Estimating on Number Lines

I have found that estimating on a number line was a big shift for my class.  At first, they looked like EXPERT estimators; I was ready to hug their third grade teachers.  But then problems kept cropping up.  Why were they suddenly struggling?  Everyone knew that 48,053 rounds to 50,000 and everyone knew 21,923 rounds to 20,000. 

It was pretty clear that when I asked them to round 34,356 to the nearest hundred and suddenly they looked like deer in the headlights that place value was the issue.  Oh, they all whizzed through chapter 1 and knew their word form and expanded form and lined up numbers in columns like pros.  And we've practiced regrouping on a daily basis in our Every Day Counts routine.  But they are still not able to put it all together to really conceptualize how numbers differ.

To fix this I designed two activities.  The first was "Pin the Number on the Number line."  I started out with a single sticky note with the number 35,421 on it.  Then I created four number lines on sentence strips based on that number.  Each number line represented a different place value:

Ten thousands:  10,000  20,000  30,000  40,000 and so on.

Thousands:  30,000  31,000  32,000  33,000  34,000   35,000  36,000 and so on.

And so on for the hundreds and tens...notice that the original number will fit on both of the number lines.  All the number lines were designed to have a space where the given number would fit into. 

Next I wrote 7 more sticky notes that could all fit somewhere on the tens number line, since of course that line would have the most limited choice.

For the activity, I put a number line at each table and had students rotate through, working with a partner to determine where to place the sticky note would go each time, and record it onto their sheets.  As they finished they switched sticky notes with others to get more practice. 

This activity was simple enough for all students, yet it gave them the practice they needed to start looking at a number more than one way.  They had to switch the focus of the place value at each spot.  Since they already had the concept of the 5 determining if a rounded number is larger or smaller than the original, I didn't even focus on that in this lesson.  It was all about find the place value and determining what the higher or lower value was.  In fact, when they sat down and looked at their recording sheets with the higher and lower value their number fell between, they automatically made the connection to circle which of the two the number rounded to.

I had an extension activity that I cycled students through, which I wrote about on my other blog.  This estimating activity was also hands on, but instead of using number lines as a tool I used money to help us estimate!