Here are some I have always heard/believed:
**Hornets nesting high in a tree means there will be a lot of snow that winter.
**Thick corn husks/silks, and onion husks mean a cold winter is coming.
**Woolly worms. The ratio of brown to black is the ratio of mild to severe cold in the winter.
**When the frost flowers bloom, you are six weeks from a frost.
**Thunder in February, frost in May.
**Fogs in August correspond to snows in the winter.
The Farmer's Almanac has plenty of these sayings in them. I would encourage you all to look for local signs to that point to weather changes. Personally, here are a few I have noticed:
**When the sweet gum turns red, Fall is just ahead.
**The clouds, and clarity of the sky usually give a hint to the season you're in. Big clouds, clear blue sky in the early Fall. Wispy clouds, and light blue sky in the spring.
**Iron weed blooming is always a good pointer to fall.
**Chickens nesting in the spring and fall.
I am also a public school teacher that deals in natural sciences too. Some projects you could do:
**Buy a rain gauge, and record the amount of precipitation in a set time period. Compare the next year. Or total for the year, and plot the data on a graph.
**Record the temperature throughout the day by the hour, and calculate the average temperature for the day. Or record the temperature throughout the week at a certain time, and calculate the average temperature.
**Record the temperature for a specific day each month, and average it for the year.
**Buy a hygrometer, and record the impacts on vegetable plants with a photo.
I literally could go all day with ideas! Hope this helps