Ideas for extra curricular when Year 3 schoolwork feels easy

If you want to develop brain power, maybe move to piano lessons from keyboard to expand repertoire and opportunities. Or learn violin or another orchestral instrument. Look at the links between academic achievement and music.

I agree with that. The dcs did music theory exams which become quite mathematically-testing!

I subscribed to learning French kids’ magazines - they start from a young age and go up to A Level. They’re not very expensive and dd really enjoyed them.

In yr 3 dd was bonkers for Lady Grace mystery books. Sleuthing with a bit of history!

Can you play chess, Bridge or Mah Jong? Or something similar which teaches strategy and problem solving but is also a game.

Agree with additional music or theory lessons suggestions but maybe a bit too young for written theory books. Look at the Kodaly method to start with and move towards more formal books or practical musicianship classes from age 10.

Chess
card games - could start simple and get increasingly complicated
Go is a Japanese strategy game.

Board games - including ones like Solitaire, Mastermind and Draughts.

Lego, mosaic kits, dot-to-dot, Sudoku, mandala colouring pages, other puzzle books.

Reference books and non-fiction. A decent atlas with descriptions of the countries, lists of waterfalls, capital cities, flags of the world etc.

Maps. Buy a good OS map of your local area. How to read a map is a dying art.

Let her watch documentaries by people like Prof Brian Cox.

Provide the wherewithal and let her stretch her brain however she wants to. She doesn't need any more 'learning' activities.

I’d add a team sport

OP, it might help you if you watch some TED talks by Sir Ken Robinson.

What interests her? DS was quite self motivated at that age. He always found the topics the most interesting subject in school and would research around the topic and delve a bit deeper outside of school. His hobbies and interests started to develop. When I say hobbies, I don't mean after schools and extra curricular especially. Music was important to him, although finding a good teacher was quite tricky until secondary where there was access to instrument lessons via local authority. I think we'd been a bit unlucky with some of the other teachers.

Music will definitely stretch and teach practice and perseverance. I don’t think brownies badges really does much to be honest. All the kids seem to get them even if they can’t be arsed to try that much.

Like the others say it depends a lot on what she's interested in. Have a think and look for suitable christmas presents maybe? e.g. mine had a lot of fun with electronics kits, or there are a huge range of kids science kits. Again, if science is her thing also look out the dyson challenge cards - lots of simple practical experiments using stuff you might already have around the house.

Or if she's a reader, explore authors she might like. Classics are quite good for younger kids as there's nothing age inappropriate but great vocabulary and the challenging of understanding the different time and culture they're written in. There are some lovely non-fiction books for primary school kids too. Even some of the older-targeted usborne lift the flap type books have some heavy duty ideas and information in them. We had a maths one and a human body one that got heavily used. The horrible history/murderous maths etc series are a lot of fun but also a lot of information.

Writers like nice (lockable?) notebooks and pens, story dice are quite fun as an idea but DD never took to them. Really just time and notebooks and scrap paper and random projects and bits of writing got strewn around the house. She does it less now, but I still occasionally find random poetic scribblings from primary school days, often on the subject of how annoying her brother is but the vocabulary is great 😂

Languages - mine liked playing around with duolingo, I know you said no screens but it's only a few minutes a day.

Anyway, give us a clue what her interests are and perhaps we can give you some more targeted ideas.

I know it's frustrating when school aren't even trying. I do think it's better to have a 'special interest' outside school than to just try to push ahead and do more advanced maths or science for the sake of it. (Unless maths or science are the special interest). More advanced writing doesn't really require any more input than standard writing, school give them the prompts they can write as beautifully as they are able. And reading you just need to find recommendations and try stuff to see what she likes.

I don’t agree with what you say about brownie badges. There are ‘skill builders’ which they work on at the meetings and yes I think as long as the kids turn up each week they’ll do the activities and get the badges.

But the interest badges have to be done at home and some are quite challenging - I help my 7 year old to achieve them as if left to her own devices I think they’re a bit tricky (to be fair brownies goes up to age 10, by then I’m sure she’ll be fine). At her brownies they are ‘tested’ and expected to bring their stuff in and talk with the tester about what they did - big step up from rainbows where we just sent some photos to the leader and they got it!

I think brownie badges might be the way to go OP, my daughter is like yours and she is very motivated by working towards the badges and I think she likes that it’s clear - do this and earn the badge - unlike school where stickers and certificates are handed out a bit more randomly basically to manage behaviour.

She also does 2 instruments, drama tag rugby, street dance, coding and a STEM club, though lots of those are basically for childcare after school.