The purpose of this activity is for students to use their understanding of place value and the relative position of numbers within 1,000,000 to partition and place numbers on a number line. Students place four related numbers on a number line and consider relationships between digits to determine how to partition a number line.

The numbers have the same non-zero digits but with different place values, allowing students to observe the closely related values of the tick marks (MP7) and the identical location on the different number lines of the numbers they plot (MP8).

• “How did you decide where to place ____ on the number line?”
• “How can splitting the number line into equal parts help you to locate and label numbers on the number line?”  

• Ask 2–3 students to share their responses and their reasoning for each problem.
• “How did you partition the number line in the first problem?” (I know that 350 is halfway between 300 and 400, so I marked the halfway point, and then estimated where 3 down from that would be.)
• “How do the number lines help you to see the relationship between the numbers?” (The number lines have endpoints that are ten times as much as the number line before. Also, each number is ten times as much as the number before. The place values changed, but the numbers are located in the same relative position.)

In this activity, students place a set of numbers that are each ten times as much as the one before it on the same number line. In doing so, they notice the impact of multiplying a number by ten on its magnitude. Unlike before, the number lines have no or fewer intermediate tick marks, prompting students to think about how to partition the lines in order to plot their assigned number.

• Ask 2–3 small groups to share their number line.
• Ask questions about structure:
  • “How did you decide to partition the number line?” (I partitioned the number line by tens, hundreds, thousands, ten-thousands, hundred-thousands—not by ones.)
• Ask questions about precision:
  • “Which numbers were easier to locate? Why?” (34,700 and 347,000, were easier to locate because they were further away from zero.)
  • “What would have made it easier to locate the other numbers?” (A longer number line would have made it easier to include more partitions)
• Ask questions about magnitude:
  • “Make some observations about where the numbers are positioned on the number line.” (Most of the numbers are much closer to zero than to 400,000)
  • “You located the same four numbers here as you did in the first activity. How are the locations of the points different from those in the first activity?” (Ten times as much looks different when they are all on the same number line.)