I'm a father of four children. Two of my daughters are this age. My son is just out of that range (15) and my straggler, my youngest daughter is under it (7).
Kids this age aren't just less-educated adults. They're different. Smart kids this age may have vocabularies that outstrips some adults' - but their concerns are different.
They want to know how everything works; why the world is how it is. Distracted and fascinated by things that adults may find mundane or boring or intimidating. They didn't live the past, so they don't understand it. The world is new and intense and they're only beginning to understand its nuances. They live in an eternal now. They're developing their own passions, making an identity for themselves. They seek out new things - often music, art, literature, technology, the other sex.
Their brains are sponges. They have an deep understanding of technology. With language roughly adult-like, they can ask both profound and child-like questions. They make up words. They use words wrong. They come to absurd conclusions about the world. They know emerging trends in pop culture, whether music, movies, video games, the internet - especially YouTube. They use words that I don't know, they know things I don't.
I doubt kids this age conceive of life prior to the internet.
They speak and dress to either establish their own identity, or lose it to the crowd, depending on their mood and their personality.
They live and breathe YouTube. There's a cultural drive to be a YouTube sensation that resembles what it was like to be a rock/pop star in my generation. They love Minecraft. They love Japanese pop culture, like anime, manga, vocaloids and Pokemon. They love video games more than movies or television. They love Mario, Luigi and MegaMan. They know memes and internet culture.
To write children this age convincingly, spend some time with them, either online or in person. They can open up new worlds for you.
EDITED: for brevity.