Hi. I used to work with the Hospital Education Education Service (we had an an outreach team for children with medical needs at home) so have an idea of what you are up against. Is there no such facility in your area? I used to have to liaise with other services all the time - from Ed Psychs to CAMHS. I found that working for them opened up a world of services which are usually hard to access. Maybe worth speaking to them? If the difficulties are radiotherapy/chemotherapy/brain tumour-related then specialist advice is available from the relevant charities. Though a lot is just trying what works - chemo tends to tire children out so may be worth avoiding teaching much just afterwards; and radiotherapy can also make them floppy and tired post- treatment, depending on which bit is being treated. One of my bright little leukaemia patients was very receptive two days after his infusion, and bouncing off the walls, so we used to try and teach new things then, rather than when he was shattered from receiving medication. Brain lesions are very unpredictable in their effects and often leave subtle learning difficulties post-treatment - these can be very hard to tackle without specialist advice. I think maybe the school will be the key here - I gather she is still in school/has returned to school, but presumably there is a case worker in the hospital ed service you could speak to? In my experience children being treated for cancer tire very quickly so short bursts are more effective than a long-drawn out lesson.
Anyway, on the question of the size of numbers, I bought a fabulous book when one of my children was tiny and was obsessed with number. I have since used it with children as old as 16 (if you approach it in the right way it can be a laugh, as it is clearly a book for little ones - but actually it does help for visualising number). 'How big is a million' by Anna Milburn - and actually the poster with a million stars is quite beautiful.
I taught children who couldn't halve and double and used to buy boxes of sweets (Quality Street/Roses type are handy for all kinds of things) and did it in a concrete way - less insulting than using counters which they associated with primary school, and the added incentive of a sweet if they did well. I did halving by using concrete examples - Divide these sweets up between both of us...it is amazing how many children have kind of missed out on really understanding what it actually means. Use small numbers first - your example could be started with 2 sweets, and then to illustrate how adding a zero adds 10, use 20. I am not suggesting buying 200 sweets but if you do enough with the numbers below 50 you can start to extrapolate slowly. We used to do fun stuff with adding 100 at a time, just to get them understanding patterns - like a game - ok add a hundred, now add another hundred, now take away a hundred - always ready to catch them if they trip up. Once they are secure on the zeros start going over the boundaries, and using the odd 9 or 11 to get them to see that once you can do 10 then other numbers are just a snip away.
Not sure this will help; but I think moving away from national expectations and getting right down to what she can do, what is fun and what she is confident and comfortable with is the key. Good luck - and hope she is well soon.
Brilliant post Amber, how very helpful