While I was walking along a trail in a local nature park I found a grasshopper that wouldn't move even as I crouched down to look at it. When I examined it very closely, I noticed that its back end was inserted into the soil. I wondered whether it was laying eggs, so while standing watching it, I took out my phone and Googled "how does a grasshopper lay eggs". It was then that I realized she was doing just that!
Since she was out in the open and very vulnerable, I stood by her to stop two young girls who were running up and down the trail from inadvertently stepping on her. I didn't realize that it would take 35 minutes for her to finish the job!
Here is my half minute video: Grasshopper laying eggs
Wikipedia has the following description of a grasshopper's life cycle:
Grasshoppers lay their eggs in pods in the ground near food plants, generally in the summer. The eggs in the pod are glued together with a froth in some species. After a few weeks of development, the eggs of most species go into diapause, and pass the winter in this state; in a few species the eggs hatch in the same summer they were laid. Diapause is broken by a sufficiently low ground temperature; development resumes as soon as the ground warms above a threshold temperature. The embryos in a pod generally all hatch out within a few minutes of each other. They soon shed their membranes and their exoskeletons harden. These first instar nymphs can then jump away from predators.
Grasshoppers have incomplete metamorphosis: they repeatedly moult (undergo ecdysis), becoming larger and more like an adult, with for instance larger wing-buds, in each instar. The number of instars varies between species. At the final moult, the wings are inflated and become fully functional. The migratory grasshopper, Melanoplus sanguinipes, spends about 25–30 days as a nymph depending on sex and temperature, and about 51 days as an adult.
Males stridulate, rapidly rasping the hind femur against the forewing to create a churring sound, to attract mates. Females select suitable egg-laying sites, such as bare soil or near the roots of food plants according to species. Males often gather around an ovipositing female; in some species she is mated as soon as she takes her ovipositor out of the ground. After laying the eggs, the female covers the hole with soil and litter.