Final answer:
The described research method of watching families at home and during shopping is known as observation, specifically participant observation within ethnographic field research. Option 5 is correct answer.
Step-by-step explanation:
The research method described in the question is known as observation. This method involves researchers watching the subjects in their natural environment without interfering.
By observing the families in their homes during breakfast time and accompanying them to the grocery store, the researcher is engaging in a form of naturalistic observation, which falls under the participant observation strategy within ethnographic field research.
In participant observation, researchers interact with or observe a group of people to gain a deeper understanding of their routines and behaviors. This method is chosen when it is important to see how individuals behave in their natural settings. The answer to the question is option 5) observation.