Surprising Number Patterns Part III – Pola Bilangan Menakjubkan Bag. III

Here are some more charmers of mathematics that depend on the surprising
nature of its number system. Again, not many words are needed to
demonstrate the charm, for it is obvious at first sight. Just 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. You
might ask them why multiplying by 9 might give such unusual results.
Once they see that 9 is one less than the base 10, they might get other
ideas to develop multiplication patterns. A clue might be to have them
consider multiplying by 11 (one greater than the base) to search for a
pattern.
0 . 9 + 1 = 1
1 . 9 + 2 = 11
12 . 9 + 3 = 111
123 . 9 + 4 = 1111
1234 . 9 + 5 = 11111
12345 . 9 + 6 = 111111
123456 . 9 + 7 = 1111111
1234567 . 9 + 8 = 11111111
12345678 . 9 + 9 = 111111111


A similar process yields another interesting pattern. Might this give your
students more impetus to search further?

0 . 9 + 8 = 8
9 . 9 + 7 = 88
98 . 9 + 6 = 888
987 . 9 + 5 = 8888
9876 . 9 + 4 = 88888
98765 . 9 + 3 = 888888
987654 . 9 + 2 = 8888888
9876543 . 9 + 1 = 88888888
98765432 . 9 + 0 = 888888888
Now the logical thing to inspect would be the pattern of these strange
products.

1 . 8 = 8
11 . 88 = 968
111 . 888 = 98568
1111 . 8888 = 9874568
11111 . 88888 = 987634568
111111 . 888888 = 98765234568
1111111 . 8888888 = 9876541234568
11111111 . 88888888 = 987654301234568
111111111 . 888888888 = 98765431901234568
1111111111 . 8888888888 = 987654321791234568

How might you describe this pattern? Let students describe it in their own
terms.

Source: Math' Wonders to Inspire Teachers and Students (by Alfred S. Posamentier)

Posted on May 5, 2013, in Mathematics and tagged , , , . Bookmark the permalink. Leave a comment.

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