Foursville: Place Value Fun

This was a great math week. I gave out worksheets and taught traditional algorithms.  But it was a great math week.

Why? Because I deeply believe students in the fourth grade should know how the traditional algorithms for addition and subtraction work. But more importantly they should know why they work. And for that I have a secret weapon: Foursville.

I learned about chip trading at Dana Hall math camp. If you've never been, run, don't walk to sign up this summer.  I didn't fully appreciate the beauty of our base 10 number system until Dana Hall but ever since then I have been in love. 

We start Foursville as a game. For fourth graders trading chips is hard work. They really have to think and work together. 

It sounds easy enough. 1 on the die means one yellow chip. 4 yellow chips = 1 blue chip.  4 blues = a green. 4 greens = a red. One red and you win.  In the subtraction game you start with a red and see if you have anything left after passing through a few tolls.  It's all the same idea as "carrying" and "borrowing" in our base 10 system but it blows their minds. 

Early ah hah moments are when they roll a 4 and just take a blue. Or figure out 1 red is worth 64. The advanced students just do the subtraction in their heads translating the amount needed into Foursville chips.  Meanwhile we are reviewing the algorithms learned in 3rd grade but now we can write them in expanded notation and see what all of that crossing out and regrouping really means. We ask ourselves questions and try to make connections. 

Soon students are realizing we could play Fives or Sevensville because there is pattern. Boom! Base systems of numbers. 

I feel good when students see why our society thinks the algorithms are a good way to do some math problems. They also know lots of efficient ways to do these problems mentally. The important thing is that they can make choices and are learning how to decide when to whip out pencil and paper and when it isn't necessary. 

We finished Foursville by noticing the place value patterns of all base systems. In Foursville the green is 4x4x4.  In Tensville it is 10x10x10.  In Fivesville it is 5x5x5. 

We'll see if they can think it through on Monday.  I might still find time to show them Mayan math in base 20, but even if not, man it was a good week. 

What It Is To Be Human

I ride the bus mostly now.  My husband's new job is in Virginia so he takes the car everyday.  On the bus you are exposed to all kinds of people.  There is the young man whose mom brings him every morning.  He is differently abled and apparently deaf since they use sign language.  I often wonder where he is going all by himself.  There is another gentleman who comments on my pretty brown eyes, He is surprised by my quiet thank you which is a recognition of his personhood, a reaction I choose instead of a rebuff to his unwelcome flirtation.

I often look out the window at sights that are not that interesting.  But today my eye caught a man with a dog keeling over.  Another man ran towards him and I knew it was an emergency so I called 911.

In a previous emergency I found I was a person with a cool head who could think of who to call and get others out of the way.  As I jumped off of the bus and ran towards the scene I had witnessed I felt good about my decision to become involved.  Really there was no other choice.

When I got there several men were with the fallen gentleman.  They were rolling him over.  He was turning blue.  I felt in that moment my limitation.  I could make the call, but I stood away and apart unconfident in my years ago CPR training, not wanting to touch his darkening, dying skin or the blood that poured from a cut where he had hit his head.

I stayed on the phone never having called 911 before.  I was trying to describe what I was seeing and convey the urgency of the situation to the operator. He was telling me to stop talking and listen.  He wanted to know about the CPR training of the men who were checking his airway and listening to his chest.  He wanted to know if they needed instructions but they didn't because despite the blood coming from a cut on the man's head and his increasingly blue face, they were doing it.  Sweeping the mouth, opening the shirt, hand over hand pressing on his chest.  A man standing above declared the CPR giver "pretty good".  I repeated the directions so the operator wouldn't get mad at me but they didn't match their actions and it was confusing and I was afraid to make it worse.  Meanwhile,  his face was still blue.  He was still dying.

A woman named Maggie was holding his dog.  He had been out walking his dog, a quick walk before work.  He was dressed for work.  A button up shirt.  A jacket.  The dog was named Diva, a doe-eyed golden retriever who just sat quietly as if she knew she needed to be a non-issue.  She had a red bone tag with two numbers.  Numbers we needed to call.  And say what?

The ambulances arrived.  I thought they were slow to get out, the firefighters.  But maybe that is how you approach a life or death situation when you see them everyday.  With slowness, with calmness, with intent to deliver the right care.

Because they did. They took over and hooked him up to a AED and did what they must do many times a week.  His face was still blue when they stopped and put him on a stretcher and loaded him onto the ambulance.

The man who had given him CPR - Chris - said he would call the numbers on the tag.  He was all in. He spoke to a woman - Claudia - a wife to tell her that her husband was being taken to the hospital in critical condition and there was a dog here.  What should we do?  He didn't think she understood.  She said she would come get the dog.  Was it her English?  Was it her shock?

Soon everyone drifted away.  Most didn't say goodbye.  What had connected us was over.  We had get to work.  Maggie gave me a hug and gave Chris a hug.  I hugged him too.  He had been so brave.   I had cried the whole time.

This morning I saw a man dying.  I also saw a hero try to save his life.  I called 911 for the first time and witnessed an emergency response.  I saw people not walk by and support one another.  I saw a woman with headphones walk over a small pool of blood and not notice and not wonder what had just happened.

I suppose scenes like this happen everyday to lots of people.  Sometimes it doesn't end with a pulse and a man breathing on his own, signs of hope and possibility that it all ended well.  Today it happened to me.  And in that moment I knew what it was to be human.  To be walking the dog and have a seizure or heart attack.  To stop and make a call or use a skill learned at some other time.  To be present with strangers and care about someone else.  To see heroism and humanism and learn they are one and the same.  To be afraid and stuck and unable to turn away.  To let go and release.  Inshallah.  God willing.  To walk forward.  Towards the day.  To go to work.


UPDATE 11/20/13: I heard from either a fire or police lieutenant that the man who had the heart attack is still alive and doing okay!  We saved his life!

Place Value Construction

As part of our review of place value concepts: