Limited edition OVA episode of Miss Monochrome.

The story of the special revolves around the Sanada brothers in their youth. Nobuyuki and Yukimura swear to each other to protect the influential Sanada clan. However, thinking of how to best continue the Sanada clan, Yukimura makes a decision, and meets with Mitsunari Ishida and Naoe Kanetsugu at the location he arrived at. On the other hand, his elder brother Nobuyuki must worry about the selfish demands made by the Tokugawa clan. (Source: ANN)

The science lessons are short "omake" bonus features originally present on the first two volumes. Each short lasts around two minutes, and stars super deformed versions of Noriko, Kazumi and the Coach explaining the various scientific aspects of the series. (Source: Wikipedia)