# Lesson 8

Round Decimals

## Warm-up: Estimation Exploration: Number Line (10 minutes)

### Narrative

The purpose of this Estimation Exploration is for students to use their experience with the number line, decimals, and fractions to estimate the value of a number located on the number line. Students may answer with a fraction but are likely to write a decimal since they have been working with decimals for the last several lessons. In the synthesis, students reflect on how having tick marks for each tenth would help improve their estimate.

### Launch

- Groups of 2
- Display the image.
- “What is an estimate that’s too high?” “Too low?” “About right?”
- 1 minute: quiet think time

### Activity

- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.

### Student Facing

What number might be represented on the number line?

Record an estimate that is:

too low | about right | too high |
---|---|---|

\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |

### Student Response

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### Activity Synthesis

- “Would having tick marks for each tenth on the number line help improve your estimate? Why or why not?” (Yes, because I could see if it is one of the tenths and if not, where it is relative to those numbers.)

## Activity 1: Name that Number (15 minutes)

### Narrative

The purpose of this activity is for students to use place value understanding to accurately label number lines and then estimate the value of a labeled point. When they label the tick marks students will use their knowledge that a tenth is a tenth of one and a hundredth is a tenth of a tenth. When they estimate the value of the labeled point, students will also use their understanding that there are ten thousandths in each hundredth. This gives students an opportunity to make sense of each quantity and place it accurately on the number line (MP2).

The activity begins with a group discussion about how Jada labeled a number on the number line. This prepares students for the work of the activity by:

- highlighting how a decimal with a digit in the thousandths place is located between two decimals to the hundredths on the number line
- highlighting that the digits in a number of thousandths give information about which hundredths the decimal is between

As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

*MLR8 Discussion Supports.*Display sentence frames to support small-group discussion: “I noticed _____ so I . . . .”, and “I agree/disagree because . . . .”

*Advances: Conversing, Representing*

### Launch

- Groups of 2
- Display the first image from workbook.
- “Jada locates 15.53 on the number line. Do you think Jada accurately located the number? Explain your reasoning.” (She placed 15.53 between 15.5 and 15.6 which is correct. She placed 15.53 closer to 15.6 than to 15.5 and this is not correct.)
- 1 minute: independent think time
- 1 minute: partner discussion time
- Make sure students identify that 15.53 should be closer to 15.5 than to 15.6.

### Activity

- 5 minutes: independent work time
- 2 minutes: partner discussion
- Monitor for students who:
- accurately label the tick marks using their understanding of place value and the values of the end tick marks
- use their understanding of place value to estimate each number

### Student Facing

Jada locates 15.53 on the number line. Do you think Jada accurately located the number?

A number is located between two tick marks on each number line. Label those tick marks and then estimate the number.

### Student Response

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### Activity Synthesis

- Ask previously selected students to share.
- Display first image.
- “How did you know how to label the tick marks?” (Since the ends of the number line are whole numbers, the tick marks are tenths. It’s the second and third tick marks so that meant they are 3.2 and 3.3.)
- “How did you estimate the value of the number?” (It is halfway between 3.2 and 3.3 so that’s 3.25.)
- Display the last number line.
- “How did you estimate this number?” (The tick marks are 1.71 and 1.72 and it is really close to 1.72. So I put 1.719 which is just 1 thousandth from 1.72.)

## Activity 2: Which Number is Closest? (15 minutes)

### Narrative

- use the given number lines or draw number lines for the second set of problems
- use place value reasoning

*Action and Expression: Internalize Executive Functions.*Invite students to verbalize their strategy for determining proximity before they begin. Students can speak quietly to themselves, or share with a partner.

*Supports accessibility for: Organization, Conceptual Processing, Language*

### Launch

- Groups of 2

### Activity

- 5 minutes: independent work
- 2 minutes: partner discussion
- Monitor for who students:
- who are using the number lines to determine proximity
- who are using the digits in the number (place value reasoning)

### Student Facing

- Round 6.273 to the nearest whole number, tenth, and hundredth. Use the number lines if they are helpful. Explain or show your reasoning.
- Round 4.158 to the nearest whole number, tenth, and hundredth.

### Student Response

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### Activity Synthesis

- Ask previously selected students to share. Have the student who used the number line share first.
- “How did the number line help you round numbers?”
- “How did thinking about the place and value of the digit help you round numbers?”

## Activity 3: Round the Numbers [OPTIONAL] (15 minutes)

### Narrative

### Launch

- Groups of 2

### Activity

- 5 minutes: independent work
- 2 minutes: partner discussion
- Monitor for students who:
- use a number line to round
- reason using the digits and place value to round

### Student Facing

nearest whole number | nearest tenth | nearest hundredth | |
---|---|---|---|

34.482 | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | ||

99.909 | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | ||

5.555 | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | ||

19.509 | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |

### Student Response

### Activity Synthesis

- Ask previously selected to students to share.

## Lesson Synthesis

### Lesson Synthesis

“Today we rounded decimals to the nearest whole, tenth, and hundredth.”

Display:

“Tyler said that 0.345 rounds to 0.3. Jada said 0.345 rounds to 0.35.”

“Who do you agree with? Why?” (If we’re rounding to the tenths place then I agree with Tyler. If we’re rounding to the hundredths place, I agree with Jada.)

“Write three other numbers that round to 0.3 to the nearest tenth and three other numbers that round to 0.35 to the nearest hundredth.” (0.342, 0.32, 0.299 round to 0.3, and 0.351, 0.349, 0.352 round to 0.35.)

## Cool-down: Round to the Nearest Tenth and Thousandth (5 minutes)

### Cool-Down

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