The purpose of this activity is for students to think about what it means for numbers to be close to multiples of 100. There is no definition given about what “close to” means during the activity, so students may interpret the term in different ways.

• “How did you decide whether a number is close to 0, 100, or 200?” (I thought about whether it was almost that number, like 94 is almost 100. I decided between the choices that were there—like for 163, it was closer to 200 than to 0 or 100.)
• “How did you decide if a number doesn’t belong to any of these groups?” (If a number seemed far away from all the choices, then I set it aside. Like 52 wasn’t close to 0 or 100 because it’s almost right in the middle.)
• “What if the table showed ‘closer to 0,’ ‘closer to 100,’ and ‘closer to 200?’ Would it change where each number goes? Would you be able to place all the numbers in the table?” (Yes, because I would just be choosing the number that’s closer than the other numbers, not saying it’s really close to the number.)

The purpose of this activity is for students to locate two- and three-digit numbers on a series of number lines. The endpoints of each number line are multiples of 100, and the space between them is partitioned into ten equal intervals. As they locate the numbers, students recognize each tick mark as a multiple of 10. Later in the activity, students use a number line to name the closest multiple of 100 to a given number. When students choose the correct number line and accurately place each number on the number line, they attend to precision and show an understanding of place value (MP6, MP7).

• “Tell me how you decided to place 216 on that number line.”
• “Can you show me where 216 would be on that number line?”

• “How can you tell which multiple of 100 is closer to a number?” (The endpoints of the number lines are multiples of 100. From the number line, we can tell whether a point is closer to one end or the other. We can tell if a point is in the lower half or the upper half of the number line. We can count the tick marks to each multiple of 100 to decide which is closer.)

• As needed, “Was 0 the nearest multiple of 100 for any of the numbers? How do you know?” (Yes. From the number line, we could see that some numbers, like 11, were closer to 0 than to 100. So, we said 0 was the nearest multiple of 100.)