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Saturday, August 24, 2013

Rounding Multi-Digit Whole Numbers

What exactly is rounding, and how can we help students understand it? When I was in fourth grade, my teacher told me to look at the neighbor to the right to round. If that number was 0-4, I should round down; if it was 5-9, I should round up.

Fast forward several decades, and I became the fourth grade teacher. The traditional strategy just didn't seem to help my students "get" rounding. I wanted my class to understand that rounding involved finding the closest multiple of 10, 100, 1000, etc.

Let's eavesdrop on this week's class discussion:
  • Me: What is rounding?
  • Student: It's sort of like estimating.
  • Me: Why do we round?
  • Students look around and act unsure.
  • Me: Let's say I go to the store with $50 in my pocket. I want to purchase three items. One item costs $19, another is $11, and the third is $13. I want to make sure I have enough money when I get to the counter to pay, so I round each amount then add to see if it's more than $50. I use rounding to figure out about how much each item costs (in this case to the nearest $10) then I add them together. That final step, adding rounded numbers, is estimation.
The conversation continued, and we discussed situations when we would round to the nearest 100; 1,000, 10,000, and even 100,000. My students were clearly comfortable with rounding to the nearest 10 and 100; they'd learned how to do that in third grade, but 100,000? Wow, they just weren't sure they could do that.

This year I've decided to have students take notes for each concept. Here's our page for 4.NBT.A.3:

When rounding, the first thing I want my students to do is ask themselves, "What is the closest 10 (or 100 or 1000, etc.)?" To me, this is the highest level of conceptualization. If that doesn't work, they draw a number line, as shown. This also allows students to conceptualize the process (with the aid of a diagram). Finally, if neither of these two strategies are working, they may use the next-door neighbor. Finding the next-door neighbor has little or no conceptual value, but for those who struggle, it will work until they gain a better understanding of the number system.

Next I modeled rounding the number to the nearest 100; 1,000; 10,000; and 100,000. After demonstrating with a few more numbers, they worked some problems with me, and finally they set off on their own.

This year we'll use rounding a lot! As students review longer addition and subtraction problems then learn long multiplication and division, I will require them to estimate. In fourth grade, students will estimate on paper, but in subsequent grades they should be able to estimate mentally. This arms them with a powerful tool! Estimation (which is addressed in 4.OA.A.3) allows students to know if the answer to a complex problem is reasonable (or if a red flag is being waved), and it allows them to go to the store with $50 and figure out if they have enough money to buy a series of objects.