Plant rows of pea vines in 1/3rd of the garden. In between those rows, sow a row of corn. Corn should not grow in one long line, nor in two, but in squares or blocks consisting of several rows. It is a greedy crop that depletes the soil. The peas protect the corn seedlings through May, yet by late June or early July they are all gone leaving the soil in fine shape - as peas always do. The young cornstalks are now in full sun.
The valuable space where the peas once grew can be used to sow more successions of other vegetables such as more corn, beans, beets, carrots, or young cabbages for fall. Whatever the choice, it is an early variety. Why? Because early types are quick-growing - and this late sowing must ripen before the first fall frost. Early varieties have another advantage in small areas. These plants are smaller than main crop versions, but by no means dwarf, and can be planted closer together.
As the peas provide space for other vegetables, so corn provides space for beans & squash. These, aptly named "three sisters of the cornfield", benefit each other. Cornstalks support the twining vines of pole beans. Like peas, beans improve the soil, sending nitrogen into it, and the corn benefits. Low-growing vines of winter squash, cucumbers or pumpkins shade the ground, keeping it cool and moist behaving much like mulch. Sow the corn and squash at the same time, followed by 2 to 3 of the quicker growing bean seeds per stalk, (which is thinned to the one best plant), after the other crops have come up.
Other companion crops consist of lettuce grown between the corn. Start the lettuce in flats outside in June, then transplant just within the shade. Lettuce can't stand full midsummer sun. In July, also set out broccoli and cauliflower seedlings (also started in flats) around the corn. They're shielded from the sun somewhat as they get established, yet in late summer after the corn is gone, they stand out in full sun and finish growing through fall.
In the remaining space of your garden, include potatoes which grow well vertically. Potato plants need to be hilled as the leaves grow. The only thing you need for this tip is a few junk tires, or you can build some wooden boxes to serve the same purpose. First, lay a tire down and fill it with dirt and plant your seed potatoes in it. When the potato plant starts to sprout and leaves have formed lay another tire on top of the first and fill with more dirt. Yes, burying the leaves. When the leaves come up through the dirt again, add another tire and more dirt. You can do this for about four or five tires high. Then leave it grow until harvest time. The leaves that were covered with dirt turn into potatoes, thus increasing your yield from the one plant. Theoretically you could end up with a bushel of potatoes from one plant!
Lastly a garden wouldn't be complete without tomatoes. I've canned over 2 dozen jars of tomatoes from just 4 plants. Tomato plants will continue to grow "up" as long as there is something to support them. Look for indeterminate varieties, those with stems that keep growing through the season and, therefore, produce a larger crop (seed packets and plant labels tell you whether a tomato is determinate or indeterminate). You need to help tomato plants grow vertically; tie them at intervals to a support with soft ties. If you prefer more decorative supports than simple bamboo poles, check out the offerings at garden centers and mail-order companies for attractive alternatives. No matter what kind of fence encloses your garden, you can train tomato plants to grow up it by using hooks (for wooden fences) or ties (for wire fences). Staked tomatoes grow as well in a large container as they do in the ground. Pinching tomato stems on seedlings will encourage even more stems to grow.
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