I understand the importance of giving students examples from their daily lives to help increase engagement and relevance, but there always seems to be some student who will shoot down the idea and try to derail the process for the class. Some examples: "The car won't start" begets I don't drive; "Which cell phone plan is better?" generates "My parents pay for it"; "Many students aren't working up to their potential" leads to "So?" (Clearly, I need to continue to work on growth mindset and combating apathy)
I have had some success with using problems from fantasy and history. This year we started with the Seven Bridges of Konigsberg. Students were engaged, asked many questions and started some great strategies. It also led into some graph theory which several students used to help with the handshake problems that came later in the unit.
So I am going to try using more fantasy and history along with current problems.