I love the summer bridge activity books, my older daughter has the 4th to 5th grade book and it is excellent. This book is a great book as well except it isn't a great bridge to 1st grade because all of the activities in the book are things she did at the start of Kindergarten. If she did this book she would be regressing, even near the end of the book it doesn't get to the level she was working at end of kindergarten.
The book never goes past adding or subtracting single digits, only in the very end of the book do they start writing words. The child starts out by practice writing numbers and letters, inserting the missing letters, circling or drawing a line to an object that starts with a certain sound, counting objects up to 10, finishing basic patterns, matching lower case to upper case,completing number sequences. There is some reading comprehension and that is when they finally begin to write single word answers which are pretty much the only point throughout the whole book where they are asked to write a word, there are about 5-7 of those pages, and each page only has maybe 3-5 words they are supposed to write.
It does include some science experiments and physical activities which I like.
Overall this would be a great book for a child just starting to become familiar with letters, numbers and the concepts that they represent (counting, phonics, and simple addition and subtraction). I think this is more a start of kindergarten book instead of something that will help prepare you for, and bridge over to first grade.