I have a story set in a fantasy culture modelled after the pre-pottery Neolithic people. One of the main characters is a child who is somewhere between 5 and 8 years old, and there are several other kids in the story too, but in this setting, people don't pay careful attention to year of birth, so the children won't be referred to by age. How do I suggest the approximate age of these kids to the reader, without having the perspective character estimating ages?
Vocabulary is a good way to show age without mentioning it. Mannerisms. Attention spans. Interests. Pragmatism. (or lack of) Innocence. You'd really just need to pay attention to how a child of the age you're looking for would act, then trust your readers. If age doesn't matter so much in your story-world, if written well, it won't matter so much to your readers either.
You could probably reference them by their place in the social order - like, "one of the mob of children too old to be tied to their mothers but too young to be any real use on their own" or "a year or two away from their first hunt" or whatever landmark events would make sense for your society.
There is a short story by Nabokov called "A Bad Day" or "A Very Bad Day." You can probably find it very easily if you look at his short story collections at your library or bookstore. You might be able to find it online even. I didn't check. Anyway, I read it a long time ago, but has a lot of children in it around the age of your characters and I don't think he ever mentioned ages either. But I did have a clear sense of exactly how old the children were. I can't remember how he got this across, but I think it might be worth taking a look at.
I like @BayView's idea of referencing where they fall on the social ladder, and to I guess kind of elaborate on that I'd suggest mentioning their capabilities - eg are they old enough to help with gathering if not hunting, are they strong enough to help fashion tools, does their play mostly involve staying in one place and fiddling with nearby rocks and sticks or are they running around, climbing trees, getting underfoot, etc. I've never really spent time around children myself so something like that would be a lot more helpful to me as a reader than dropping a numerical age anyway
One fairly clear age is toddler age. You could tie others to that. Joe is running so fast! To think he just started walking last spring. No, it was the spring before that, remember? Right after the big flood; he was a walking ball of mud until midsummer. Oh, yes, I remember. Jane had to drag him home every evening; she was barely big enough to lift him. This tells us that Joe is four or so, and Jane is six or seven. It's all a little "As you know..." backstoryish, but I think you could scrub that off with some context to put it in. You could similarly ramp down from puberty.
I just wonder if there were such people; I figure that hunter/gatherers or farmers are even more tied into the seasons than moderns are. I can see them not knowing the kids birthdays, but to know that Ug was a winter baby, and this was his third spring seems more realistic than "He's getting too big not to help in the fields" being the sole determiner of age.
I was wondering about this, too. Not having written dates wouldn't, to me, equate to not knowing people's ages, especially children's ages.
I wonder if, in a non-industrial society, ages might not matter as much as they do with us. We have kids going to junior kindergarten at three years old simply because they're three years old and that's when JK starts, and the kids come in with hugely different stages of development, readiness for school, etc. But we glob them all into the same classroom and work pretty hard to keep marching them in lockstep through the annual grade progression for the next fourteen years, and then the next four or whatever. Maybe we're kind of obsessed with age, and non-industrial people might have a different system of keeping track? The neolithic kid who goes on his first hunt when he's thirteen just because he's thirteen would probably be pretty screwed if puberty hadn't hit him yet and he was still physically a little boy. I couldn't tell you the ages of the people I work with--there are some still-young-and-partying people, some young-family people, some kids-are-teenagers-parents-are-getting-their-lives-back people, etc. Knowing their numerical age isn't that important (until the retirement countdown begins!) TL/DR: I like the idea of them going by stages rather than ages.
In early industrial revolution schools, the whole school would be in the same classroom, and often only had the one teacher, who would teach you what you could cope with. There was no national curriculum. Fully agree with the "lockstep" mentality. My daughter was categorized as above-average intelligence so, when she started school she was bumped up 2 years because she was too bright for reception. She suffered because she wasn't mature enough; she fell asleep in class because she was little more than a toddler; and she was still bright enough to be marking the work of the kids 2 years older! She bounced around all the way through infant school, up a class, down a class. Her intelligence and her emotional maturity weren't in step, and the system doesn't know how to cope with that. Fortunately, she grew up pretty level-headed in the end!
Are there strong seasonal differences where these people live? Adults may not pay much attention to the exact age of children, but the children themselves may be more acutely aware of their own ages compared to their peers as they progress from being seen as "baby" to "child" to "almost adult", and then to "adult". If your story is set somewhere where winter and summer are markedly different phenomena, kids may well know how many winters or summers they've seen in the context of interaction with other youths. If I've seen eleven summers and dad takes me bow hunting today for the first time ever and my little brother tries to get in on the action, I may well remind him that he's only seen 5 summers and is going to have to wait his turn for this special day. If it's set somewhere where seasonal changes are more subtle, then perhaps not. Where I live now (Puerto Rico) would be a such a place. Not that it's impossible to tell the difference between one season and the next, but it's a subtle thing, easily overridden by other factors consuming one's attention in a life like the one you propose in your story. I mention this only as something to consider as part of your choice for setting. ETA: None of the above, in my opinion, precludes you in any way from including this feature as regards how adults engage children age-wise, but @BayView's example of the "late bloomer" brought to mind some interesting ideas as regards the different way in which adults and children, respectively, could possibly engage one another. I could easily see the late bloomer Bayview mentions feeling slighted for being passed over, yet again, for his first hunt and giving a surely "I've seen twelve summers. I'm not a baby."
I was wondering that, but a hurried Googling tells me that there's evidence (tick marks) that paleolithic humans used counting.
Just focus on writing realistic children - so long as YOU know their age, it's fine. If year of birth is not important, then neither would your characters be guessing at people's exact age, since age as a concept wouldn't really matter as much to such a society. If your children are realistic to their age in their behaviour and thinking, your readers will be able to infer from that. Does it even matter anyway?
This is true. If you know the children's ages, and write them accordingly, then after the book is done and you've let it sit for a while, you can re-read it and see if there's any actual confusion that needs un-confusing. And if you have beta readers, see if they ask you any questions.