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).

• Ask previously selected students to share.
• Display the 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 means the numbers 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.)

The purpose of this activity is for students to round a decimal number to the nearest whole number, tenth, and hundredth. Number lines are provided for the first set of problems but not for the second set. Monitor for students who:

• Use the given number lines or draw number lines for the second set of problems.
• Use place value reasoning.

• 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?”

The purpose of this activity is for students to practice rounding numbers to the nearest whole, tenth, or hundredth. Students may choose to use a number line or any other strategy that makes sense to them.

• Ask previously selected students to share.