teach "brain games"
(I don't mean to say that you shouldn't try to get the school to challenge him more. Others had great suggestions about that. This is something to do in addition.)
Everybody has times when they get bored because they already know the material that's being taught, or they are waiting for something to happen (like waiting for a bus). Boredom is your brain getting antsy and wanting some exercise! There are all kinds of exercises it can do.
Say you're bored by the lesson about vowels. Look around the room and count all the vowels you can see; which vowel shows up the most? How many different vowel SOUNDS are in the words you can see? You say you already know this stuff the teacher is saying--so can you guess what she's going to say next? Think of an example for every vowel sound she talks about, and see if she uses the same example. Look around the room and think of the vowels in everybody's name--whose name has the most vowels, and whose has the least?
You also can play brain games that don't have anything to do with what's going on around you. Make a mental list of everything you ate today, yesterday, and as far back as you can. Can you remember what everyone in your family was wearing this morning? Turn your head a little to one side and try to remember everything that's on the wall on the other side of the room, then turn back and see if you were right. How many numbers can you see in the room, and what do you get if you add them all together? Take a mental walk down your street and see if you can remember all your neighbors' names. Pretend you're talking to a detective who needs to know exactly where you were one week ago today; how much detail can you give her? Imagine what you will do on this day 5 years, 10 years, 20 years from now. Imagine it's 50 years ago; how would your classroom, your clothes, your home be different? Pick an object in the room and try to figure out all the steps in manufacturing it.
etc., etc., etc.
We had a session on brain games in the gifted program when I was in 4th grade. It changed my life!!! I found so many fascinating ways to occupy myself inobtrusively during boring regular school. (I still wished that the gifted program was every day instead of 1/2 day a week, but c'est la vie!) I still play them whenever I get the slightest bit bored. I think this has been a major factor in sharpening my memory and attention to detail--I grew up to be a proofreader and then a data analyst!