I might also suggest a training regimen of tracking their single-leg jumps.
For the first couple of classes, have your students do single-leg jumps in parallel standing between two chairs (or anything that supports either side of them—I often use my kitchen counter and a kitchen chair). Start by doing five single-leg jumps in parallel on each leg, focusing on proper rolling-through the foot on the way up and down. Mark down what they noticed between the two sides and if it was challenging. (Also note whether their heel pops off on either side, etc.) Next, increase the number, letting the weaker side determine the amount. For example, if they found they fatigued at five single jumps on the left leg, then only do five on the right side, as well.
Next they can start doing the single-leg jumps without holding on to anything—in either parallel or turnout. Always pay attention to where they begin to get fatigued. I know it's strange not to do sautés in first position, but it really is an opportunity for them to strengthen their jumping and balance their strength on the two sides. It's such a common pattern to favor one leg as the strong side and subtly shift how you land and push off when on two feet. When on one foot, there is no cheating.
You could put single-leg jumps into some type of combination that doesn't require much space to execute (like jeté temps levé). In a way, shifting out of the regular type of jump sequences is really a training opportunity for them, and they will see faster progressions in strength.
Working on balancing the two sides to have equal strength will mean their jumping will really improve once they get back into the studio.