You'll Need:
Cardboard egg carton
Plastic wrap
Small bag of planting mix
1pkg of seeds (marigold, cosmos or petunia start easily)
Spray bottle of water

First pour soil into the bucket or dish pan. Add just enough
water to make it damp, not "soupy". Use a soup spoon to place a small amount of soil into each egg cup. Following the package instructions, make a small depression into each cup of soil. Place ~ 2 seeds in each hole and cover
with a light layer of soil. Mist with the water. Then cover loosely with plastic wrap and place in a dark room or closet*. Be sure to keep the soil moist Have your child check the seedlings daily and older children can even chart the progress. When sprouts show, replant according to the package instructions. Cosmos, Marigolds, and petunias will do well in a flower garden or pot. After replanting & placing in a sunny location give your child the responsibility of plant care e.g. watering and cutting back if they get to full.

* You may have luck placing your seedlings in a sunny window. However, I've found that the plastic wrap creates too  much moisture and will rot the seed. 
Trying both locations will be a good experiment.

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