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!

More Spheres, Cones, and Cylinders

Besides finding the volumes of the Kansas sphere, cone, and cylinder,
A student traveled all the way to DisneyWorld and found another set containing a large sphere, cone, and cylinder.
Check it out!

What is the radius of this "cylinder"?

How was the volume found for Epcot?  What would the math look like?

How was the problem worked backwards to find the radius?
What information would you need to look up to be able to find the radius?
Find the volume of Mickey's Hat.

Figuring It Out

This last week, students spent their time in class attempting to answer the following questions.  It was exciting to see their minds at work!

1.  What is the linear dimensions of this gigantic ball of twine found in Cawker City?  

2.  How long would it take to fill up the hand dug well in Greensburg from a regular water hose?  

What would the equation look like?

3.  What would a graph look like if we were able to fill the TeePee in Lawrence to the top at a steady rate? 

Student examples...

Check out the following video for the 16 Habits...

1)  Did the student(s) show persistance in solving the problem?  How can you tell?

2)  Did the student strive for accuracy and precision?  What evidence shows this?

3)  How did the student communicate clearly?