Need help to identify a quilt design
 

An elderly lady has presented me with some quilts to finish, her (departed) sister started them, but no pattern or picture. One has pinwheel blocks about 10 1/2", and I'm not sure if the others are meant to fit with them or are a totally different quilt. The 5" blocks are sewn once across the middle to another square of unbleached calico, and I am at a loss to figure what was meant to be done with them.
[ATTACH=CONFIG]590927[/ATTACH]
If they had been sewn twice I could easily cut between and fabricate something, but am not sure how good the calico would be in patchwork, it will probably shrink. Some thoughts on that would be appreciated too. So, does anyone know of a pattern with blocks made this way? Also the pinwheels are stitched to the calico the same way.

The only thing I can think of is the maker intended to make a summer quilt with those pinwheel blocks without batting and only an unbleached muslin back. (I think you meant unbleached muslin, not unbleached calico, right?) Maybe she intended the straight stitching down the center to be the "quilting" and intended to join the blocks quilt-as-you-go style.
And I don't see how the 5" blocks could possibly be part of the same quilt.

Thanks for your input, I am on the verge of undoing the sewing and doing my own thing, am sure this lovely lady wouldn't mind. I think there is meant to be enough for 2 QS quilts, a finished lap size flimsy, and a small yo-yo quilt. Not totally sure what all has been used for the backing pieces, but there is also a 20 mtr roll of unbleached calico - for the backing, which I am not using, will replace that. The pieces include curtain and deco fabrics so it's a real hodge-podge.
I was mostly stumped over those sewn squares, but they won't take too much to unsew, will they? Oh I do love a challenge.

Yeah, I wouldn't have any problem taking out that center line of stitching and doing something else if you don't like it. Last night I was thinking that you could use the 5" squares as an alternate block for the pinwheel blocks if you put four together as a four patch with a narrow horizontal and a narrow vertical strip in between them like a plus sign. Let's see: a four patch made of 5 inch squares would finish at 9.5" square, so those center strips would need to add an inch, thus need to be cut 1.5" wide. Good luck and have fun with whatever you do with them. I think the end product is going to be superior to what they would have been in plan A.