The purpose of this activity is for students to plot the same number on different number lines and recognize that the location of the number on the number line can only be accurately determined when it lies on a tick mark. As they work on locating the number, students reinforce their understanding of place value as the tick marks on the number lines are tenths, hundredths, and thousandths (MP7). Students may struggle to locate 0.001 on the first two number lines. The important take-away is that when a decimal does not lie on a tick mark, estimation is needed to locate the number and it can be difficult or impossible to locate it precisely (MP6).

• Ask previously identified students to share.
• “How did you decide what to label the tick marks on the first number line?” (There are ten tick marks and there are ten tenths in one whole so I counted by tenths.)
• “Where is ten tenths on the first number line?” (The number 1 is ten tenths.)
• “How did you decide what to label the tick marks on the second and third number lines?” (There are 10 hundredths in 1 tenth. There are ten thousandths in 1 hundredth.)
• “How was locating 0.001 different for each of the number lines?” (It was so close to 0 on the first number line that I could not plot it. I could estimate its location on the second number line and then it was the first tick mark on the last number line.)

• Ask previously identified students to share their solutions and reasoning.
• “Which number line would you choose to compare 0.534 and 0.537?” (I liked the middle one because those numbers were labeled tick marks and I could see which one was further to the right.)
• “Which number is greater, 0.534 or 0.537? Why?” (0.537 because it is further to the right on the number line.)
• Display inequality:
• “We can also say that 0.534 is less than 0.537 with symbols.”

• “How do number lines help compare decimals?” (We can put the decimals exactly on tick marks and then see which number is farther to the right.)