Visualizing Rounding with Vertical Number Lines and Midpoints

In third grade, your student used place value understanding to round whole numbers to the nearest 10 or 100.

Fourth graders are expected to round multi-digit numbers from 1-1,000,000 to any place.

Here's how we rounded 399,499 to the nearest thousand using a vertical number line and finding/comparing the number we were rounding to the midpoint:

To use a vertical number line to round our number, first, we thought about how many thousands our number has (399 thousands) since we are rounding to the nearest thousand.   We labeled the endpoint on the bottom.  Then, since we are rounding to the nearest thousand, we thought of the number that is 1 thousand more than 399 thousands, which is 400 thousands and labeled the other endpoint on the number line.  Our number is somewhere between these numbers.

To find the midpoint, some students found it helpful to remember that since we're rounding to the nearest thousand, the difference between how many thousands our number has (399 thousands) and the number that's 1,000 more (400,000) is 1 thousand (or 10 hundreds).  The midpoint splits those 10 hundreds into 5 hundreds and 5 hundreds, so, this means the midpoint would be 399 thousands 5 hundreds, or 399,500.

Next, we placed the number we are rounding (399,499) on the number line.

Since we can see that the number we are rounding is less than half-way, it is closer to 399,000.

So, 399,499 rounded to the nearest thousand is 399,000

This week in class (briefly) and for home learning over the next several weeks, your student will practice rounding four-digit numbers to the nearest thousand, hundred, and ten.  We'll gradually practice rounding five and six-digit numbers to the nearest ten and hundred thousand as well.

Why bother with a vertical number line?  It visually reinforces what is happening when we round numbers--we are looking for the closest number to the number we are rounding, and visualizing greatly helps most learners retain what they are learning.  What students remember they will be able to apply in solving real-life problems!