Baby Steps to Differentiation

I tried something new today in my quest to learn to differentiate instruction.  We were reviewing fraction operations in 7th-grade pre-Algebra and I needed to know where students were starting out.  So, I had them get personal whiteboards and wrote 1/4 + 2/3 on the board.  I asked them to raise their boards when they finished so I could see their answers, and noted down anyone who missed the problem.  Then we did a subtraction problem.  Not surprisingly, the students who missed the addition problem were the same students who missed the subtraction problem.  Since it was only 4 kids from the whole class, I moved on to the next part of the lesson, with a plan to circle back and review with those four individually.  I informed the kids of the plan.

Next, I started the whole class on drawing area models for fraction multiplication.  They told me that I’d taught them area models for fraction multiplication in 6th grade, which surprised me because I didn’t remember doing those last year!  Still, we drew them and used them to multiply the fractions.  I was impressed because these students were much more willing to use the model to answer the question rather than jumping to the algorithm they had memorized in 5th grade.  I assume this is because they had me last year, so they are more used to using pictorial representations in math.

Once everyone was progressing on the area models, I called the four students who needed review of addition and subtraction into my office, with their personal whiteboards.  We sat around the round table and reviewed finding a common denominator to add and subtract.  We were able to use a variation on the area model to show cutting pieces to be the same size (common denominator) before we added.  I kept the office door open so I could see and hear the rest of my class as they continued drawing area models.

When the small group was finished, we rejoined the large group.  A few minutes later I had a student who had noticed the connection between the area model and the standard algorithm show his discovery to the class.  We wrapped up with a discussion of what the small group had discovered about how to use a modification of the area models to get a common denominator and why denominators stay the same when you add or subtract (because you’re counting pieces that are all the same size), but change when you multiply (because you’re cutting the pieces up into smaller pieces.)

I’m hoping that the kids in the small group didn’t feel awkward going into the office to work with me.  I asked them about it, but they didn’t say anything.  They did say that the review time was helpful.  Hopefully, this is a strategy that I can continue to use in the future.

If you have other techniques that you like to address issues like this one, please share them in the comments!


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