Educated Estimation

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How many of you remember those huge jars filled with jelly beans that graced the hallway of your elementary school with a big sign that read:


I always wanted to win that jar, but my guesses were so far out in left field that I had a better chance of winning the lottery, which is really something since I was too young back then to even play the lottery. 

But you get my point.  Next time you see a similar contest, take a peek at the entries left by kids.  You will see a large range of guesses.  Some kids are really good at taking a guess, because it is an educated guess.  Some kids don't even know where to begin.

I wanted to help my daughter learn to estimate the number of objects in a jar (and no....not so she can have an extra trip to the dentist this year), so that she would be able to effectively estimate how much material she should buy the next time she makes a craft.  Whether or not she has enough flour in the pantry to make her favorite cookies. So that she can estimate how many calendar days until her birthday.  So that she can estimate how much 5 things in her shopping cart will cost her.  So that she can feel successful and confident the next time she has a math test.  So that she can learn how to use it in her everyday life.  

To do this, I needed to help her find a starting point in order to make an educated estimation.  So, I grabbed three jars.  One was very small.  The next jar was about twice the size of the small one.  The largest jar was about twice the size of the middle jar.  

I loaded the smallest jar with tiles and asked her to count the tiles.  She did.  Her answer was 24.  I asked her to compare the second jar with the first jar.  She thought it was about twice the size.  We talked about that observation.  What would that mean?  With some nudging, I helped her conclude that if she doubled the amount in the small jar, she might come close to guessing how many the middle jar could hold. So, she wrote out her math problem, (24 + 24) found her sum (48) and then guessed that the middle jar would hold 48 tiles.

We counted tiles by making piles of 10 to make our counting easier and more accurate.

66 tiles!  (5 piles of 10 + 6 individual tiles = 66 tiles)

She was very disappointed that she didn't have the right answer.   I assured her that the goal was not the right answer at this point in time.  The goal is to find a "measure", so to speak, for estimating the total number of tiles in the jars.  

So then, armed with the number of tiles counted in the middle jar, we made observations about the size difference from the middle to the large jar.  Was it twice the size?  More?  Less?  This time, she said she thought the large jar would house 3 times the amount of tiles that the medium jar held.  So, she added together the following numbers:  66 + 66 + 66.  When she found her answer equaled 198, her eyes got real big.  It was obvious that she felt uncomfortable with that answer.  In response, I asked her if she would like to keep that number, go higher, or go lower.  She decided to go lower.  In fact, she decided to go quite a bit lower, and decided that maybe the large jar was twice the size of the middle jar, and not three times the size.  So she instead added together 66 + 66.  She felt good with her estimate: 136.  

The counting piles of 10 began again.  This time, she was closer!  The actual number of tiles counted were 127.  

This was a very easy, quick way to teach this first grader about educated estimations. You can use almost anything you have in your house already.  You could use marshmallows, pretzel sticks, marbles, or anything else of a consistent size and shape.  

Remember:  Math is a journey.  Have fun!