Round Numbers Successfully

Use Rounding Models to Learn

Rounding can be yet one more math operation with rules they must memorize that is hard for many students to grasp. Models and other multisensory methods make it easier.

Prime students for success by counting aloud by whatever number is being rounded to. (Example: 10, 20, 30, 40,…) That is the set of possible answers. Anything not an even ten (or hundred, thousand, etc.) is not possible.

A surprisingly effective tool is to teach students rounding by using a rounding model resembling a hill. Students hear that it's a numberline, which are straight lines, but is shown this way as a thinking tool, a model to use to understand rounding.

A sine curved black line ending in an arrow, with a vertical mark at the midpoint of the “hill.” The arrow shows the direction of increase, left to right.

Note the arrow at the end. It indicates numbers increasing left to right.

Sine ray with 85 at the midpoint and 80 at the beginning of the line and 90 at the end. Next all the numbers between 80 and 85 and then between 85 and 90 are filled in on the number line.

It's designed with a midpoint. If rounding to the nearest ten, the midpoint of a ten is 5. Say, the number being rounded to the nearest ten is 86. Which even ten is the one just below 86? (Count by tens to reinforce the set of possible answers.) What's in the tens place in 86? 8, so the even ten just lower than 86 is 80. 80 + 5 gives the midpoint of 85. Which ten is after 86? 90. 86 is between 80 and 90.

Show where 86 would fall on the numberline. (After the midpoint.) To round to the nearest ten, 86 would roll downhill to which number? Yes, 90, because 86 is closer to 90 than 86.

All the numbers before the midpoint would roll downhill to the lower ten and all those after it would roll downhill to the higher one. So what about the exact midpoint? The rule is that it always rolls forward, never backwards.

In a similar way, to round to the thousands first count by thousands. The answer will be an even thousand. To find the midpoint, ask what is half of a thousand. 500.

Suppose the number to round is 3,499. What's in the thousands place? Yes, 3. So the thousand before the number is 3000. What's the next thousand above 3000? Yes, 4,000.

So 3,400 is between 3,000 and 4,000. Add 500 to the lower thousand to find the midpoint, and mark 3,500 at the midpoint.

Next fill in the even hundreds between 3,000 and 4,000, starting with 3,100, 3,200, 3,300, 3,400 before the midpoint then 3,600, 3,700, 3,800, and 3,900 between the midpoint and 4,000.

Where on the numberline would 3,499 be? Before or after the midpoint? Which even thousand would it roll downhill to?

In the top model, the thousand before 3,499 is 3,000, the thousand after is 4,000 and the midpoint is 3,500. The second shows the sine-shaped number line with increments of 100. 3,100>3,200>3,300>3,400 between 3,000 and 3,500, and 3,500>3,700>3,800, and 3,900 between 3,500 and 4,000.

Wait…what about the rule?

This approach to rounding relies on the visual aid and storytelling for its effectiveness. Imagining the numbers rolling downhill provides an analogy rather than memorizing a rule. Storytelling and imagination are both right-brain activities which is linked to long-term memory.

“Tell me the facts and I’ll learn. Tell me the truth and I’ll believe. But tell me a story and it will live in my heart forever.” ~ Native American Proverb

“Stories are the way we remember; we tend to forget lists and bullet points.” ~ Robert McKee

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