How to Teach Rounding

Students begin learning to round to tens and hundreds in third grade.^{[1]XResearch source} Rounding is an important skill that students often struggle with because they do not have mastery of place value and/or struggle with skip counting. When teaching rounding it is important to first ensure students have this prior knowledge. Then you can teach rounding using a number line. Only after mastering these skills should students be taught the abstract rules, methods, and “tricks” for rounding.^{[2]XResearch source}

Part 1

Part 1 of 4:

Practicing Skip Counting

1
Count by ones to 10. If students needs help, they can use their fingers or manipulatives.
- Before learning to round, students must be able to skip count. ^{[3]XResearch source} Skip counting allows students to identify the nearest ten or nearest hundred to a number that is being rounded. Students also need to understand the difference between counting by ones, tens, and hundreds, to activate their understanding of place value.
2
Count by tens to 100. Choose random tens, and ask the students which ten is above it.
- Students can use a hundreds chart if need be.
- For example, after the students can count by tens to 100, ask, “What ten is above 20? 30 is the ten above 20.”
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3
Count by hundreds to 1,000. Choose random hundreds, and ask the students which hundred is above it.
- Students can use a thousands chart if need be.
- For example, after the students can count by hundreds to 1,000, ask, “What hundred is above 400? 500 is above 400.”
4
Continue to practice skip counting other groups of numbers. The skip counting you do will depend on the type of rounding you expect the students to do.
- For example, if rounding to the ten thousands place, practice skip counting by thousands and ten thousands.
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Part 2

Part 2 of 4:

Reviewing Place Value

1
Write a four-digit number. Choose a number that has different digits in each place value, for clarity's sake.
- It is essential that students have a complete understanding of place value before attempting to teach them rounding. If students have already mastered place value, you can skip this part.
- This assumes you are teaching rounding to the tens or hundreds. If you are teaching rounding to the thousands or more, you might want to write a number that has 5 or more digits.
- For example, you might write the number 3,892.
2
Review the ones place. Point to the digit farthest to the right. Explain the value of the digit in the ones place. Count by ones until you reach the value.
- You can use base 10 blocks or other manipulatives to help illustrate the value of each digit.
- For example, in the number 3,892, point to the 2 and explain that the 2 is in the ones place, and the value of 2 twos is 2. Count: “1, 2.”
3
Review the tens place. Point to the digit second from the right. Explain the value of the digit in the tens place. Count by tens until you reach the value.
- For example, in the number 3,892, point to the 9 and explain that the 9 is in the tens place, and the value of 9 tens is 90. Count: “10, 20, 30, 40, 50, 60, 70, 80, 90.”
4
Review the hundreds place. Point to the digit third from the right. Explain the value of the digit in the hundreds place. Count by hundreds until you reach the value.
- For example, in the number 3,892, point to the 8 and explain that the 8 is in the hundreds place, and the value of 8 hundreds is 800. Count: “100, 200, 300, 400, 500, 600, 700, 800.”
5
Review the thousands place. Point to the digit fourth from the right. Explain the value of the digit in the thousands place. Count by thousands until you reach the value.
- For example, in the number 3,892, point to the 3 and explain that the 3 is in the thousands place, and the value of 3 thousands is 3,000. Count: “1,000, 2,000, 3,000.”
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Part 3

Part 3 of 4:

Using a Number Line to Round Pictorially

1
Define what rounding is, and why we use it. Rounding is changing a difficult number to a number close by. We round a number to make it easier to use.^{[4]XResearch source}
- For example, if you are trying to figure out about how many total cookies you and your friend ate last year, and you ate 327 cookies while your friend ate 286, you could round both numbers to 300, because 300 + 300 is easier to calculate than 327 + 286.
2
Explain that we round to a particular place value. We often round to the nearest ten, hundred, or thousand. Review what place value the students are rounding to.
- For example, you might want student to round to the nearest hundred. Review where the hundreds place is, if necessary.
3
Choose a number to round. The number should go to at least the same place value students are rounding to.
- For example, if students are rounding to the nearest hundred, you might choose the number 892.
4
Ask students to locate the target place value in the number. Determine the value, and ask for the rounded number above it.
- For example, if rounding 892 to the nearest hundred, students should locate the 8, and understand that its value is 800. Ask, “What hundred is above 800? 900 is above 800.” Emphasize that students are rounding to the nearest hundred.
5
Draw a number line. The number on the far left of the line should be the value of the digit in the target place value. The value on the far right should be the rounded number above it. Use hash marks to skip count up the number line.
- For better accuracy, it is helpful to use preprinted number lines instead of hand-drawn number lines.
- For example, if rounding 892 to the nearest hundred, the number on the far left of the number line would be 800, and the number on the far right of the number line would be 900. In between, the hash marks would skip count by tens: 810, 820, 830, 840, 850, 860, 870, 880, 890, 900.
6
Ask students to determine the halfway point on the number line. Mark this point on the line.
- You can mark the point with a star or dot, or you can trace over the first half of the number line in one color, and trace the second half of the number line in another color.
- For example, if using a number line that begins with 800 and ends with 900, the halfway point would be 850, so you would draw a star on the 850 hash mark.
7
Plot the number students are rounding on the number line. Use the additional hash marks on the number line to denote other place values as necessary. Draw a dot on the appropriate hash mark, and write the number above the dot.
- For example, if plotting 892, you would draw nine hash marks between 890 and 900, and draw a dot on the second hash mark after 890.
8
Ask students if the number is above or below the halfway point on the number line. Determine whether the number is closer to the first number on the number line, or the last number on the number line.
- For example, ask students if 892 is above or below 850. Since it is above 850, it is closer to 900 than it is to 800.
9
Explain that we round up or down. Whether we round up or down depends on which rounded number our actual number is closest to.
- If the actual number is closer to the lower rounded number, or below the halfway point, we round down.
- If the number is exactly at the halfway point, explain that the rule is that you round up. ^{[5]XResearch source}
- If the actual number is closer to the higher rounded number, or above the halfway point, we round up.
10
Determine your rounded number. Circle this number on the number line, and draw an arrow pointing to it from the actual number.
- For example, since 892 is above the halfway point, we round up to 900. So 892 rounded to the nearest hundred is 900. Draw an arrow pointing from 892 to 900. Circle 900.
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Part 4

Part 4 of 4:

Using the Rules of Rounding to Round Abstractly

1
Write down the number you are rounding. The number should go to at least the same place value students are rounding to.
- This part is for students who can think more abstractly about rounding. It is helpful to use only after students have mastered rounding using a number line.
- For example, if students are rounding to the nearest hundred, you might write down the number 892.
2
Ask students to locate the target place value in the number. Circle the digit in this place value and determine its value. Ask students what rounded number is above it.
- For example, if rounding 892 to the nearest hundred, students should circle the 8, and understand that its value is 800. Ask, “What hundred is above 800? 900 is above 800.” Emphasize that students are rounding to the nearest hundred.
3
Explain that to round, you look at the place value below (to the right of) the one you are rounding to. The place value below gives us the information we need in order to determine whether we round up or down. It is the deciding digit. Underline the deciding digit in this place value.
- For example, if rounding 892 to the nearest hundred, students should look to the tens place and underline the 9.
4
Explain the rules of rounding. If the deciding digit is 5 or more, we round up. If the deciding digit is 4 or less, we round down.^{[6]XResearch source}
- It might be helpful to draw a 5 next to an arrow pointing up, and a 4 next to an arrow pointing down.
5
Look at the underlined digit in the number. Determine whether it is tells you to round up or down.
- For example, in the number 892, you would look at the 9. Since 9 is above 5, it tells you to round up.
6
Determine the rounded number and write it down. Draw an arrow pointing from the original number to the rounded number. Make sure students can identify what place value they were rounding to.
- Students can be confused when rounding down using this method. For example, they might think they should round 412 down to 300, because 300 is the hundred below 400. Emphasize that they should consider the original number they are rounding and find the hundred below the original number, not the hundred below the hundreds place of the original number.
- For example, 892 rounded to the nearest hundred is 900. Draw an arrow from 892 to 900.
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Question
How do you round numbers to the nearest hundred?
Community Answer
Look at the tens place. If the digit in the tens place is 5 or more, you round up to the next hundred. If it is 4 or less, you round down. For example, if rounding 730 to the nearest hundred, look at the tens place. Since 3 is in the tens place, you would round down to 700, since 3 is less than 5.
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Question
What are the rules for determining whether your round up or down?
Community Answer
Look at the place value to the right of the place value you are rounding to. If the digit in that place value is 5 or more, you round up. If the digit in that place value is 4 or less, you round down.
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To have students practice rounding, write numbers on the fronts of flash cards that contain numbers that need to be rounded. Underline the place value where the number should be rounded. Put the answers on the backs of the flashcards. Students can even create a set of flashcards to use at home.
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To help students remember the rules of rounding, teach them a song, rhyme, or rap with the rounding rules as the words. You can use any familiar tune to create a song for the kids to sing to help them remember when to round up and when to round down.
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