In the book, Katniss doesn't give Prim the mockingjay pin.
Madge, the Mayor's daughter gives the pin to Katniss after the reaping.
In the movie, Katniss says "I got this for you today" and hands her the pin, then proceeds to say "as long as you wear it nothing bad will happen" as prim is scared for the reaping.
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Spoiler Alert: Katniss resembles the mockingjay which leads a war between the districts and the capitol in the third book. The mockingjay is also on the pin that Madge gave Katniss. (this is how she was called the mockingjay in the first place)
Actually, that was only in the film. In the book, when the Reaping was over and people were coming to say goodbye to her, right after her mother and Prim left, her friend Madge, the daughter of the Mayor, gave it to her. The reason behind that is in the second book Catching Fire
After the reaping before she leaves District 12, she is visited by Madge who gives her the mockingjay pin, Gale, Prim and her mom, and the Baker who gives her cookies.
In the hunger games what is true about a bird called jabberjay
Before her first Games, Katniss received a pin that had a mutt on it, a mockingjay. When she unknowingly started the rebellion by out-smarting the Capitol, the mockingjay turned into her persona. When she went into the *Spoilers* Quarter Quell Games in Catching Fire, she was rescued by the Rebellion, and they called her the Mockingjay and she was the face of the rebellion of the Districts against the Capitol and President Snow, in the book Mockingjay. :)