Thursday, October 11, 2012

Math in Focus Chapter 2: Making Long Division Easy

Today I made long division easy.

Last year, when we adopted Math in Focus, we were all shaken up about bar modeling during our 2 in service days at the start of the year.  Once we started teaching the first unit on place value, things did not seem quite so bad.

And then we started Chapter 2.

With NO background in division and little experience multiplying beyond their facts (which most of them forgot) this was a nightmare for children and teachers alike.  I was frustrated that it was so new to me that it was all I could do to keep up with the materials gathering and pre-teaching, and it was killing me to see kids who used to think they were smart, now feel like failures.

I was NOT going through all that again. 

The second year is always better.  Their third grade teachers had the same frustrations with the new program last year, but at least this group of kids got a taste of the methodology.  I had a better sense of what they need to do BEFORE hitting Chapter 2 (5 weeks of extra facts and regrouping practice for identified students for a start) and also what they needed to know by the end (they don't actually need to be expert long dividers or 3 by 1 digit multipliers because that comes later, in Chapter 3)  Instead, I could focus on the bigger picture:  developing stronger number sense.

So as I went through the chapter again this year, and they hit their first significant stumbling block, instead of feeling overwhelmed, I was ready.  I realized that all the place value work that seemed silly in Chapter 1 (why do they need to know 140 is 14 tens?) suddenly made perfect sense.  Suddenly, I realized that this is the key to why the long division algorithm actually works!  And then, the day after a lesson that semi-failed (5 kids mastered it, 8 got it but only with support, and 6 felt like they would never be able to do it) I had an epiphany.  I saw just how to set up a long division problem so that they wouldn't forget where to write that multiple and where to write the answer (any 4th grade teacher knows it is SO hard for some kids to get used to writing their answer at the top instead of bottom!)

Now, when the first lesson (the purple visual on the left) didn't work out, I took a step back and whipped up a quick worksheet for homework that got them practicing one isolated step:  namely, step 3.  I gave them a problem like the 4 divided by 14, and modeled on the worksheet how to count by 4s and write 12 under the problem.  And NOTHING else.  No zero, no place values, no estimated quotient.  Just listing multiples to find what to write underneath.  That was something they were ALL successful with, because we'd been practicing multiplication and division facts since the first week of school.  But that wasn't my stroke of genius.

Look again at the diagonal red line.  It crosses out the 14, leaving the 4, 12, and 3 fact family plain as day!  As I told the kids before I started, "You're going to love this, it's going to be like a magic trick."  And they ate it up.  I knew I created a system that worked when more than one student thanked me for teaching this to them.  "Mrs. Thomas, I finally GET it now!"





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