So WHY is 10 raised to the zero equal to 1 again?

This is a topic that recurs annually as we move traditional skills/concepts to lower grades according to the Common Core standards. I believe there will be a temptation to give rules without motivating them or explaining them. 

So perhaps raising a number to the power of 0 could be a fourth grade topic these days. I did publish a post several years ago on developing exponent concepts in the middle grades but I guess it can't hurt to revisit it now for even younger students.

One approach I have found useful is to have students construct a table in which the left column is the exponent and the right column is the corresponding power of 10.

I will start the table, suggest some questions but leave the rest for you to bring your own ideas and expertise to the  "table"!


EXPONENT  POWER OF TEN
          3           10^3 = 10x10x10 = 1000
          2           10^2 = 10x10 = 100
          1           10^1 = 10


Teacher: So what do you notice?
Remember --- a mathematician must first be very observant like a good detective!

You and your partner have 1 min to write as many observations as possible...

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