This problem continues the theme of error detection and correction from the field of Information Theory explored in the problem Secret Transmissions.
Begin by giving students some time to try the problem Secret Transmissions. Once they have had a go at making sense of and understanding the error detection and correction method, set them the challenge:
"What if I wanted to send more than four digits? Can you come up with a way of extending the error detection and correction method?"
Invite students to work together in small groups to try out their ideas, and once they have come up with a possible solution, encourage them to compose simple binary strings and 'transmit' them with one bit switched for someone else in the group to detect and correct.
Finally, allow some time for discussion of the methods that emerged.
What do you notice about the position of the check digits in the message?
Where might you put the next check digit in a longer message?
How can you determine which message digits 'belong' to each check digit?
The extension tasks suggested in the problem should offer a challenge to any student who wants to explore further.
See the Teachers' Notes to Secret Transmissions for some suggestions of how to scaffold the original task.