Nikon Universcale and Number Patterns

Our discussion on the use of base 10 and large numbers in Indian mathematics today reminded me of this resource: https://www.nikon.com/company/corporate/sp/universcale/scale.html

Also, here's a note on the quick "notice and wonder" activity with multiplying by 9999 and 99999.

1234 * 9999 = 12338766

7813 * 9999 = 78122187

45916 * 99999 = 4591554084

Usually after three examples, students are eager to get started. Once students had some time to investigate the patterns, I'd invite a group that thinks they've cracked the trick to come up to the board and try it (and preferably not the group with the top student of the class), without revealing why it works so other groups could keep thinking. 

As many of you probably already noticed during the activity, corresponding digits in the first half and second half add up to 9. Now after learning about Nikhilam Sutra, or shortcuts to multiply numbers when they are closer to the powers of 10 in Indian mathematics, I'd certainly incorporate the history of mathematics in this activity. Something we would want to emphasize with the students though: math isn't just about speed or shortcuts — the point of this exercise is about uncovering patterns and understanding why they work. :)