At the NCTM Regional Conference in Kansas City, MO, the TMTG team presented their approach to kicking off lessons in ways that motivate and engage students (presentation slides). The inspiration for this approach comes from the storytelling techniques of film and literature — inciting incidents.
Inciting incidents are the major events that happen early in a story and propel the main characters into the central action.
- A photographer in a wheelchair thinks he sees a neighbor kill his wife; he’s not sure but he needs to find out. (Rear Window).
- A friendly ogre is content to let others think he is mean and scary because they leave him alone in the peace of his swamp, but suddenly one day his isolated swamp is swarmed by countless fairytale characters. How will he get rid of everyone and get back to his normal, isolated life? (Shrek)
- A young woman is growing up on an island of women, in the protective arms of her mother and safe from the dangers of Man’s World. Then a mysterious airplane crashes near the shores of the island and a man (!) arrives on the island, bringing with him the violence and dangers of World War 1. (Wonder Woman)
These inciting incidents hook people into the story—they naturally want to see what will happen next and how the main characters will resolve the issue. In the NCTM Regional session, the TMTG team brought this idea into the context of mathematics lessons. They shared several examples of how typical lessons can be invigorated with some incitement!
One example is that, instead of starting a lesson on quadratic equations by giving the definition of quadratics and showing the typical form (y=ax2+bx+c), you can try to interest the students by creating a sort of mystery. “Here is a set of equations that look varied but they are all quadratic, and here is a set of equations that look kind of similar, but they’re not quadratic. Can you figure out the difference?” Further detail on this example
More examples were shared during the session and a discussion of the key features of inciting lessons were discussed. If you have some ideas about lessons that start with inciting incidents, please share them in the comments below.
Two-Minute Teacher's Guide 
Another example of an inciting incident in math:
Here is an equation, 7x=24. There are infinitely many numbers that we can plug in for x, but only ONE number will actually work. Only one number will make this a true statement. Today we are going to find out how to find that one number, one needle in an infinite haystack.
LikeLike