My daughter goes to a nature preschool so her days are full of getting dirty outside. If you can get your kids outside in a fenced backyard or a space safe enough that you don't have to watch them constantly, a lot of these activities can keep them entertained for free for a long time. If you can't send them outdoors, you can bring some of these inside with a little bit of upfront prep time.
This is a favorite of all the kids at my daughter's school. It's pretty simple, send them outside with some pots, pans, utensils, (any kitchen items you don't mind getting dirty or wouldn't devastate you if they are broken) and some water and let them have at it. Kids love putting mud in muffin tins, mixing it, adding plants. If you have only one child and they're bad at entertaining themselves, give them your "order" and ask them to make it. You can also extend this by playing restaurant where they first wait on you and take your order then they make it. This is one of my daughter's favorite activities.
Collect and Paint Rocks
This one is pretty self explanatory. Find rocks - you can give your kids instructions like "find ones the shape of animals" or "flat so you can paint a picture on them", wash and dry the rocks, then paint using acrylic or poster/tempera paints. If you want some more rock painting ideas, look here: https://www.pinterest.com/pin/381961612123482968/
Have a printer? Here's a link to printable scavenger hunts for small kids: Printable Scavenger Hunts (not all are suitable for playing alone so choose wisely). Don't have a printer? Help your child make a list of their favorite things in nature. Then send them on a hunt (around your house or yard) to find those things. If you do this in the house or your yard has limited items, encourage them to look for the items in books, art on the walls, in games, as stuffed animals, or even "look alike" items (i.e. this rock looks like a butterfly).
This sounds gross but, believe it or not, it's a favorite of almost every kid I know. Find worms in the yard - it's really that simple. Give them sticks to dig, encourage them to turn over rocks, look under leaves. If they're not good at sticking with something like this, I find that giving them a number to spot and a way to tally up the total (you can even do this with rocks) helps. Make sure they understand that they're just supposed to observe the worms, not hurt or kill them.
I wish I had time to write up everything but, I don't (at least not yet, let's see how long this lasts). So here's a lot of other suggests with links when needed: