sign up for (something)
When you "sign up for" an event or activity, it means that you fill out a form that shows that you want to join. For example:
I signed up for an aerobics class at the gym.
We decided to sign up this year for the Walk Against Cancer.
You can also "sign up" someone else (usually a child) for an activity:
Maybe we should sign Gavin up for violin classes.
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