English:
Reading
Daily reading is really important. It should be enjoyable, and sometimes challenging. If a book is too hard, it can be demotivating; if a book is too easy it is unlikely to lead to progress. Make lists of words that you don't understand, patterns that you notice, things you like about the book and things that you don't. Try to summarise the book (tell it in short - perhaps just three sentences for a chapter or even the whole book).
Try to read a variety of books: fiction, non-fiction and poetry.
Spelling
You can find the list of words that year six should be able to spell at:
You will need to scroll to the bottom of the page.
Maths
There are lots of excellent problem solving activities and mathematical investigations on the nrich website:
Some problems are open; you can submit your solutions to the problems on the website. Others have solutions.
Children who use prodigy are invited to to as much as they would like; the activities are mapped to the national curriculum and the game adapts to their mathematical level.