Current interactions for the Internet of Things are often constrained behind a screen. With the Internet of Tangible Things (IoTT) we aim at promoting the design of richer interactions, embodied in physical IoT objects. To this purpose, we propose a card set for the design of tangible interaction with IoT objects, which contains 8 cards for tangible interaction properties and 8 for IoT properties, in order to explore how tangible properties can be exploited for enhancing the interaction with IoT objects. We tested the card set in a dedicated workshop, observing that participants were able to explore most of the tangible and IoT properties. To complement the IoT card set, a hardware prototyping toolkit with examples for each of the 8 tangible properties is currently under development.