The kids are at an age where they can start making a lot of their own spending decisions. Give them the education and tools now and allow them to practice and make mistakes in a low risk setting (as opposed to when they are moving out for the first time or already have entrenched ideas of the inflated life style they deserve)
Here is the rough process I recommend for parents who have their own financial house in order. This in-depth is what I would recommend for teens, since your kids are younger you could start with just a couple of categories and go from there, seems like "entertainment" would be a good bet for you:
1. Figure out how much you are spending per year (or what the reasonable ideal is ) on each child in each variable category that you would like them to start paying for. These are the extra things like clothing, extra curriculars, entertainment, snacks, cell phone bills,etc. Figure out a yearly amount and divide by 12 (to get monthly, or to whichever time frame is common for your area) This is the amount you will be giving your kids each "pay period" It might seem like a lot, to all of you - you need to make it clear what this money is suppose to cover and there will be no more, they are expected to take money out of their own budget/account for everything they want.
2.Sit down with your kids and help them to set up a budget. Figure out the categories they should be working with. Include savings both long term and short term. Include savings categories for one off expenses like yearly club registration fees and things like that. Give your kids a notebook or help them create a spreadsheet, or use the envelope system to get them into the life long habit of tracking their spending. You might want to stick with cash or open a bank account with a debit card.
3. Have regular money check-in meetings where the kids can ask questions, talk about some of their experiences, you can help problem solve or adjust the budget as needed. A great time to do this is at the end of the month (pay-period).
Your kids will struggle, they will make mistakes, they might have different spending priorities, blow their money or miss out on experiences or something they want to do because they spent their money elsewhere. The hardest part of this process is letting that all happen. The idea is to give them the tools and set them up for success but resist the urge to swoop in and save them with extra money if they make a mistake.
The positives: Your kids will be learning life sills early, they will learn how to use money as a tool, they will gain confidence and freedom as they master their money.
*note: I'm not a parent, but I have taught financial education classes to all ages and this is the general strategy I use and have seen great results with.