• The Round and Round and Round practice worksheet (M-3-6-1_Round and Round Practice Worksheet and KEY.docx) can be used to determine how well students can round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred.
• Use the Lesson 1 Exit Ticket (M-3-6-1_Lesson 1 Exit Ticket and KEY.docx) to evaluate the level of students’ understanding of rounding.

This lesson focuses on rounding numbers to the nearest ten and the nearest hundred.

To prepare students for this lesson, first help students review counting by 10s and 100s using base-ten blocks. To do so, distribute base-ten blocks to groups of two or three students. Each group should receive at least 10 hundreds, 10 tens, and 30 ones. Introduce the lesson as follows.

“How much did the groceries cost? How many people came to the party? How many marbles are in the pail? People often answer these questions by saying about how many. The groceries cost about $40. About 20 people came to the party. There are about 100 marbles in the pail. Today we will learn to round numbers, a strategy used often to answer questions that ask about how many. But first we will review counting by 10s and counting by 100s using base-ten blocks. This will help get us ready to learn how to round numbers.”

Review—Counting by Tens and Hundreds

Hold up one of the tens, the long, narrow base-ten block representing ten units. Write the value on the board, 10. Now hold up a second of the tens, and write the value 20 on the board. Continue holding up additional tens to help students count by tens and visualize each multiple of ten using base-ten blocks. Be sure to write the multiples of 10 on the board as students say them, and continue counting by tens until at least 100.

            10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, . . .

Now, hold up one of the hundreds, the flat, square base-ten block representing one hundred units. Write the value on the board, 100. Then hold up a second of the hundreds, and write the value 200 on the board. Continue holding up additional hundreds to help students count by hundreds and visualize each multiple of one hundred using base-ten blocks. Be sure to write the multiples of 100 on the board as students say them, and continue counting by hundreds until at least 1000.

100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, . . .

Aunts, Uncles, and Many Cousins! Practice Worksheet

Distribute a copy of the Aunts, Uncles, and Many Cousins! practice worksheet to all students (M-3-6-1_Aunts, Uncles, and Many Cousins Practice Worksheet and KEY.docx).

Guide students in completing the first example. Ask, “Will someone please volunteer to read the sentence about Ryan aloud?” After a student reads the sentence, ask students to use base-ten blocks to build 32. “Please use base-ten blocks to build the number 32, the number of cousins Ryan has.”

Ask a student to show the class how s/he built 32 using base-ten blocks. Be sure to use base-ten blocks that can easily be seen by all students in the class. This can be done using large magnetic demonstration base-ten blocks and a whiteboard, virtual base-ten blocks and an interactive whiteboard, base-ten blocks and a document camera, or overhead base-ten blocks and an overhead projector. It is important for students to be able to model their thinking for their classmates.

Next, ask students to draw 32. “Draw a picture of 32 on the hundred grid.” While students are drawing 32, display 3 tens and 2 ones altogether. This will model the portion of the hundred grid that represents 32. Use this to help students verify that they correctly drew 32.

Refer to the multiples of ten written on the board at the beginning of the lesson. Ask students, “On a number line, which two multiples of ten is 32 between?” Students will likely say 30 and 40. Ask students to explain how they know this is true.

Explain to students, “The final step is to decide whether 32 is closer to 30 or 40. Please work in your groups to decide this, and then complete the rest of the practice worksheet.” Do not ask students to help you answer this question. The purpose of the Aunts, Uncles, and Many Cousins! practice worksheet is for students to work together to decide which numbers between 30 and 40 are closer to 30 and which are closer to 40. This will support students’ understanding of the rule for rounding numbers to the nearest ten.

Monitor the groups of students while they are working. If students are struggling to decide whether a number is closer to 30 or 40, help them compare the number of units that need to be removed to have only 30 and the number of units that need to be added to have 40. For example, 32 is closer to 30 because only 2 units need to be removed to have 30 but 8 units have to be added to have 40.

Listen very carefully when groups are discussing whether 35 is closer to 30 or 40. The number 35 is the same distance on the number line from both, so 35 is not closer to either 30 or 40. This is an important point; it required mathematicians to write a special rule for how to round numbers ending in 5 to the nearest ten.

After the groups of students are finished with the Aunts, Uncles, and Many Cousins! practice worksheet, draw the portion of the number line between 30 and 40 on the board.

Work through the last example on the practice worksheet as a class. Most groups will already have completed this, but this is an opportunity to discuss the reasoning students used.

As shown below, students should have drawn a circle around the numbers 31, 32, 33, and 34, indicating they are all closer to 30 than to 40. Students should have drawn a square around 36, 37, 38, 39, indicating they are closer to 40 than 30.

Ask a student or pair of students to volunteer to build the number 36 for the class. (Working in pairs, students feel less threatened when sharing their work, and students can support each other in demonstrating, recording, and explaining processes to the class.) Provide a means for students to demonstrate their use of base-ten blocks that all students can see, using demonstration options discussed earlier. Ask a different student or pair of students to use the model for 36 to explain whether 36 is closer to 30 or 40. Continue to ask for students to explain their thinking for other numbers between 30 and 40.

Be sure to discuss 35 last. Be sure all students understand that 35 is the same distance from both 30 and 40, so there is no correct way to answer the question about 35 on the practice worksheet. The number is not closer to one or the other.

Round to the Nearest Ten

Distribute a copy of the Round to the Nearest Ten practice worksheet to all students (M-3-6-1_Round to Nearest Ten Practice Worksheet and KEY.docx). Ask students to work in groups to complete the first two number line examples. These examples use the same directions as the number line example on the Aunts, Uncles, and Many Cousins! practice worksheet.

Monitor the groups while they are working. Be sure all students understand how to determine which numbers are closer to each multiple of ten. Once all groups are finished with these two examples, draw both number lines on the board. Ask a student or pair of students to put the circles and squares around the appropriate numbers for each example, as shown here.

Introduce the concept of rounding. “Ryan has 32 cousins. Although this is true, we might instead say Ryan has about or approximately 30 cousins. Often we round numbers to describe about how many instead of saying the exact number. First we will learn how to round to the nearest multiple of 10, more often referred to as rounding to the nearest ten.”

Write this example on the board.

Ryan has 32 cousins. About how many cousins does Ryan have?

Guide students through these steps for rounding to the nearest ten. Write each step on the board. Ask students to help you fill in the blanks.

Example: Round 32 to the nearest ten.

Ask, “If we count by tens, 32 is between what two multiples of ten?”

            Step 1: 32 is between 30 and 40

Ask, “Is the number 32 closer to 30 or 40?”

            Step 2: 32 is closer to 30

Ask, “Since the number 32 is closer to 30, we say 32 rounds to 30 or 32 rounds down

to 30.”

            Step 3: 32 rounds to 30

Write this example on the board.

Juanita has 36 cousins. About how many cousins does Juanita have?

Guide students through these steps for rounding to the nearest ten. Write each step on the board. Ask students to help you fill in the blanks.

Example: Round 36 to the nearest ten.

Ask, “If we count by tens, 36 is between what two multiples of ten?”

            36 is between 30 and 40

Ask, “Is the number 36 closer to 30 or 40?”

            36 is closer to 40

Ask, “Since the number 36 is closer to 40, what number does 36 round to? About how many cousins does Juanita have?”

            36 rounds to 40

Write this example on the board.

Miriam has 85 cousins. About how many cousins does Miriam have?

Guide students through these steps for rounding to the nearest ten. Write each step on the board. Ask students to help you fill in the blanks.

Example: Round 85 to the nearest ten.

Ask, “If we count by tens, 85 is between what two multiples of ten?”

            85 is between 80 and 90

Ask, “Is the number 85 closer to 80 or 90?”

            85 is closer to neither 80 or 90

Explain “Since the number 85 is the same distance from 80 and 90, mathematicians had to decide how to round 85 to the nearest ten. They decided since 85 ends in 5, they would round 85 up to 90. Miriam has about 90 cousins.”

            85 rounds to 90

Now ask, “If rounding to the nearest multiple of ten, which of the numbers between 70 and 80 would round to 70? Which would round to 80?” Help students make the connections between rounding and the relative distances from the multiples of 10. Students will likely say that numbers circled round to 70 as they are closer to 70, and numbers with a square will round to 80 as they are closer to 80.

Now ask the question, “Will 75 round to 70 or 80?” Help students understand that mathematicians agreed that 75 rounds to 80. Since 75 is not closer to 70 or 80, they made a rule to round up to 80.

Have a similar discussion about the number line from 40 to 50. Again, be sure students understand that 45 is the same distance from both 40 and 50. Yet, 45 rounds to 50 because that is a rule mathematicians decided upon.

Ask students to work in their groups to complete the remaining examples on the Round to the Nearest Ten practice worksheet. Review these examples as a class to ensure all students understand how to round to the nearest ten.

Round to the Nearest Hundred

Distribute a copy of the Round to the Nearest Hundred practice worksheet (M-3-6-1_Round to Nearest Hundred Practice Worksheet and KEY.docx) to all students. Ask students to work in groups to complete the first two number line examples. These examples use the same directions as the number line examples on the Aunts, Uncles, and Many Cousins! and Round to the Nearest Ten practice worksheets.

When most students are finished with the two number line examples, write this example on the board.

Taya has $362. About how many dollars does Taya have?

Use this example to introduce the concept of rounding to the nearest hundred. “Taya has $362. Although this is true, we might instead say Taya has about or approximately $360 or $400. Often we round numbers to describe about how many instead of saying the exact number. We will now learn how to round to the nearest multiple of 100, more often referred to as rounding to the nearest hundred.”

Each group should still have at least 10 hundreds, 10 tens, and 30 ones from the previous work on rounding to the nearest ten. Ask the groups of students to use base-ten blocks to build 362 and to draw 362 using the hundred grids. Ask them to also build and draw 347. Also, encourage them to try to complete the statements in each of these examples.

As a class, review both examples. Guide students through the steps for rounding to the nearest hundred. Write each step on the board. Ask students to help you fill in the blanks.

Example: Taya has $362. About how many dollars does Taya have? Round 362 to the nearest hundred.

Ask, “If we count by hundreds, 362 is between what two multiples of one hundred?”

            Step 1: 362 is between 300 and 400

Ask, “Is the number 362 closer to 300 or 400?”

            Step 2: 362 is closer to 400

Be sure to ask how they know 362 is closer to 400. This requires students to use the other steps provided. First, recognizing the halfway point between 300 and 400 is 350. Next, recognizing that 362 is greater than the halfway point of 350.

Explain, “Since the number 362 is closer to 400, we say 362 rounds to 400.”

            Step 3: 362 rounds to 400

Example: Jamal has $347. About how many dollars does Jamal have? Round 347 to the nearest hundred.

Ask a student to volunteer to explain each of the steps for rounding 347 to the nearest hundred. (The steps are provided here, but a student might be able to explain these without you providing them.) Peer-to-peer instruction is very valuable. It empowers students to work together and encourages students to take responsibility for their own learning.

Ask, “If we count by hundreds, 347 is between what two multiples of one hundred?”

            Step 1: 347 is between 300 and 400

Ask, “Is the number 347 closer to 300 or 400?”

            Step 2: 347 is closer to 300

Be sure to ask how they know 347 is closer to 400. First, students should understand the halfway point between 300 and 400 is 350. Next, students should recognize that 347 is less than the halfway point of 350.

Explain, “Since the number 347 is closer to 300, we say 347 rounds to 300.”

            Step 3: 347 rounds to 300

Ask students to work in their groups to complete the remaining examples on the Round to the Nearest Hundred practice worksheet. Review these examples as a class to ensure all students understand how to round to the nearest hundred.

Be sure to have students ask questions about anything they don’t yet understand. It is important that all questions are answered before students begin the practice activity.

The Round and Round and Round practice worksheet (M-3-6-1_Round and Round Practice Worksheet and KEY.docx) can now be completed by students either in class or assigned as homework. This practice worksheet can be used to assess students’ understanding of rounding to the nearest ten and the nearest hundred.

Extension:

• Return to the use of base-ten blocks to support students who have not yet mastered the concept of rounding. Have students determine how many units would be added to make the next multiple and subtracted to make the previous multiple. For example, if rounding 36 to the nearest 10, four units must be added to get 40 and six units must be taken away to get 30. This should help them decide which multiple the value is closer to. Additional resources are provided in the Small Group section for students who might benefit from further instruction or practice.

Students who are ready for an additional challenge should be introduced to rounding four digit numbers to both the nearest ten and the nearest hundred. These students can also be introduced to rounding to the nearest thousand. Specific resources for students who are ready to go beyond the requirements of the standard are provided in the Expansion section.

• Routine: As real-life situations arise during the school year, have students practice rounding numbers to the nearest ten or nearest hundred. For example, the daily temperature or the cost of technology items can often be rounded to the nearest ten and nearest hundred, respectively. Students can also use rounding to estimate solutions to many problems throughout the mathematics curriculum.
• Small Group: Students who need additional practice can be pulled into small groups to work on the following activity.

One student in the group should roll two 10-sided number cubes. The first number rolled is in the tens place and the second number is in the ones place. All students should write down the number rolled. Students should then be encouraged to round the number to the nearest ten. It will be very important to listen carefully to identify and correct errors in their thinking. This process should then be repeated using three 10-sided number cubes and rounding to the nearest hundred.

If students struggle with rounding, they should be encouraged to use base-ten blocks to investigate the concept of rounding. For example, if rounding 36 to the nearest 10, four units must be added to get 40 and six units must be taken away to get 30. This should help students decide which multiple the value is closer to, so as to determine how the number should be rounded. Do not focus on a specific rule for rounding. Focusing instead on the relative distance of the number from multiples of 10 or 100 will develop greater conceptual understanding of rounding.

These two Web sites can be used for additional practice. The first is an interactive game that focuses on rounding to the nearest ten and the second is similar but focuses on rounding to the nearest hundred.

• http://www.mathnook.com/whichonerounds.html
• http://www.mathnook.com/whichonerounds100.html
• Expansion: The following Web sites are recommended for students who are prepared for a greater challenge. The first two sites focus on rounding four-digit numbers to the nearest ten and the nearest hundred. This challenges students to go beyond working with strictly two- and three-digit numbers. The third site focuses on rounding four-digit numbers to the nearest thousand. This challenges students to go beyond rounding to the nearest ten and hundred.
  • http://www.free-training-tutorial.com/rounding/rounding-spaceships.html
  • http://www.free-training-tutorial.com/rounding/sharks.html
  • http://www.mathnook.com/whichonerounds1000.html