Teaching binary to 6-8 year olds I'm teaching some introduction lessons to a classroom of 6-8 year olds about basic 21st century skills. A fundamental part of this is how computers represent numbers, words and images, which all starts with understanding binary representation of a number.
When explaining this in the past, I have never not confused anyone with notation. For example trying to explain the difference between '11' (binary) and '11' (decimal) is hopelessly confusing because it looks like the exact same thing, and saying 'one one' almost always leads someone to think 'well one plus one is two, what is this dude going on about it being 3'.
I think the problem is that we use the same symbol for decimal and binary notation here, while there is not strictly a reason for it (it's convenient if you already know how it all works, but not before that).
So I'm thinking of using different symbols. Like ● for 'this bit is on', and ⊗ for 'this bit is off', so that I would write e.g.
3 = ●●

and
5 = ●⊗●

Any ideas on this? Would this help? Are there already other symbols being used for this purpose, symbols that don't rely on the glyphs we use for 0-9?
Use money.  Tell your students to image a country has bills that are in denominations of powers of 2:  1, 2, 4, 8, 16....  Now tell them this:  For a given number, count out that money with as few bills as possible.  You use a "greedy algorithm:"


Use the largest bill possible.
Repeat this until you have counted out the amount.


Questions to ask:


Did you ever use more than one bill from any denomination?


They should observe this is never necessary.

Now write a 1 for the largest bill.  If the next denomination down is not present, put a 0; otherwise, put a 1.  Repeat until you descend through the denominations.  You have the binary expansion of the integer you specified.  

This is concrete and very easy for students to grasp.  This "greedy algorithm" works for any base: Use the largest bill you can can count out as many as you can at each stage.