I was cleaning up the Estimation Table at my last Family Math Night event when I noticed a slip of paper next to the Hershey’s jar.  Taking a closer look at it, I realized I was looking at the thinking behind someone’s guess as to the number of Hersheys in the jar.

This piece of paper is priceless to me as an educator.  It allows me to clearly understand the steps this child took to arrive at his/her answer – an answer that turned out to be exactly two Hersheys kisses off!

It starts with a multiplication problem:  4 x 27.  It’s hard to see from this photo, but if you counted the number of Hersheys that can be seen on the side of the jar, I’m guessing this student got ’27’.  Then, if you look at the number of rows of 27 that could be made from one side of the jar to the other side, I’m guessing that that’s where the ‘4’ came from.  From there, the student knew s/he had to multiply the 27 Hersheys by the 4 rows.  Since, from this point forward the student uses addition, I’m going to guess that the student either wasn’t comfortable with double-digit by single-digit multiplication or simply did not know how to do it.

So, instead, s/he used number sense by breaking down 4 x 27 into a simpler problem:  (27 x 2) + (2 x 27) which s/he wrote as (27 + 27) + (27 + 27).  From there it was simply finding the answer of ’54’ and adding that twice to get 108.

This is an amazing example of a student that has a clear mastery of number sense – breaking a multiplication problem down into a more manageable addition problem.  It’s also a great example of the distributive property of multiplication, although there’s a good chance the student has no idea what ‘distributive property’ means.  It doesn’t really matter; it’s the concept that’s important.

And this is what I love about the estimation jar – it gives kids an opportunity to practice number sense within the context of something fun…candy.  And because there’s a sense of excitement and anticipation over who will get the closest and win all the candy, kids want to participate.

From now on I’m going to make sure I include scrap paper at all of my Estimation Tables.