Jim:
I love to see teens experimenting! It’s a very good thing. Learning how to propagate plants from suckers/leaves/etc is a very useful skill.
But an easier way to maximize your tomato harvest easily is to grow from seeds – I keep extra seedlings around (still have some!) to pop into any spare space that turns up.
And the best way to extend your harvest is to make sure that some of your plants are indeterminate.
Those of us who can tomatoes plant a lot of tomato varieties that are determinate – the bulk of the tomatoes on the plant ripen within a short span of time. Thus, you get bushel loads to can at once, not one or two tomatoes a week for a long period of time.
On the other hand, for eating tomatoes as they ripen and having that happen over a long period of time, what you need are indeterminate varieties of tomatoes. These plants will set plenty of tomatoes, and keep setting lots pretty much until the first frost. However, only a couple will ripen every week. A few indeterminate plants will keep a family in ripe tomatoes for salads, sandwiches, and such, but a garden full will frustrate a canner!
When it looks like there will be a frost, I simply cut the plant off just above the ground, and hang them inside. The plant will wilt, shrivel (and falling leaves WILL need to be swept up), and the tomatoes will continue to slowly ripen for at least another month to six weeks. – FernWise