Estimation as a game

Such estimation problems are called http://en.wikipedia.org/wiki/Fermi_problem and they are recommended as real life class room exercises. In Germany you can buy such exercises as a box: http://www.vpmonline.de/index.php/fermi-box_produktdetail/items/1935

This is a game I play often when it comes to estimating time - probably the most frequent estimation that I conduct in day-to-day life. When on a New York City subway, for instance, I'll make a 50% confidence range guess on how long it will take the subway to get to my stop. The game works equally well when waiting for a light to change, a lecture to end, an elevator to arrive, etc.

I started doing this at a fairly young age when - in response to asking "are we there yet," - my parents told me to guess how long it would take to reach a travel destination.

There was a phase where my 7 year old asked me how many X there are (X being like your examples) and after he knew that things are made of particles (German: 'Teilchen' which also build nicely on 'part'/'Teil') aka atoms he asked lots of questions like "how many water particles are there in a cloud" (or in a water drop).

See also http://lesswrong.com/lw/iha/raising_numerate_children/ esp. the comment http://lesswrong.com/lw/iha/raising_numerate_children/9o8z

I remember that I counted and then calculated lots of things when I was in primary school (windows in a building, squares on the floor), but these were fairly concrete items where you did lots of multiplication but cound still count them in theory.

From an early age I've been constantly calculating various kinds of estimates - e.g. "how many people live in this building", "how long will it take to cross the US on foot", "what's the height of that tower", "how many BMWs are manufactured annually" and so on.

Did you do this spontaneously, or did your parents or teachers encourage you to?

Do you practice anything similar with your children?

Nope, but I will (once he's a bit older; at two and a half his grasp of "counting" is still limited).

I have questions. How can one get feedback on the accuracy of the estimates? Can one get feedback on the accuracy of the estimates? Is there value in the practice without feedback?

I think it's easy and natural for children to grasp if this method is introduced through everyday experiences. By making this into a game children can gain intuitive understanding of quantitative techniques. I suspect many children can enjoy this kind of games.

You can certainly introduce it, and it's a good idea to try, and some children will be interested, but others will find it boring and go back to playing with their dolls or trucks. In my limited experience, when you say "many children can enjoy this kind of games", "many" refers to less than half (and fewer girls than boys, for whatever reasons).