To relate it to STEM I found an activity on NASA. Instead of making it an egg drop the students were told they have been asked by NASA to come up with a way to safely land a Mars Rover. They don't want any of the expensive components to break. The egg would be modeling the rover. This gave them a real word context.
My students had a great time with this activity. I had a variety of ages, so there were some challenges. I learned that is much easier when students know how to blow up their own balloons and tie them. They also had trouble putting the string through the holes for the parachute. We also learned taping a balloon to the sides is not the best way. We also learned that you learn just as much from your failures as you do your successes.
Here is what we did.
Engage: I engaged the students by showing them how strong an egg is. We talked about how the curved shape helps spread the force evenly. We also talked about how they are fragile if you tap on them. We then placed cans on top of 4 eggs to show their strength. This always gets them focused.
Then the students got to work. This was a very open ended exploration. They could build it anyway they wanted to. I provided lots of different supplies. Different sized boxes, lots of tape, zip ties, plastic bags, packing material, foam, newspaper, whatever you can find. Many students had success and many learned that their container needed less mass and a way to slow down. I wish I had a video, but I was too busy dropping the containers.
I found several directions on-line. This is the site I used. I like the use of cereal boxes for the space capsule. The only change I would make is how the balloons were attached. Tape does not work well. I would follow the directions from the video. They show placing a hole in the center of each triangle. The end of the balloon gets pushed inside. This would hold the balloon much better. We had great success with this model. The parachute size was perfect.
For the complete directions go here: https://solarsystem.nasa.gov/docs/Egg_Drop_508FC.pdf
I will definitely do this lesson again. The kids just love it. Very memorable.