Previously, students identified two multiples of 100 that border a given number, reasoned about their relative distances from the number, and then named the nearest multiple of 100. The purpose of this activity is for students to practice naming the nearest multiple of 100 and apply the same reasoning to identify the nearest multiple of 10. They determine the two multiples of 10 that are closest to a given number (two intermediate tick marks on the number line) and then identify which multiple of 10 is closer.

• “For each number, how do you know which multiple of 10 is nearest?” (If we label and locate the number on the number line, we can see to which tick mark the point is closer. We can see how many numbers to count up or back to get to a multiple of 10. For example, we only count up once to get from 89 to 90, but we count back 9 times to get down to 80.)

In this activity, students identify the nearest multiples of 10 and the nearest multiples of 100 for given three-digit numbers. They may do so by using the number lines from earlier, but they also may start to notice a pattern in the relationship between the numbers and the nearest multiples and decide not to use number lines. The work here prepares students to reason numerically in the next lesson.

When students notice and describe patterns in the relationship between the numbers and the nearest multiples of 10, or the nearest multiple of 100, they look for and express regularity in repeated reasoning (MP8).

• “How have you tried to find the closest multiple of 10 (or multiple of 100)?”
• “How could you use a number line to find the closest multiple of 10 (or multiple of 100)?”

• Invite students to share their responses and reasoning for the last problem.