I have heard of and seen this idea a few times, so I decided to give it a go.
This is a good exercise for kids of all ages, working on varying goals.
I call it the Peek-A-Boo Box.
The idea is to put a bunch of objects into a can (or a babywipe container in my case).
The objects need to be hidden from view, so
if you use a can (one that held formula, hot chocolate, etc), cut the toes of a tube sock off and stretch one end around the opening. That way the kids can reach through the sock without seeing what is inside.
Like I said, this can be used for several different activities.
For Lincoln (almost 2), I use it specifically for object recognition and speech.
Since we just had his tubes put in a few weeks ago, this is a good way for him to associate objects with the sound of the word.
Once he pulls out an object, his attention is solely on whatever he has in his hand, so it is easy for me to say "dog", "spoon", and so on.
Or you could work on colors, shapes, what sound the animal makes, etc.
For Cannon (age 4), it is a good problem solving exercise.
When he puts his hand in I tell him to try to identify what it is he is holding on to.
Or I ask him if he can find the horseshoe, the car, etc.
Another good exercise would be to practice textures: asking your kids if they can find the soft / hard / squishy objects.
You can easily mix it up for whatever will work best for you and your kids.
Other objects my kids enjoy pulling out of the box are cause and effect toys:
pop-ups, wind and release toys, etc.
I think next time I will use a can instead of a babywipe container.
Some of my objects were too big to get out with my kids' fists wrapped around them.
Either way, this is a quick activity that can get some mental juices flowing.