My Continuing Battle With 3.MD.B.4

     Captain Ahab had Moby Dick. Wile E. Coyote's got Road Runner.  I have 3.MD.B.4.  Teaching kids how to measure to the nearest quarter inch bedeviled me as a grade 3 teacher, and has continued to do so in my role as math specialist.  Recently I described our attempts to tame this unruly standard, and while I was pleased with the results, I felt we needed to look for more ways to attack this beast.  My latest inspiration came from an unlikely source:

I found this book buried in a closet.  

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    The game was familiar.  This past summer, at the Middlesex Math-Science Partnership program at Middlesex County Community College, Dr. Milou had challenged us, playing from 1-20.  He took great pleasure in trouncing all combatants, one after another, until someone in the group figured out the winning strategy.

This caught my eye.  Might this game be employed in the struggle against 3.MD.B.4?  

      I asked Jen if I could use her class to experiment, and she agreed.  First, I taught the kids how to play a basic game, with the first player saying either the number 1 or the numbers 1 and 2, and the players then alternating the count by one or two numbers in sequence from where the other player left off, with the player saying 20 the winner.  I channeled Dr. Milou, beat everyone in class, and left the defeated third graders with the assignment to play the game with each other whenever they could.
   When I came back the following week, they were excited to tell me that they had figured out the strategy: the player who can say 17 is assured of winning.  They hadn't gotten any further, but it was a start, and I urged them to continue playing.  In the meantime, I explained that I had a different game to teach them.  I explained the "fraction variation": same rules, but instead of using whole numbers and counting from 1 to 20, we were going to count by 1/4s from 1 to 5.

I played a demo game on the board.  I recorded my count in red and the student's in blue.  I wanted them to record their counts, in the hopes that we could connect this number line to the quarter inch ruler.

They picked it up quickly.

 

We had to tape two pieces of paper together to get the right length.

This sample, placed under the document camera, provided the teaching points at the lesson's close: I love how these kids wrote a 1 on top of 4/4 and a 2 on top of the 1  4/4.  We also talked about how to write a mixed number, so that 3 and 3/4 would not be confused with  33/4.

 Jen reported that the kids liked this game, and when I did an item analysis on the unit assessment I was pleased:

This is the item I was interested in.  17 out of 18 kids had gotten all three parts correct. 

     But 3.MD.B.4 never sleeps, and I knew we couldn't rest on our laurels.  The conceptual groundwork we were developing here would only help the kids as they moved into the more complex measurement and fraction standards awaiting them in the upper grades.

I took our standard grade 3 ruler and photocopied and enlarged it.

I whited out the numbers and put two on an 11" by 18" page.

Would you look at that!   It's a ruler!  And marked at quarter inch intervals, too.

     My hope is that, if they play enough, the kids can start to notice certain patterns: that the whole numbers live on the longest lines, the 1/4 and 3/4 on the shortest, the 2/4 right in between.  (And I would like to transition the kids to writing 1/2 instead of 2/4, although this is a good way to reinforce these equivalent fractions.)
     My hope is to avoid Captain Ahab's fate, and one day vanquish 3.MD.B.4 once and for all.  So... what's your white whale?