An estimate is, very simply, a good guess. Working with estimations is a great way to play with numbers and work on those logical reasoning skills. My girls seem to love any thing that involves guessing and checking, so this was perfect for them!
We started with estimating how many cups of water it would take to fill a small pitcher. We used three different size cups for comparing. Starting with the smallest cup, we estimated, then filled the pitcher to check. My five-year-old guessed 10 cups (and was right!), while my three-year-old guessed 3,000 cups. As you can see, maturity and experience make a lot of difference in making reasonable estimations.

We continued on with a medium and large cup, discussing how our estimates should change. My older daughter told me, "These cups will definitely be less than 10 because they are a lot bigger!"
Our second estimation project was to see how many legos it would take to cover a book. The estimates were 34 and 100 legos. Actual result: 56 legos. Think of all the good counting practice we had checking our estimates!

Here's some more ideas for estimating fun:
How many steps will it take you to walk from the front door to the back door?
How many times can you jump in 10 seconds?
How many goldfish crackers will it take to fill this bowl?
How many blocks can you stack before the tower falls?
How many scoops of sand will it take to fill the bucket?
And, a great one for waiting rooms: How many babies/dogs/meals do you think we can find in this magazine?
Remember, this is all about exposing our little ones to the vocabulary and process -- it doesn't really matter how accurate they are with guessing or checking!
Happy playing!