Hi PasstheTwiglets:
It's so hard to directly interpret what 'I'm bored!' means.
It could be that the delivery of lessons is dull.
As you have suggested above - it could be that 'school work' isn't her thing - she'd rather be doing something else.
It could be that gradually your DD is finding the work harder and harder - and doesn't like the struggle.
--
As Periwinkle suggested - it is important to make the learning going on in school relevant.
Learning division helps you to work out how much you need to earn a month to pay your bills or save a month to buy those cool things you just can't live without.
Good skills adding, subtracting, mutliplying & dividing means that you can double check figures people are giving you - when you're buying a car, a house, and yes...even signing that big record deal.
Reading lots of different types of books broadens your knowledge of other cultures, classic stories, turns of phrase, etc.... Has she really sat down and picked up on the lyrics of some songs - there's often a lot of reference to cultural, social, and historical events; as well as literature and literary figures (I give you Heathcliff and Kate Bush/ Sting & Don't stand so close to me (book by Nabakov line). And yes I definitely know it dates me!).
It's understanding that Star Wars episode IV is frankly a pretty close reworking of Kurosawa's film The Hidden Fortress.
It's Dr. Who episodes including historic figures like Vincent Van Gogh or Einstein.
My DD1 (Y5) often says the documentaries DD2 and I enjoy watching (fantastic programme on BBC Four on bubbles recently); sadly DD1 finds painfully dull - but when it's live and a bit funny (say Volcano LIVE, Spring Watch/ Autumn Watch or Sky at Night) she absolutely adores it. So part of the battle is finding that happy medium of educational & entertaining enough to hold their interest. And that is tricky - because at least for us no two days are the same at our house. DD1 can be happy reading quietly one evening and then making dramatic sighs and pouting about the place about being bored the next.
DH and I have agreed one thing and that was to always stress that we value education and that sometimes getting to grips with something which is tricky simply does involve hard work and there really is no short cut. In fact, I suspect if you asked those idolized movie stars, singers, dancers, etc.... you'd find more often than not that there are years and years of solid work leading up to those 5 minutes of fame your DD just witnessed.
One of the things we really enjoy doing with the girls is watching the extras on DVDs about how the film was made, the original story boards, the CG work, the score, the voice over recordings, the costumes, the script re-writes, the sets, etc.... It really is useful for them to understand that hundreds of unseen people are behind the actors, animals, special effects and sets they've just seen in the film.
Hang in there and fight the good fight to keep her plugging away at school, even if it isn't always that interesting - she'll thank you for it in the end.
HTH