Students begin learning to round to tens and hundreds in third grade. Rounding is an important skill that students often struggle with as they lack place value mastery or have trouble skipping counting. When teaching rounding, it is important that you first ensure that students have this prior knowledge. Then you can teach them to round using a number line. Students should be taught the abstract rules, methods, and "tricks" for rounding only after these skills are mastered.

## Steps

### Part 1 of 4: Practice Skip Counting

#### Step 1. Count one at a time to 10

In case students need help, they can use their fingers or use manipulatives.

### Before learning to round, students should be able to skip counting. Skip counting allows students to identify the nearest ten or hundred to the number being rounded. In addition, students must understand the difference between counting from one to one, from ten to ten, and from one hundred to one hundred to activate their understanding of place value

#### Step 2. Count from ten to ten to 100

Pick a random ten and ask the students which ten is above it.

- Students can use a hundreds chart if necessary.
- For example, once students can count by tens to 100, ask, "Which ten is above 20? 30 is the ten that is above 20."

#### Step 3. Count from one hundred to one hundred up to 1000

Pick a random hundred and ask students which hundred is above it.

- Students can use a thousands chart if necessary.
- For example, once students can count from 100 to 100, ask, "Which hundred is above 400? 500 is above 400."

#### Step 4. Keep practicing skip counting with other groups of numbers

The type of skip counting you do will depend on the type of rounding you expect your students to do.

### For example, if you are rounding to the tens of hundreds place, practice skip counting from a thousand to a thousand and from ten thousand to ten thousand

### Part 2 of 4: Review Place Value

#### Step 1. Write a 4-digit number

For clarity, choose a number with different digits in each place value.

- It is essential that students fully understand place value before you try to teach them to round. If students have mastered place value themselves, you can skip this part.
- This assumes you are teaching rounding to tens or hundreds. If you are teaching rounding to thousands or more, you may need to write a number with 5 or more digits.
- For example, you could write the number 3892.

#### Step 2. Review the position of the units

Point to the digit to the far right. Explain the value of the digit in the ones place. Count one at a time until you reach that value.

- You can use base 10 blocks or other manipulatives as a way to help illustrate the value of each digit.
- For example, in the number 3892, point to 2 and explain that 2 is in the ones place and the value of two units is 2. Count: "1, 2".

#### Step 3. Review the tens place

Point to the second digit from the right. Explain the value of the digit in the tens place. Count from ten to ten until you reach that value.

### For example, in the number 3892, he points to 9 and explains that it is in the tens place, and that the value of 9 tens is 90. Count: "10, 20, 30, 40, 50, 60, 70, 80, 90 "

#### Step 4. Review the hundreds place

Point to the third digit from the right. Explain the value of the digit in the hundreds place. Count from one hundred to one hundred until you reach that value.

### For example, in the number 3892, he points to the 8 and explains that it is in the hundreds place and that the value of 8 hundreds is 800. Count: "100, 200, 300, 400, 500, 600, 700, 800 "

#### Step 5. Review the thousands place

Point to the fourth digit from the right. Explain the value of the digit in the thousands place. Count from a thousand to a thousand until you reach that value.

### For example, in the number 3892, he points to 3 and explains that it is in the thousands place and that the value of 3 thousands is 3000. Count: "1000, 2000, 3000."

### Part 3 of 4: Using a Number Line to Round Pictorially

#### Step 1. Define what rounding is and why it is used

Rounding constitutes exchanging a difficult number for a close number. We round up numbers to make them easier to use.

### For example, if you are trying to determine the approximate number of cookies that you and your friend ate in total in the previous year, and you ate 327 cookies while your friend ate 286, you could round both numbers to 300, since 300 + 300 is easier to calculate than 327 + 286

#### Step 2. Explain that it is rounded to a particular place value

It is usually rounded to the nearest ten, hundred or thousand. Review the place value to which the students are going to round.

### For example, you might want your students to round to the nearest hundred. If necessary, review where the hundreds place is

#### Step 3. Choose a number to round

The number should come up to at least the same place value your students are rounding to.

### For example, in case your students are rounding to the nearest hundred, you could choose the number 892

#### Step 4. Ask your students to locate the place value they are targeting in the number

Determine the value and ask them for the rounded number that is above it.

### For example, if you are rounding 892 to the nearest hundred, students should locate 8 and understand that it has a value of 800. Ask "Which hundred is above 800? 900 is above 800 ". Emphasize that students are going to round to the nearest hundred

#### Step 5. Draw a number line

The number on the far left of the line should be the value of the digit in the place value you are pointing to. The value on the far right should be the rounded number above it. Use measuring lines to skip counting up the number line.

- For better precision, it is helpful to use pre-printed number lines instead of hand-drawn number lines.
- For example, if you were 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 would be 900. Between them, the measurement lines would count as Sauteed ten at a time: 810, 820, 830, 840, 850, 860, 870, 880, 890, 900.

#### Step 6. Ask your students to determine the midpoint of the number line

Mark this point on the line.

- You can mark this position with a star or dot, or you can trace over the first half of the number line using one color and trace over the second half with another color.
- For example, if you are using a number line that starts with 800 and ends with 900, the midpoint would be 850, so you would draw a star on the 850 measurement line.

#### Step 7. Record on the number line the number that the students are going to round

Use the additional measurement lines on the number line to denote other place values as needed. Draw a point on the appropriate measurement line and write the number above the point.

### For example, in case you are recording 892, draw 9 measurement lines between 890 and 900 and plot a point on the second line after 890

#### Step 8. Ask students if the number is above or below the midpoint of the number line

Determine if the number is closer to the first or last number on the line.

### For example, ask your students whether 892 is above or below 850. Because it is above 850, it is closer to 900 than 800

#### Step 9. Explain that it is rounded up or down

Rounding up or down depends on the number rounded to which the original number is closest.

- In case the original number is closer to the lowest rounded number, or below the midpoint, it is rounded down.
- If the original number is right in the middle, you should explain that the rule says to round up.
- In case the original number is closer to the highest rounded number, or above the midpoint, it is rounded up.

#### Step 10. Determine the rounded number

Circle this number on the number line and draw an arrow pointing to it from the original number.

### For example, because 892 is above the midpoint, it rounds to 900. So, 892 rounded to the nearest hundred is 900. Draw an arrow from 892 that points to 900. Circle 900

### Part 4 of 4: Use Rounding Rules to Round Abstractly

#### Step 1. Write down the number to be rounded

The number must come up to at least the same place value to which the students are going to round.

- This part is for students who can think more abstractly about rounding. It is useful to use it only after students have mastered the method of rounding using a number line.
- For example, if students round to the nearest hundred, you could write the number 892.

#### Step 2. Ask students to locate the place value they are targeting in the number

Circle the digit in this place value and determine its value. Ask your students which rounded number is above it.

### For example, if you are rounding 892 to the nearest hundred, students should circle 8 and understand that it has a value of 800. Ask them "Which hundred is above 800? 900 is above 800 ". Emphasize that students are going to round to the nearest hundred

#### Step 3. Explain that to round, look at the place value that is below (or to the right) of the one to which you are rounding

The place value below it gives us the information we need to determine whether to round up or down. It is the determining digit. Underline the determining digit in this place value.

### For example, if 892 is to be rounded to the nearest hundred, students should look at the tens place and underline 9

#### Step 4. Explain the rules of rounding

In case the determining digit is 5 or more, it is rounded up. In case the determining digit is 4 or less, it is rounded down.

### It might be helpful to draw a 5 next to an arrow pointing up and a 4 next to an arrow pointing down

#### Step 5. Look at the underlined digit in the number

Determine if it tells you to round up or down.

### For example, in the number 892, you would look at the number 9. This is above 5, so it tells you to round up

#### Step 6. Determine the rounded number and write it down

Draw an arrow pointing from the original number to the rounded number. Take care that students can identify the place value to which they were rounding.

- Students can get confused when rounding down using this method. For example, they may think that they should round 412 to 300, since 300 is the hundred that is below 400. Emphasize that they must take into account the original number that they are going to round and find the hundred that is below of the original number instead of the hundred below the hundreds place in the original number.
- For example, 892 rounded to the nearest hundred is 900. Draw an arrow from 892 to 900.

## Advice

- You can have your students practice rounding by writing numbers on the front of flashcards that contain numbers that need to be rounded. Underline the place value where the number should be rounded. Put the answers on the back of the cards. Students can even create a set of flashcards to use at home.
- If you want to help your students remember the rules of rounding, you can teach them a song, rhyme, or rap whose lyrics are the rules. Any known tune can be used to create a song that children can sing to help them remember when to round up and when to round down.