Sunday, January 3, 2016

Straight Talk on Rounding

When I teach or spiral for rounding, I begin by asking students,
“What do you already know?” 

The most common answer is something along the lines of:
“5 or more, up the score, 4 or less, let it rest.” 

Or, they show me their fist as they mime grasping the string of a balloon.  The number stays the same, they explain, for 1,2,3, or 4 fingers but by opening the 5th finger that leads to an open fist, the balloon flies free.  The balloon rises up as does the number.  (In the past, I’ve taught these two strategies and more along the same lines.) 

Even though students can often chant the rhyme or explain the balloon analogy, when it comes to applying this to whether 0.86 should round to 0.8 or 0.9, students struggle.  Some circle the number to be rounded and underline the digit to its right.  Others underline the number to be rounded and circle the digit to its right or draw an arrow to the digit to its right.  Why the number to the right, you ask them?  They often cannot say.   Why indeed?  We know it’s because of the base 10 number system within the construct of the place value chart but students often don’t know the underlying context.

Math is among other things, a language of patterns and connections.  I’ve taught rhymes to help students remember yet I see now that rhymes, albeit useful in the short term, give students a disconnected, isolated view of math concepts, instead of capitalizing on connections.   As a result, when students don’t remember the rhyme perfectly, they can’t reason their way through to a solution as they might if they had deeper conceptual knowledge of the process.     

I now teach rounding using a number line and knowledge of place value.  

While I enjoy creating my own videos and materials to teach concepts, there are just so many valuable tools and resources already created and available.  One of those great resources that I like to use is called LearnZilliona resource developed for Common Core.  (Our district does not have a Common Core curriculum but the resources on this site can be used interchangeably with other curriculum):
Go to LearnZillion to access math resources
Learn Zillion

If you’d like to see videos about rounding, click on the hyperlinks below:

After showing an instructional video, I model rounding for students.  As they follow along, copying modeled problems on their white boards, I encourage them to draw a number line with 10 ticks.  They use this number line consistently by renumbering the ticks according to the problem. 

I ask questions like:
What digit should we round?
If we round to (tens, tenths, etc.) What should our upper limit be?  What should our lower limit be?   Is our number to be rounded closer to our upper limit? or lower limit?  How do you know?

When we’ve labeled our tick marks, we plot our point. 
Together we choose the limit our point is closer to.
If students are not sure, we count the spaces (the intervals not the tickmarks!) between our plotted point and the upper limit and lower limit.

I give students practice problems for independent practice to solve on their whiteboards.  I encourage students to work together collaboratively and communicate while practicing.  I question as they work, "How do you know?" or ask another student, "Do you agree?" "Why or why not?"  

To close the lesson, I give students an exit ticket I make on post it notes – click here for the template:  Rounding Exit Tickets.pdf

I hope these resources are useful.  I would love to know your thoughts on rounding, teaching conceptually, or anything!  Please feel free to leave a comment!  Thank you for letting me share. 

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