Excuse me Miss, I think I found a pattern…

One of my 7th graders stopped me while I was going over squares and square roots.   We have just finished up some work on the distributive property using the area model and were about to get into a little geometry.  Anyhow, he said that he noticed when he was squaring numbers that if he took the number that he just squared and added it to the number squared, then added the next number, it came out to be the next number squared.  What a gem!  I was pretty excited.  I said, “That is super!  You have just found a wonderful link between algebra and geometry.”

I used the area model to show him why this worked.  I let “n” be the original number and n+1 be the next number.  Using an area model made it clearer to the students in 7th grade.  We had seen this done before with the distribution property in the CMP book.  I reminded the class of this before we started and created a model first with numbers then with “n” and “n+1.”  They wanted to know if it also worked with other values, such as “n+5.”  We used the same area model and showed that it would work with those values too.  It was one of the best classes we had all year, in my book.

 

 

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