Potential Love Interest
Some have speculated that this is meant to indicate that she and Ryan are meant to be paired together, and many fandoms actually do pair them together but it is unknown if Disney will. During the fireworks scene before "All for One", the official parings for High School Musical 2 were introduced, and while Martha was pictured with Ryan, But in the last movie she went to prom with Jason Cross and Ryan went with Kelsi.
In the first movie, her role is rather minor. She does not appear until when Troy, Gabriella, Sharpay and Ryan are selected for callbacks. She confesses in the cafeteria that she loves dancing (while singing Stick to the Status Quo), but everyone in her presence tries to persuade her into doing what's truly hers; studying.
In the second movie, Martha's role a little larger in High School Musical 2, where she works in the kitchen of Lava Springs Country Club. She is friendly with Kelsi and Taylor, as well as Ryan, with whom she dances in the movie's last number, All For One, until Ryan and Zeke switch partners, in which case, Sharpay is with Ryan and Martha is with Zeke.
In the third movie, she has become a cheerleader and is working up for the spring musical with everybody else.
On graduation day, while giving his speech, Troy mentions her and her dancing skills. She was late for school.