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Day 52: GD Parentheses

September 29, 2010

For a 4th grader, one of the most intimidating mathematical quandries you can face is a multiple-term expression.

Life is tough for you, as it is.  You’re constantly attempting to toe a fine line between the boundary of “be a carefree kid!” and “Shape up!  5th Grade is coming!!!”  State standards require you to spend 50% of your school day staring at reading selections you struggle to comprehend.  If you get restless, you risk getting tested for ADD/ADHD.  And for the last few months you’ve been cramming basic addition, subtraction and multiplication facts for quick recall and you’ve FINALLY gotten to the point where you can calculate the sum of two numbers without using your fingers.

Great.  Now add three…then four…then five, six, seven…

One of my first lessons as a student-teacher today was to introduce the concept of parentheses; the idea that you can simplify a problem by doing a smaller part of the problem first, then inputting it to find the value.  When you see (6 + 4) – 1, you know you’re going to work your way to 10 – 1 before you come up with an answer.  Easy; do the parentheses first, then everything else.  No sweat.

It startes to get hairy once you deal with multiple parenthetical sets: (14 -7) – (7-3), etc.  Even if you can get a class this far, the frustrated student who gets the concept will always snipe back with the timeless “Why do we even need to do this??”

Luckily, a good portion of the class plays soccer.

Using the current English Premier League standings (a.k.a. The Table) and the season’s results to date, I challenged students to calculate the goal differential of the Top 5 teams in the league.  The students were fascinated by the idea of a league where you get kicked out by not doing well and where a draw doesn’t just mean that nobody lost.  They were able to determine, without looking at the table, that Arsenal should be placed ahead of Manchester City with a +4 advantage in GD.  They were surprised to find out how Newcastle could be in the positive GD despite only winning twice so far.  And they figured that Chelsea looks pretty damn good this year despite their away defeat at Man City.

Prior to introducing the Premier League’s goal differential as a use for parenthetical calculation, the students seemed to grasp the concept pretty well.  The ones who initially struggled with it the most were mostly male, mostly athletically aware, and generally in need of a different perspective on math.

All they needed was just a brief glimpse of how useful it can be.

DR

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One Comment
  1. ghTHREE permalink
    September 29, 2010 9:30 PM

    As a student-teacher myself, I can appreciate your use of sports and real-world examples in the classroom. Nice job!

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