Teaching binary to 6-8 year olds
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.