Hi Awful Maureen:
DD1 (Y6) sat the 11+ earlier this year here and didn't quite make the grade (we think she'll be 10 points from the cut off). Now here, grammars are state funded, the test is free and frankly you have very little to lose by going for it. I felt it was worth doing because DD1 was keen to do it (I suspect because many of her friends were and she wanted to go on to grammar school with them). My view was definitely NOT: pass the 11+ or else! - but was doing this extra work, reading better quality fiction, etc... was a huge improvement to what her school was doing and would help greatly to get DD1 to where I would notionally expect a reasonably bright primary pupil to be at the end of 7 years.
My first piece of advice is invest in the Bond's Parent's Guide to the 11+ (link: www.amazon.co.uk/Bond-The-Parents-Guide-11/dp/1408515822/ref=sr_1_1?ie=UTF8&qid=1391682003&sr=8-1&keywords=bond+parent%27s+guide+to+11%2B). This will explain what the 11+ involves and includes an assessment test that let's you gauge whether you child has a reasonable chance or not. (DD1 was borderline for passing on this - and indeed that seems to be what happened in the end).
You can 'dip your toe' into this whole 11+ thing with Bond 10 minute practice books. See how your child does. If they're freaking out, saying it's way to hard and they're using a book for 8 - 9 year olds when they're nearly 10 - that doesn't bode well. If on the other hand if your 9 year old is sailing through books for 10 - 11 year olds - they really should go for it.
In reality - the issue with maths is sound calculation skills sure - but primarily good comprehension. Most of the 'tricky' problems are about understanding what the question is asking and answering it appropriately (so getting a paragraph with information about the number of toys different children might have and then being asked to work out what a new child has in relation to this data: i.e. Sally has 8 more bears than Sam, Sam has 4 more bears than Tony and Tony has 5 bears. How many bears does Sam have? You may have lengths in Km and m but they want the answer in cm or prices in pence and in pounds and they want the answer in £ - so knowing how to convert that).
Finally - you know your area. What are the alternatives. Here the comprehensives are uniformly dire - around 40% attaining 5 A-C GCSEs and one secondary in special measures. If you're facing that - you do have to consider the impact being educated in such a poorly performing environment is going to have on your child. Sure it can be poorly performing for all sorts of reasons, other than poor quality of teaching, but nonetheless on the face of it the odds looked stacked against your DD getting 5 As at GCSE. (1% of pupils at our local comprehensive).
Genuinely - go to an open day - let your DD see what they have to offer at both the grammar and the comprehensive. Start simple - insist of good quality fiction (e.g. www.elevenplusexams.co.uk/advice/english/reading-list) - which certainly won't hurt and if you use school/ public library won't cost much. Have your DD read to you - ask her what she thinks more challenging words mean (my DD1 often fudged this - so it was a real eye opener to the fact she was skipping difficult words in her reading - and too lazy to look them up). But also discuss the books. How the other uses certain 'tricks' of writing to make it more interesting, how characters feel, etc... Again - all low budget - and certainly good for preparing for 11+ - but generally good no matter what.
With maths - look into things like Kahn Academy - which has now set up US curriculum & is entirely free. US grades are -1 year behind UK Years - so US Grade 5 = Year 6. link here: www.khanacademy.org/ - click learn on black menu bar, then math, then click the grade number 1 more than your DC's year.
Encourage maths video games/ apps - there's tons out there - to improve speed of calculation skills.
There are tons of on-line maths tutorials - many cheaper than a tutor: mathsfactor, maths whizz, mathletics & komodo maths have all been praised here.
Going for the 11+ can be seen as a snobby choice - but in reality it's an academic one where you're consciously choosing to aim high and to send your child to a school where it's likely they'll be working at a fast pace and pushing your child to perform. In effect your choosing a school which is designed to prepare your child for entrance to a Russell Group type University degree programme. This isn't for everybody, it does require children who can persevere & who aren't afraid of hard work - but the reasons grammar's are popular is that they do get some rather exceptional results with the pupils they teach.
HTH