We do use a curriculum from time to time if the kids request it. Dae requested a math curriculum this past year. Interesting story. She had never had a set math curriculum before. We had always done games such as Math BINGO, The Math Game Get a Clue!, comparison shopping, cooking and doubling recipes, etc. If she had been in the public school system, she would have been in the 5th grade. We did a 5th grade placement test on her, and she got every problem correct. We then did a 6th grade placement test which she also aced. I started her midway through the 7th grade curriculum and she did great. I found that to be very interesting.
Another interesting story. The only set curriculum Dalton has ever used has been math. When he took his ACT test, he scored a 28 on everything EXCEPT math which was an 18. I found that to be very telling.
How do you know they are learning? Talk to them. Listen to their conversations with others. Pay attention to what they are doing, reading, watching, etc. Introduce them to rich environments, experiences, people, etc. They will learn. They can't help themselves.
There are tons of ways to "educate" that don't include the traditional "seat-work" type lessons. After fieldtrips and other educational activities, we spend time discussing what we learned and what the kids think about it...often coming up with more questions to research when we return home. Sometimes you even have an opportunity to *review* by presenting a "remember when we learned about..." In short, a fieldtrip/activity lasting only a few hours can actually be stretched into a whole day of learning and include much more than the initial event/subject.
When my boys were younger, we did often use unit study type learning, which didn't monopolize quite as much of our schedule. We also didn't stick to the schedule that was often laid out with a unit study--we just finished it when we finished it. That's the beauty of homeschooling!
Your kids are still pretty young, so I would definitely suggest taking advantage of this more flexible time to enjoy being together and building strong family bonds. You know, even things like making cookies or planting a garden is "educational"--you can cover measurements of all kinds with both of those activities! If it makes you uncomfortable to be that "free", then--especially with your kids' ages--just cover the basics of reading and some math...the rest will easily follow!
Obviously, this is just what works for us, and you will have to find what fits your family the best. Good luck and remember not to lose sight of the best parts of homeschooling...relaxing & having fun learning!