I agree that being rewarded for doing each individual chore is counter productive to teaching that everyone in the household has a share in making it run as smoothly as possible. I do give an allowance that is based on their involvement in the household. They don't have to meet any particular criteria from week to week but the amount is negotiable just as a wage is negotiable.
Also, for me, getting treats, such as ice cream from the ice cream van, is also a given just because the child is loved. One doesn't have to work to earn treats.
My daughter came to live with me when she was 7 and we never reached the point that enforcing doing chores was consistent on my part. I was dealing with too many other emotional issues. Looking back, I do wonder if it would have helped if I'd focused on incorporating her into the household by consistently requiring chores. If I had to do it over again, I would.
However, I would not give rewards. I'd use a check off sheet or chore chart that listed the chores to be done and when so that my child would be able to see in writing what was required and be able to check off when they were done. Being able to make that check is a reward in its self. For myself, I am more organized and get more done when I make a list and I do feel good when I'm able to cross things off. I think a chore chart with check offs is good training for being an adult.
I've seen several really good charts. I suggest that if you found one that is awesome for you that you're more likely to follow thru. If the chart is fun for you you'll be more involved in using it.
A point about treats. Treats are another way to provide incentives for right behavior. When the child hasn't yet completed a chore that was to be done by a certain time then there is not time to have an ice cream bar. This is a realistic way to teach time management. I don't know how to do this with an ice cream bar when there is such a wide age difference in children.
There are other situations that are more easily managed in a consistent way. For example, my daughter told her children that they'd go to the park once their room was clean. They dawdled all morning and when it was lunch time they were ready to take that picnic to the park. My daughter told them they couldn't take a picnic to the park because their room wasn't clean. So they had lunch and went back to their room. They didn't get the room clean and never went to the park that day. Oh, well, maybe next time you'll get your room clean so that we can go.
I would have done some parts of that differently based on the children's personalities and earlier experiences but I agree with the idea. We finish our work before we play. When all of us do our best to be consistent and work together to get the work done we do have more fun. That is a natural reward.
I would be sure to include lots of praise, letting each child know that you are proud of how well they completed the chore or even how proud you are that they tried even when they weren't able, for a reasonable reason, to not complete the chore. Proud that they started and know that next time they'll finish. That sort of thing.
One thing that I've learned and wish I'd understood when I was raising my daughter is that assigning chores is only the beginning. Make a list of chores and let the child choose at least one of them for themselves. I have done that and it works. However, that is just the beginning.
The parent needs to be involved in the chore. Not by doing it but by talking about the process. Discuss with the child what is the criteria for being "done properly?" What is considered proper depends on the age of the child and their experience. Start with a loose description and talk about it in a casual way until the child understands and is able to meet the criteria and feel good about doing it. Increase your expectations over time while giving the child plenty of opportunity to be proud of their work.
This means the parent needs to maintain a calm and positive attitude about the chore and teaching it. No nagging! No put downs! When the child is dawdling or not doing the chore, focus on the dawdling or the lack of compliance without criticizing the chore. For example, if the child was to make their bed before lunch and hasn't done it then the child isn't able to do anything else until the chore is done. You could combine this with a time out. All said in a calm way not in a frustrated or nagging way. This is just the way it is.
Working along side the child when the child is beginning to do chores helps tremendously. I tended to think that I could explain, show the child what to do, once they were in grade school, and then go about my own chores. Always, I'd find the child playing and the chore undone when I went back to them. And I would once more tell them to get busy and walk away. I would get so frustrated. And so now I work along side them. If they're to put dishes in the dishwasher, I'm in the kitchen, picking up and putting away. We're talking together as we work. Once their routine in doing this chore is established then I can work in a different room. Children need our help to learn good work habits. They don't come naturally for most children.
The reason that I and I think my daughter abandoned chore charts is that by themselves they don't work. They have to be a part of a detailed plan that teaches children to follow thru. Only when we follow thru are they able to follow thru.