Weedwhacker said: I plant both potatoes and carrots in late May or early June 
My one grandfather planted potatoes on May Day, depending on weather; I generally try to get them in , in early May but have put them in in early June and late April, again depending on weather.
Both of my grandparents gardened by old school signs, and both had very productive gardens.
Temperature and Humidity
Potatoes should not be planted until the soil temperature reaches at least 45 degrees Fahrenheit, and preferably 50 degrees. Summer crops do best in areas where the summers are cool, as the potato tubers grow best when the soil temperature is 60 to 70 degrees Fahrenheit, and they stop growing when the soil hits 80 degrees Fahrenheit. Mulching around the plant, such as with a thick layer of straw, can keep the soil as much as 10 degrees Fahrenheit cooler. Areas with hot summers often plant potatoes as a winter crop. Potatoes don't have a preference when it comes to air humidity.
Moon phases and garden tasks
Certain garden chores should be done in sync with specific moon phases. After the crescent during the waxing phase, moonlight gets brighter and the gravitational pull stronger, encouraging above-ground growth of stems and leaves. This is a good time to plant leafy annuals such as greens, corn, grains, broccoli, and cabbage.
Between the first quarter and the full moon is the best time to plant annuals with seeds in the fruit, such as beans, tomatoes, squash, peas, and peppers. When the moon is full, the light and available moisture are at their peak.
After the full moon in the waning phase, moonlight and moisture begin to decrease. Growing energy shifts to below-ground growth, making this a good time to plant root crops, such as beets, carrots, turnips, onions, and potatoes. In the ornamental landscape, it's time to plant bulbs, biennials, and perennials. Do your pruning now, divide perennials, and plant trees.
In the final moon phase, heading back to the dark of the new moon and the least amount of gravitational pull, it's time to let the garden rest. Take care of maintenance by weeding, mulching, fertilizing, and harvesting. Do not plant until after the first crescent. When you harvest vegetables near the new moon, they will keep longer. Use this time to pick and store things like apples, potatoes, and winter squash.
