One thing I would ask is are you sure she's actually getting it all?
When I was a teacher I often was told by parents that the child was not challenged by the class content and found it too easy. While that may have been true in earlier years, their years of staring out of the window and not listening meant that in some areas they had fallen behind.
Eg one child whose parents were constantly contacting me that they needed pushing but they were one of only 5 children in the class who could not do long multiplication.
While they were very good at critical thinking and naturally intelligent, they weren't actually breezing through the content like everyone assumed because they'd stopped listening and engaging.
I spent so much time and effort trying to support this child but in practice they were essentially acting as one of my lower ability children.
This narrative that they were naturally gifted and didn't need to try actually meant they had no idea how to cope when they came across something they didn't easily understand with zero effort.
Assuming they genuinely are getting it all easily then I would also say... Often there is a bit of a misunderstanding about learning and lessons. E.g. when a child is off sick often we are asked to provide them the work we will do and the parent seems to think that sitting and doing the work will just teach them how to do it. But without the input in class and actual teaching, they can't do the work because they've not been taught how to do it.
So unless someone is teaching them, giving them more work to do isn't particularly helpful other than to practice and consolidate skills they already know.
If the class are revising long division and your child can do it backwards with their eyes closed standing on their head then giving them more work (ie more long divisions) isn't really very useful. If they can do 20 of them they can do 50.
If they understand it but make mistakes then yes they need more practice but they can also just create their own questions to practice with at that point. They can push themselves to try larger number or decimal numbers but in the end, if they can do it and have practiced then they can do it.
To actually stretch them and give them work that challenges them they need something they don't already know which is going to involve either direct teacher input or independent research. The former is not an option at this point but the latter is in some cases.
Your DD is the one who wants more work so to some extent she is going to need to take control of her learning herself. Assuming your DD is high flying, it's just not possible at SATS time that she can be given that independent input by the teacher.
I would suggest coming up with a list of things your DD can do quietly when she's finished and run this by the teacher to check it's ok. The teacher wont need to prepare and mark extra work but you're giving DD direction, encouragement and showing her the importance of learning for fun and improving for her self.
Examples:
Reading/Writing:
- Come up with a statement about a character or event in the book you are reading that you absolutely do not agree with but someone else might think is true eg "Tyler is lonely in class" and find three pieces of evidence that it is wrong. Then as much evidence as you can that it's right. Form a debate with both sides arguing their case.
- Imagine two characters are trapped in a lift. Write a script about what happens. Try to make the characters behave and speak just as they do in the book.
- At your next chapter cliffhanger write what you think happens next. Read on and see if you were right.
- The next time the main character is experiencing an intense emotion, stop and write a diary entry as them. What would they say?
- Give a way you are similar to main character and a way you are different.
- Write a newspaper article about lunch time. Make it as serious as possible and structure it like a real newspaper article.
Maths:
- Wrong answers only. Put a calculation in the middle of the page (eg 157 + 28) and work out the correct answer. Then try and find as many mistakes as you can that someone might make and come up with as many wrong answers as you can. Eg in above example, perhaps the forgot to "carry the 1" in the first column so for the 175 instead of 185. Maybe they subtracted instead of added so got the incorrect answer of 129 etc.
- Try and explain this maths concept to someone who cannot speak English. Use pictures, cartoons, symbols, arrows.
- Make up your own maths board game eg land on squares and have to solve a maths problem etc. If wrong, go back spaces.
- Create a 3D city. Each building needs to be made with a net of a shape. You must have at least 3 cylinders, 4 cuboids and 5 triangular prisms. You can also have any other shapes you like. You must be able to get everywhere in your city using the roads. If you can't make a net of it, it can't be built in your city.
I won't carry on unless anyone cares enough to want me to.
It does require work to get the list made but if your DD isn't challenged then this can be her first challenge.
You can help. But I do think unfair at this point to expect the teacher to be able to teach, prepare work for and then mark and give feedback.
I think it's more likely that revision is just boring (it is!) and I would be wanting to check how well she's actually doing in her SATS practice first.
If she is advanced then she will spend a lot of her life (school, work etc) being dragged behind by people much slower than her.
Developing the skills to stretch herself, research, ask questions, find things out for herself and take control will be helpful. She's not too young. She might need help to get ideas going but if she's clever enough to understand everything in class easily then she's capable of pushing herself in this way too.