  In 2010 Zagier introduced the notion of a quantum modular form. One of his
first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce
a new example of a quantum modular form by making use of some of Ramanujan's
mock theta functions. Using these functions and their transformation behaviour,
we also compute asymptotic expansions similar to expansions of $F(q)$.
