Looking for Patterns in Math - Working with Exponents

Math is full of patterns, and mathematicians leverage these patterns when they are solving problems; they are all around us, we just have to notice and use them to our advantage.

This is evident in our Mathematical Practice Standards (student behaviors in mathematics); especially Mathematical Practice Standard #7 Look for and Make Use of Structure, where mathematically proficient students look closely to discern a pattern or structure.


We began with this problem:
What patterns do exponents make when the base is 10?
We ran through an example and then students were sent off to explore the patterns.

Students organized their thinking in many different ways. Some created charts, while others wrote the expressions down on separate lines.

And did we find a pattern?  Of course! (Keep reading below to find out what it was...)

One pattern that we discussed was the idea of "add a zero" based on the number of zeros within the sequence of 10 we were multiplying.  So I wrote this on the board:

10 + 0 = ?

We talked about if we were actually "adding a zero". 

Mathematically we aren't "adding a zero", rather the digit 1, in this case, is changing place values and the product (answer) is increasing by a factor of 10.

We then extended out our thinking by determining what 10 with an exponent of 23 might look like. 

Math patterns are all around us, it is so important to notice these patterns to make us stronger math students.