Not a house plant but pole beans might work.

Thank you for the advice dellis326, how high would you estimate a pole bean plant to grow from a seed in a month and also from a seedling in a month? Thanks again,
Katy

Morning,

Katy, when is your project due?

Most tropicals and succulents sowed from seed, 'especially this time of year,' take time to germinate, let alone grow 'x' height/width for your experiment.

Marigolds germinate within 10-days. Not a typical house plant. Although I've sowed seeds indoors..problem is, Marigolds, and other annuals, need fresh, circulating air, quite a bit of sun. If air is stale, annuals attract Spider Mites.

To be honest, I can't think of one tropical or succulent that will germinate and grow enough in one month.
Perhaps, somone here who lives in a warm climate, sows seeds, has an answer.

There's a plant called Mimosa. Mimosa germinates fairly fast.. It's annual in cold areas, perennia in warm climates.
Mimosa 'might' do.
A plus is, when leaves are touched, they move. You may get extra credit for a moving plant. :)

Good luck, Toni

From the very basic questions you asked, and unusual premise, I don't understand what's going on. Agreed, that is a very short amount of time for this experiment. Also agreed, plants usually called house plants are rarely available as seeds. Is this for high school or a college class? If varying quantities of water is the experiment, why would you ask how much to use? What is this experiment intended to prove or disprove?

Coleus might work. Mirabilis jalapa (4'o'clocks.) Basil, dill, oregano.