Gradual typing integrates dynamic and static types. Since its introduction, it has been successfully applied to several extensions of simple types, including subtyping, parametric polymorphism and substructural types. This work studies its application to intersection type systems. We introduce a new approach to define a gradual version of the original intersection type system of Coppo and Dezani. We then present a new operational semantics for terms typed with static and dynamic intersection types, which enables dynamic type casts and identifies the causes for type errors in a framework inspired by the blame calculus. Finally we prove several properties of our system including a correctness criteria and soundness of the extension of the original gradual type system.