My First 3 Act Task...Dedicated to Dan Meyer

On Wednesday I attended my first Dan Meyer workshop.
On Thursday my first 3 act task was born.
Such is the power of a dynamic speaker with a genius recipe for engaging students.

We were going to be studying the property of dividing exponents with the same base.
Such a boring task.
And one where the students can easily miss the objective.

I knew the numbers had to be large enough that the students could just do the problem in their head or on the calculator.
And this where the universe came into the picture.

Act One
Question:  How many Earth's would fit across the Milky Way?  (disclaimer...the Earth is not proportional to the Milky Way in this pic.)

Write down your guess.  This way others will believe you when we find the answer.

Students seemed to really get into this.  Answers were all over the board and we brought up a website to help with numbers greater than a quadrillion.  Some students wrote their answers in words, some in powers of 10, and some just wrote down a number in standard form.

Act Two

What information do you need?  How will you find it?  Be as specific as you can.  MP 2

Now guess the diameter of the Earth based on this new information.

This discussion took us in a direction that was a great foreshadowing of negative exponents.  Several students guessed a diameter of 10 to a negative power.  We were then able to talk about 10 to the first and compare it to the size of our room.  10 to the zero power required a calculator in some classes, but students were able to see that this was equal to one.  Using our Math Practice 2, students reasoned that a negative exponent would give us something less than one, thus making that guess unreasonable for the Earth's diameter.

Upon revealing the answer to the diameter of the Earth, the question was asked, "How do we now find out how many Earths will fit across the Milky Way?"  Students quickly responded that at this point we needed to divide.  I wrote the problem up on the board and asked, "How do I do this?"

With some we literally wrote out 10x10x10x10...21 times over 10x10x10...7 times.  

With some we wrote the number out in standard form and then cancelled out zeros.

With some, they were impatient and wanted a short cut.  

This is what I was waiting to hear.  I just kept writing out zeros, knowing that they now had a need to find a shortcut.  

Finally, someone yelled out, just subtract the exponents.

Yes.

Learning based on a need.

Wonderful.  :)

Sequel

To help show that this shortcut works on all integer exponents, we used found the solutions for the following situations.