Based on Ekaterina Kurae's chapter 16 from the manga, and episode 10.5 of the anime.

Learning to ride and tame dragons comes easy to most students at Ansarivan Dragonar Academy—except for first-year student Ash Blake, who is known by his fellow classmates as the number one problem child. Poor Ash is the laughing stock at school because, despite his unfashionably large star-shaped brand that marks him as a future dragon master, he has nothing to show for it. His dragon has never appeared. Until now, that is. One fateful day, Ash's dragon awakes in full glory, but appears different than any dragon ever seen before—in the form of a beautiful girl! What's worse, Ash soon discovers that this new dragon has attitude to spare, as she promptly informs him that she is the master, and he, the servant. Ash's problems with dragon riding have only just begun. (Source: ANN)

Short specials included on the BD/DVD volumes of Sekai de Ichiban Tsuyoku Naritai!

When Tomo Yamanobe's father—the former headmaster of Saint Mikhailov Academy—disappeared, he left nothing behind except for a piece of art called the icon. Soon after his disappearance, rumors of a serial killer attacking female students of the academy began to spread. As Tomo and her sister Mafuyu Oribe head home after being tormented at school, Tomo trips over an injured silver-haired boy who abruptly vanishes while being tended to. Mafuyu goes to look for him, only to discover that the church holding the icon is burning down. When she tries to save the painting, the rumored serial killer suddenly attacks her with a mysterious ability to control magnesium. Appearing out of nowhere, the silver-haired boy, who can control iron, rescues Mafuyu. Mafuyu finds out that the boy, named Alexander Nikolaevich Sasha Hell, is a qwaser—a being who is capable of controlling an element through the power of soma, received through the act of breastfeeding. Confused by the ordeal, Mafuyu attempts to move past it with little luck, as Sasha transfers to her class the next day. What will become of Tomo and Mafuyu's normal school life with the danger of other qwasers looming close to them?