Unbundle

Subtraction came back to my 2nd grade math class.  "Two digit" scares these little people successfully, even though they have been successful of "bundling" in additions.  One says, "I can't subtract."  Another says "I don't subtract."  To start with, I threw a story problem.  "Shelby picked 35 oranges.  6 of them were rotten.  How many oranges could she save?"  Surprisingly, but almost predictably, some said, "35+6=41."  My response, "Hmmm.  Is she adding 6 rotten oranges into the basket?  Really?  Would you do that?  I don't need any more rotten oranges!"  Then they all took a deep breath and laughed, "It's subtraction!"  I felt a bit better.  Their subtraction concept was coming back.

Then, I started explaining how "un-bundle" works in the place value chart, using dimes as 10s, pennies as 1s.  About half of kids looked like statues.  Not significant light bulbs.  I pretended not to freak out, and announced, "Ok, let's meet up in the circle.  I will explain about the shopping game."  Did I had a plan for the shopping game?  Heck, no.  As I walked to the circle, my brain was sparking everywhere trying to find the best way for kids to understand "unbundle" in the engaging activity.  Click!  I sat on my spot and start explaining.  Here is the banker.  The Banker will exchange one dime to 10 pennies.  The shopkeeper takes money from the customers but only the exact amount.  Each pair gets five dimes, choose items labeled in the classroom, and shop together.  I grabbed the sticky notes and started labeling items in the classroom while talking, e.g., the mini white board 7 cents, marker 3 cents, etc.  I chose a student who had most difficult time understanding this unbundle concept and paired up with another student.  The shopkeepers were students who can count money correctly.  To make kids more engaged, I told them that the Fairy Godmother would give them $1 when they run out of their money.  They had to prove they were nice to each other to the Fairy Godmother to get her approval.  Now they had to go to the bank to break one dollar to 10 dimes.  That was an extended activity for the advanced students.  It turned out to be a great activity.  Students were engaging, collaborating, and understanding how unbundling works at the bank when they exchange their dime to pennies!

After that activity, we came back to the place value chart.  90% of students demonstrated their understanding of dime coming to the 1s place, but it needed to be 10 pennies.  Unfortunately, some still had no idea.

Next day, we went back to the worksheet that we started two days ago.  Some pairs started working independently.  I facilitated a particular pair to take turn to be a banker and a shopper, just like yesterday.  They completed all tasks by themselves after I left.  Other groups in the table, I encouraged them to play a banker and a shopper.  I added a little circle in the 10s place and draw an arrow line from it to 1's place.  Then, I made a big circle that they can put 10 pennies.  After they put 10 pennies, they discard a dime from the small circle.  As students repeated this manipulation, one student exclaimed, "I am getting it!  The place value chart really works!"  Another said, "Now I know why I was exchanging a dime to 10 pennies."  

Unexpectedly, the first plan didn't work well, however, unexpectedly, the spontaneous made-up game triggered their concept building.