Elizabeth:
Try magazines this summer. Let her select what interests her - but there are tons of age appropriate children's magazines related to tv shows. They have math games/ word searches/ colouring/ craft/ cooking ideas + lots of reports/ stories.
You'd be surprised how much reading is hidden in something your DD will perceive as a treat.
I used to go through a huge song and dance with DD1 (a very reluctant/ poor reader - really only 'got it' in Year 4). 'Oh,' I'd say, 'that's a really expensive magazine. Hmmm. I don't know. I'll have to think about it - maybe next time' or maybe 'let's get the shopping and then we'll see.'
DD1 was absolutely desperate for the magazine after I hesitated. First it was CBEEBIES type magazines, then Club Penguin and now I fear it's Dr. Who but somewhere along the way reading took off and now she reads nightly and for pleasure.
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It's counter intuitive but DD1 (the slow reader) worked hard on working out instructions on her various video games (especially DS) - the drive to work out what she should do and get the 'hints' meant she really concentrated.
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Don't rule out cartoons/ comic books/ graphic novels.
DD1 was hugely into Pokemon (Y3/Y4) and was a very slow reader at the time. However at the start of Y4 (after a summer of reading these things - a careless purchase in an airport sparked this interest) she rushed out of class to me and said 'Mum, you'll never believe it, my arch nemesis is sitting at my table!' - Thank you Pokemon!
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Consider reading to her as well. Go for childhood favourites or stories they're desperate to read but maybe don't have reading skills for yet. I read Charlotte's Web and Charlie and the Chocolate Factory at this age. DD2 was very into the solar system - so I used to read 'fact books' about space/ the galaxy/ Jupiter/ etc.... - whatever she could find at the library/ book shops/ Oxfam/ etc...
Use your finger as you read so she can see the words your reading and have a cup of coffee/tea or water/ juice to hand. Now and then ask her to take over (maybe just a sentence) while you have a quick sip of your drink. They just think they're helping out. Gradually extend it over the summer - maybe 2 sentences, then a whole paragraph.
DD2 (now Y4) and I frequently read alternate pages (the deal is if your page has a picture so be it - less reading for you - we've been doing this successfully since late Year 2). I tend to work out the pattern (usually a book has illustrations on odd or even pages) and then chose odd or even - initially DDs got pages with pictures but gradually 'fate' would intervene and I'd get all the picture pages or would need a drink as I had a sore throat (cough cough....).
Yes I am evil....
...but it worked.
HTH