National Debt, Cell Size and Scientific Notation

The week before spring break I wanted to give the students a chance to explore scientific notation.  

Tuesday:

I began by using real life data based on the national debt of a few countries/states: USA, California (our home state), Canada, Greece(it has been in the news and it was during the crisis in Cyprus).  I wanted to use the debts because they are very large numbers and they spark conversations among the students about debt that allow me to give them the chance to explore, research and share with each other.

I wrote each debt up on the board and then I wrote the same number in scientific notation right next to it.  I informed the students that these two numbers are equivalent or the same.  I then asked the groups to come up with the rules I followed to change the large number into scientific notation.  After some time, we came together as a class and listed the things they noticed and formulated guidelines or rules.  

HOMEWORK: use the following link: World Debt Clocks to pick four countries and write their national debt and then convert the numbers into scientific notation.  

Wednesday:

For the warm up I had each student pick one of their countries and give that number to the group to re-write in scientific notation.  They would do four to six problems depending on the size of the group.  I took roll and monitored what the students were doing as they worked to guide the discussion.  I posted the guidelines/rules to help the students if they got stuck on the process.  We shared, discussed, and clarified the guidelines.

The discussion revealed the need to do an exploration on the powers of 10.  The students wanted to know why the base of the exponent is 10.  So we took out calculators and started multiplying 5 10’s and 2 10’s and 7 10’s.  After each problem, we looked at the resulting number and wrote out the expanded form of the multiplication and set it equal to the exponential form of the same number.  The light bulb went on and the groups wrote explanations as to why scientific notation uses 10 as it’s base.  The rest of the period students worked on problems from the textbook.  Those that do not have access to a computer at home, completed the homework from the night before on one of the classroom computers.

HOMEWORK: use the following link: World Debt Clocks to pick four different countries and write their national debt and then convert the numbers into scientific notation.

Thursday:

For the warm up I posted a couple of large numbers and asked the students to re-write in scientific notation.  I then introduced really small numbers.  I used the following link: Cells Alive - What is the Size? which is an interactive tour from the head of a pin down to a rhinovirus.  It has conversions which allowed us to write the size of each cell as a decimal.  I then wrote the scientific notation for each number next to it and we started the process of creating guidelines or rules for re-writing numbers less than one in scientific notation.  The rest of the day the students worked on scientific notation problems from the math book knowing that they would have a formative assessment on scientific notation Friday before spring break.

Friday:

Formative Assessment - What I decided to do for the assessment was give the students 8 multiple choice questions converting a number in standard notation to the re-written scientific notation.  I circled answers on the test and the students had to first decide if my answer was correct or incorrect.  Then if it was incorrect they had to write a detailed explanation about what I did wrong.  They were allowed to use the guidelines we wrote together to help them decide on correctness and write their explanations.