# Lesson 15

Round to the Nearest Ten and Hundred

## Warm-up: Choral Count: Tens and Hundreds (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 10 and 100 and notice patterns in the count. These understandings help students develop fluency and will help students see that multiples of 100 are also multiples of 10, and prepare them to round large numbers to the nearest ten and hundred.

### Launch

• “Count by 10, starting at 0.”
• Record as students count.
• Stop counting and recording at 200.
• “Count by 100, starting at 0.”
• Record as students count.
• Stop counting and recording at 900.

### Activity

• “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “Why do 100 and 200 show up in both of these counts?” (You say 100 and 200 when you are counting by tens or hundreds. You can think of 100 as 10 tens or 200 as 20 tens. 100 and 200 are multiples of 10 and multiples of 100.)

## Activity 1: Can the Nearest Ten and Hundred be the Same? (20 minutes)

### Narrative

The purpose of this activity is for students to round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. Students think about what it means to round a number that is exactly halfway between two tens or two hundreds and are introduced in the synthesis to the convention that these numbers are rounded up (MP3).

MLR1 Stronger and Clearer Each Time: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to “What does 97 round to when we are rounding to the nearest 10? To the nearest hundred? Why does that happen?” Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most useful to solve the problems. Display the sentence frame, “The next time I round numbers to the nearest ten and nearest hundred, I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• “Let’s round some numbers to the nearest ten and the nearest hundred. Remember ‘round to the nearest ten (or hundred)’ is another way of saying find the nearest multiple of 10 (or 100).”

### Activity

• “Work with your partner to complete the table.”
• 3–5 minutes: partner work time
• Monitor for students who notice 97 and 601 round to the same number whether rounding to the nearest ten or the nearest hundred.
• Select previously identified students to share their responses.
• “Why did 97 and 601 round to the same number when we rounded to the nearest ten and the nearest hundred?” (The closest multiple of 10 was also a multiple of 100. 100 and 600 are multiples of 100, but they are also multiples of 10.)
• 3–5 minutes: partner work time
• Monitor for the following in student explanations to share in the synthesis:
• 415 is halfway between 410 and 420.
• 415 is the same distance from 410 and 420.
• 415 has two closest multiples of 10: 410 and 420.
• 750 is halfway between 700 and 800.
• 750 is the same distance from 700 and 800.
• 750 has two closest multiples of 100: 700 and 800.

### Student Facing

1. Round each number to the nearest ten and the nearest hundred. Use number lines if you find them helpful.

number nearest ten nearest hundred
18
97
312
439
601
2. Kiran and Priya are rounding some numbers and are stuck when trying to round 415 and 750.

• Kiran said, “415 doesn’t have a nearest multiple of 10, so it can’t be rounded to the nearest ten.”
• Priya said, “750 doesn’t have a nearest multiple of 100, so it can’t be rounded to the nearest hundred.”

Do you agree with Kiran and Priya? Explain your reasoning.

### Activity Synthesis

• Select previously identified students to share their responses.
• “Kiran and Priya are correct. There isn’t one closest multiple of 10 to 415 because it’s right in the middle of two multiples of 10. There isn’t a closest multiple of 100 to 750 because it’s right in the middle of two multiples of 100.”
• “In cases like this, we round up. For example, since 415 is halfway between 410 and 420, we would round up to 420 to round 415 to the nearest ten.”
• “Since 750 is halfway between 700 and 800, we would round up to 800.”
• ”In both of these situations we could go the other way, but it is helpful if we all do the same thing in these situations.”

## Activity 2: Round to Estimate (15 minutes)

### Narrative

The purpose of this activity is for students to practice rounding to the nearest ten and hundred in context. Students work with numbers from a previous lesson to estimate the total number of students in a school. They learn that how you round (to the nearest ten or hundred) can give different estimates for the same situation.

### Launch

• Groups of 2
• “Let’s revisit the number of students in different areas in a school. We’re going to use rounding to help Andre and Lin make an estimate of the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten.”
• “Make a prediction: Whose estimate is going to be greater? Be prepared to explain your reasoning.”
• 30 seconds: quiet think time
• Share responses.

### Activity

• “Work with your partner to complete the table and the last problem.”
• 7–10 minutes: partner work time

### Student Facing

The table shows the numbers of people in different parts of a school at noon during a school day.

Andre and Lin are trying to estimate the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten.

1. Make a prediction: Whose estimate is going to be greater? Explain your reasoning.
2. Work with a partner to find Andre and Lin’s estimates. Record them in the table. Then find the totals.
location number Andre's estimate
(nearest hundred)
Lin's estimate
(nearest ten)
playground 94
cafeteria 163
art room 36
library 13
classrooms 216
gymnasium 109
music room 52
total
3. Make two observations about the completed table. Was your prediction correct?

### Activity Synthesis

• Invite students to share their observations about the completed table, including whether it matched their predictions.
• “When we are estimating a total, rounding to the nearest ten or the nearest hundred can give us different results. If you were rounding to estimate a total, would you round to the nearest ten or nearest hundred?” (The nearest ten because you get an estimate that’s closer to the total. The nearest hundred because multiples of 100 are easier to work with.)
• “Keep these ideas in mind as you use rounding to estimate in future lessons.”

## Lesson Synthesis

### Lesson Synthesis

“Today we rounded numbers to the nearest ten and the nearest hundred.”

“What important ideas about rounding did we learn today?” (Rounding to the nearest ten and the nearest hundred sometimes gives the same number. When a number is right in between two multiples of 10 or 100, we round up. We can round to estimate. How we round can change our estimate.)