Chalk

Chalk was a drawing and writing tool.

The Doctor often carried a piece of chalk, from his first incarnation (TV: "A Desperate Venture") to the twelfth. (TV: Listen)

The scientist Rubeish used chalk to write equations over the Third Doctor's TARDIS. The Doctor scolded him for using his ship as a writing surface. (TV: The Time Warrior)

Liz Shaw used chalk to explain to Patricia Haggard and Lou Bayliss the situation regarding the closure of a number of English psychiatric care facilities, with the notable exception of Hawthorne. After Patsy left, Liz used the chalk to draw on her photograph of the Brigadier. (HOMEVID: The Zero Imperative)

In Castrovalva, the Fifth Doctor used it to draw a map of the town. (TV: Castrovalva) When he visited Sair, he found chalk drawings on the floor of his room, and traced them with a piece of chalk to reveal their shape. (PROSE: Fascination)

The Seventh Doctor gave a piece of chalk to Ace in order to draw a protective circle around her, Shou Yuing and Excalibur to protect them from Morgaine. (TV: Battlefield)

The Seventh Doctor made chalk markings to find his way around Vilgreth's ship. (AUDIO: Last of the Titans)

The Twelfth Doctor found a piece of chalk in his bedroom, in the house of the Paternoster Gang, and acting irrational from post-regenerative trauma, used it to write equations on the floor. (TV: Deep Breath) Later, when the trauma had subsided and he had become collected, he kept on writing on a blackboard in the TARDIS control room. (TV: Into the Dalek onwards)

While talking alone in the TARDIS about the possibility of never truly being alone, the Twelfth Doctor wrote various points on his chalkboard. After placing the chalk on a book, he returned seconds later to find it missing and that someone or something had used it to write the word "LISTEN" in what looked like the Doctor's handwriting onto another board. When the Doctor told Clara he couldn't have just written it and forgotten, Clara asked him, "Have you met you?" (TV: Listen)

The Twelfth Doctor gave a piece of chalk to his tenth incarnation to aid the latter in remembering their conversation. (COMIC: Vortex Butterflies)