If you have been anywhere near homeschooling you have met the phrase living book without anyone stopping to define it. Here it is in plain words. It means a book written by one person who is obviously in love with the subject, telling it in warm ordinary prose the way they would tell you at a table, instead of a book assembled by a committee to cover a syllabus. One voice, one enthusiasm, whole sentences. That is the whole idea, and you do not have to follow Charlotte Mason or any method to want it. This shelf is seven of them for math and for the natural world. Pick the one that fits the child in front of you this week and put it down finished. The first one is a good place to start.
Read this bit before you pick, because it is the thing you actually need. These are two different subjects sharing one shelf. They are here together because they share a philosophy, not a topic. Four of them are math: Penrose, Life of Fred, One Grain of Rice, and Mathematicians Are People, Too. Two are the natural world: the Burgess birds and Pagoo the hermit crab. Archimedes sits across both, since Bendick teaches the physics and the mathematics inside one man's life. So if you came for math, take the first four and leave the tide pool alone. If you came because you want your child outside looking at things, the two Holling-and-Burgess titles are your shelf and the rest can wait. Now the honest sorting. Every one of these is one enthusiast in their own voice, which is the test, and they are wildly different to live with. Pappas and Bendick and the Reimers are teachers explaining, warm and direct, and their books are about ideas rather than plots. Demi is telling a real folktale where the math is the plot, and it is the most straightforwardly good story here. Schmidt is a math professor who cannot stop digressing, and Fred is the one families split over. Burgess and Holling are old and read old, and their pleasure is patience, one bird a night for a term. Penrose is first only because it is the cheapest way to find out whether narrative math suits your child at all: two pages, no commitment, no program to buy into.