We've all had the same problem. When they are home for extended periods of time, kids get bored and want to eat! And good heavens, can they eat!
I will have to admit, I got this idea from a Super Nanny episode and adapted it for the kids.
Here is what we do. The big baskets contain snacks. The top blue one is for cupboard snacks, the one on the right is for stuff in the fridge. The kids then each have their own, smaller basket. For things such as popcicles, etc, I have a craft/popcicle stick with that treat written on it that they put in their basket. They were able to choose 2 treat snacks, at least 1 had to be healthy (string cheese, raisins, etc).
Each night BEFORE BED, they pick out three snacks for the next day and put them in their own basket. Then, during the day, they are allowed to eat those snacks anytime they want, without asking, before 4pm.
This gives them choice, an opportunity to plan and think and they can see it all visually.
No more "can I have...." questions all day long!