Ok, if she is having trouble translating the fun applications of maths with the formal application of it so work on that. Yes summer is for fun but it is 6 weeks which is an age to a 6yo, she will suffer for spending 10 mins a day doing some maths stuff!
Try the necklace of beads approach, string up sets of beads (1,2,3...) and ask har to arrange the beads into groups of 10 (2 strings to a group) hopefully she will pick, eg, 6 and 4 you congratulate her and ask her to write it out as a sum. THe first time you show her how it is done at the top of the sheet so she can copy down from your example.
She should get the idea from this how to think of a sum as stings of beads, once she has the idea you can give her some sums written down and ask her to make the bead strings herself from the sums. After a while ask her to do the sums but imagine the beads.
Get her taking beads away and writing down how it works (start with 10 take 3 off and put them in a new pile, write out the sum 10 - 3 = 7). As she gets the idea she should find the application easier.
Once she is confident bring out the workbooks and apply the same logic, work through the questions with the strings, start imagining the beads more and more as you go on.
You are not teaching her maths, you are teaching her a different way to see the maths problems she is set. I truely believe that anyone can learn maths effectivly if you can find a way to teach it to them that speaks to them. good luck, hope it goes well