Making Sense of Exponents

Exponents are the little number "sitting on the shoulder" of the base number.

They basically tell how many times that base number needs to be multiplied by itself.

This week 8th graders explored various operations with exponents.

~ What happens when you multiply exponents?

~ What is the short cut when you divide exponents?

~ What do you do when you have to find powers of powers?

~ What does an exponent of zero mean?

~ Yikes!  You can have negative exponents???

They first found patterns and wrote hypotheses for what they thought the rule (we called it a shortcut) was.

Then the next day, we acted the problems out so we could actually make sense of what was going on!

a(to the 5th power) divided by a(to the 3rd power)

a(cubed)squared

By just playing around with the numbers, students came up with their own questions.  

Wondering outloud in math definitely moves our thinking!

~ When working with negative exponents, will the top numbers ALWAYS be a 1?

~ What happens when there is a negative exponent in the denominator of the fraction?

~ Does the rule still work if I use a negative exponent?

Students were using several math habits as they tried to decipher through the exponents.

1) Patterns

2) Finding structure

3) Wondering

4) Perseverance...there were four properties we had to get through!