Sunday, September 14, 2014

Rounding in a Round About Way

Have you ever seen an assessment item like this one?

I have.  As a matter of fact there is a similar question on my district's third grade unit 1 assessment.  The expectation is that the student's would read the word "about" (which has been bolded, italicized, and underlined for emphasis) and they would then know that they should not perform exact arithmetic on this problem, but instead round first, then add.  Why?! Because it's easier?  I think not.  Not to mention the conundrum of the teacher who gets two answers to this problem: $70 if they rounded before adding, and $60 if they rounded after adding.  Which is correct?  Who cares?  I have been fighting this battle in my head throughout the last week as I attempt to get my third graders to see a purpose for rounding. 

They don't, by the way.  See the purpose I mean.  The majority of my students came to me fluently adding 2-digit numbers (as the Common Core Standards say they should have).  Most of them can look at those two numbers and add them in their head using mental math.  Most of them do just that when presented with a problem such as this. So the question remains, how do I get them to solve this type of a problem correctly?  I don't.  Hear me out...

I spent some time this weekend searching for a purpose that my students could connect with.  In the process I read my standards again, and I happened to notice some key words that flipped the switch in my head.  So here we have it... 3.NBT.1 says students should be able to "Use place value understanding to round to the nearest 10 or 100." and 3.OA.8 says "Assess the reasonableness of answers using mental computation and estimation strategies including rounding."  There's the purpose statement.  At this level, students should be using rounding as an approximation strategy, after they've solved the problem, to make sure their answer makes sense. 

I'm not saying it's never appropriate to round before you add.  I'm just saying, with the size of numbers that we're working with right now, why would you.  So from now on, in my classroom, we'll be focusing on Standard for Mathematical Practice 1, which says (among other things), "Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' "  Rounding will be one of our strategies for making sure our answers make sense. 

I feel good about this decision.  I feel like this approach really matches with the intent of the standards.  Just to make sure, though, I looked up the topic of rounding in the Progressions for the Common Core State Standards in Mathematics (written by the Common Core Standards Writing Team).  After some explanation about how rounding to the nearest 10 in a three digit number can be more difficult for students, they ended their section on rounding with this statement, "Rounding two numbers before computing can take as long as just computing their sum or difference."  No wonder my students couldn't see the purpose. 


  1. Every time I read your blog, I think "Man, so smart!" Brilliant, really. I am amazed. Thank you for continuously sharing all of your fabulous ideas.

    1. Thank you so much! I'm just out here trying to figure it out as I go. Some days I think, "I have no idea how to do this." Some days a lightbulb flashes on and I've got it. :-)