Surprising Number Patterns I

There are times when the charm of mathematics lies in the surprising nature of its number system. There are not many words needed to demonstrate this charm. It is obvious from the patterns attained. Look, enjoy, and
spread these amazing properties to your students. Let them appreciate the patterns and, if possible, try to look for an “explanation” for this. Most important is that the students can get an appreciation for the beauty in these number patterns.
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12 321
1 111 x 1 111 = 1 234 321
11 111 x 11 111 = 123 454 321
111 111 x 111 111 = 12 345 654 321
1 111 111 x 1 111 111 = 1 234 567 654 321
11 111 111 x 11 111 111 = 123 456 787 654 321
111 111 111 x 111 111 111 = 12 345 678 987 654 321

The Beauty in Numbers 3
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1 234 x 8 + 4 = 9 876
12 345 x 8 + 5 = 98 765
123 456 x 8 + 6 = 987 654
1 234 567 x 8 + 7 = 9 876 543
12 345 678 x 8 + 8 = 98 765 432
123 456 789 x 8 + 9 = 987 654 321