I want to teach my kids how to cook because I think it's a generally useful life skill. In addition to working in the kitchen and actually preparing dishes, how can I get them more involved in the ingredient acquisition process? Currently their presence in the store is largely just "I'm here because Parent needs to shop."
(The ages range from 3 to 11, so this is not particularly focused on one age group. I expect this to be a long-term habit for me and them, anyway!)
For us it was two simple information radiators: the shopping list on the fridge and the weekly meal plan hung up nearby. Once a child could write, if they used something up they had to write it on the shopping list. If they wanted something we didn't have, they had to write it on the shopping list and we generally bought it. Yes, this resulted in some adorably written requests for MASHMLLS or CHKLIT, some of which we granted. Visiting children were also taught that when stuff was used up it has to go on the list. And we allowed our children, and visitors, to prepare food with an appropriate level of supervision.
It's simple enough, when you're making the meal plan and having trouble thinking up 7 meals, to ask the kids what we haven't eaten lately that they would like, and to put that on the meal plan and then add the items to the list. These two things will have them routinely engaged with the shopping list when they are at home.
In the store, they can perhaps push the cart (badly pushed carts frustrate parents and other shoppers, so make this a privilege that is easily revoked) and definitely get things from the shelves for you. We need canned tomatoes, get me 4 cans. No, that's not our brand, the one to the right of it. (For a young enough child, this is great for practicing counting, left and right, colours etc.) Hm, this size of the oil is 3.99 and this size is 5.99 and if you look at these tiny numbers on the sticker you can see that the larger size is a better buy. Let's get the large one. This label means the soup we like is on sale. We're going to buy more than usual because it's cheaper today. We need some sweet peppers. That one is wrinkly, don't buy a wrinkly pepper. We need apples. What kind of apple should we get this week? We need avocados. Make sure they are not rock hard. We need some meat. Wow, $11 for one steak? We can't afford that. Maybe we can afford the pork chops. I could buy this blade roast and pot-roast it, we like pot roast right? It's less than half the price of the sirloin roast. We don't buy chicken here sweetie, they inject salt water in it and I don't like how the chickens are treated. We can get chicken at the farm this weekend when we get the vegetables. There is already sweet cereal at home and it's not on the list, so I'm not getting that. Yes I know you wrote marshmallows on the list again, but they are a once in a while treat, not every week, so I'm not getting them. Hey! I saw that! Do you really like tuna that much? Don't put soft stuff down in the bottom of the cart, your brother might put a can on it and we don't want to squish it do we? I'll put it up here. How many bananas do you think we need for a week? Remember there's no school on Friday so everyone will be home for lunch.
Yes, it takes a LOT longer. But it's an apprenticeship. My kids are great cooks. One was able to be vegan (which requires a lot of attention to detail and willingness to cook for yourself) for extended periods of time and one is a chef (went to culinary school, works in restaurants and catering.) One of the visitors even followed those footsteps, also went to culinary school, and also works cooking.
For younger kids:
One thing that worked for us (once the kids learned to read) was a 2-prong approach:
Explain in detail the heathfulness of specific ingredients (starting with "junk"/"good for you" at early age, to more in depth science later on).
Have them read all the ingredients on any item in the kitchen, and discuss the items overall healthfulness.
This is easy to gamify in many ways, e.g. "find the healthiest item in a bunch", or "which of these items are good for your eyes?" (find VitA/carrotine filled stuff), or "Sort these items by how much calcium it has" for higher maths skills.
To parrot an ealier answer, it's very helpful to involve them in making a shopping list (in our case, a more-fun experience since it involves a specialized shopping-list web site + smartphone app) - both as "clerk" work adding items on parents' behalf; and on their own when they wish something to be bought.
The usual approach to teaching younger kids - games. Many kids play-act shopping trips (including playing both shopper and cashier).
For older kids:
Another way to gamify (especially for older kids): you have to contribute to reap the fruits.
only cook some much-requested but high-effort treat if they do X amount of help with whatever cooking related chores you wish them to participate in, including shopping. Those who didn't pitch in get basic, low-maintenance food.
if a specific kid asks for specific (less usual) meal requiring specific ingredient, it only gets made if they got that ingredient themselves last week's shopping.
To address the update that the concern is mostly with older kids who become apathetic:
First, one possible approach to take is to not as closely associate ingredient shopping with cooking. While they are intrinsically linked for high-level chefs who must discriminatingly choose best quality ingredients, for a 15 year old, merely knowing that a specific ingredient is junk or OK may be quite enough, and would be for the rest of their life.
For one thing, if you live in a large city in USA, in 10 years your kids may very well never do their own grocery shopping, and use Fresh Direct or its like. I know plenty of coworkers in their 20s who never go to shop for food, between Amazon and Fresh Direct.
If you consider food shopping to be incredibly important for their development as cooks - despite the points above - merely treat (rom both their side and yours) food shopping to be the same as any other chores, with the same approaches/incentives/punishments that other chores involve.
A slightly different (and perhaps, better for you?) approach is to treat it as any other "learning skill - make it required that they demonstrate proficiency as a necessary requirement for making the skill practice optional. E.g. "if you want to sit in a car and read a book when we go to the supermarket; 3 weekends in a row you must perfectly pick good and correct food items in the store according to my criteria".
This approach has 2 benefits - on one hand, it gives them a goal and an incentive to actually become proficient (unlike a regular chore); on another hand, it actually achieves your goal that you seem to state (not that they food shop instead of you, but that they know HOW to food shop).
You plan a day.
You ask them what they want to eat. You then write a shopping list. (You might want to buy some food magazines so that you can cut out pictures of food and use some glue-stick to stick them to your shopping list.)
You go shopping. You show them how to buy fruit and veg and meat (if you eat meat).
You come home and you cook and get them to help you.
That's obviously a busy day, but you only need to do it once a month or so for the lessons to stick. And the individual parts can be done any day.
You could also set up "meal planner boards", with pictures of food and they stick what they want to eat in the box at the top.
