Suprising Number Patterns II

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 share these amazing properties with your students. Let them appreciate the patterns and, if possible, try to look for an "explanation" for this.

In the following pattern chart, notice that the first and last digits of the products are the digits of the multiples of 9.

It is normal for students to want to find extensions of this surprising pattern. They might experiment by adding digits to the first multiplicand or by multiplying by other multiples of 9. In any case, experimentation ought to be encouraged.