Paige Swanson is first introduced in Dr. John Sturgis's class as another 10 year old genius. She later appears at a lecture at a museum and dares Sheldon to sneak out and climb into a closed exhibit.
Paige first appeared in "A Rival Prodigy and Sir Isaac Neutron" during another of Sheldon's classes with Dr. Sturgis. She is (almost) as smart as him, causing him to be jealous, especially when Dr. Sturgis praises her too much in front of Sheldon. Mary invites Paige and her family over for a play date
Paige reappears in "Carbon Dating and a Stuffed Raccoon" when she goes to attend a lecture on carbon dating at a museum, which Sheldon is also attending. A little into the lecture, they both become bored by it and wander into a closed area of the museum. In there, Paige tells Sheldon about her parents probably getting a divorce because them fighting all the time. They are then caught by a security guard who then calls in the children's fathers, followed by Paige's mother.
Paige reappears in "A Stunted Childhood and a Can of Fancy Mixed Nuts" when she and her mother in the mall and they meet Sheldon, Mary and Missy at the shoe store. Missy and Paige go off to the Hello Kitty store at Medford's shopping mall where it is revealed that they had a good conversation together. Missy and Paige have a sleepover, during which Paige warns Sheldon that his excessively mature personality might cause him to be a social misfit and weirdo as an adult. During the stay, they play with Missy's dolls, tie Georgie's ankles to his bed so he'd trip and fall (which he eventually does the next morning) and Paige tells Missy am imagined scary story to which Sheldon is a pompous, annoying little brute about due to his lack of imagination.
In "Body Glitter and a Mall Safety Kit", Paige's parents, Barry and Linda, have gotten a divorce and it has negatively affected her appearance (she no longer wears dresses, but now wears denim outfits, has changed her hairstyle and has dyed a pink streak in her hair) and her attitude (she has become snarky, mouthy and rebellious, has turned to shoplifting and has grown indifferent to her schoolwork, resulting in her grades falling), so she goes to spend the weekend with the Coopers. Her devastation over her parents' divorce results in Sheldon learning to listen and he soon offers to make the distraught Paige a hot beverage, which he does when he heads to the kitchen to make her a cup of tea.
- Paige is fluent in three languages.
- Like Sheldon, she shares a room with her sister.
- Paige is not fond of Professor Proton, much to Sheldon's fury.
- Unlike Sheldon's mother Mary and wife Amy, Paige would've called Sheldon out on his bad behavior. 
- Ironically, Paige would engage in some bad behavior herself in "Body Glitter and a Mall Safety Kit" when she shoplifted a tube of body glitter from the Hello Kitty store by sticking it into Sheldon's backpack.
- In "A Stunted Childhood and a Can of Fancy Mixed Nuts", after seeing Sheldon's homework, Page reveals that she already learned it a year ago, which leads to the conclusion that she went to high school a year earlier before Sheldon, in that case, at age 8.