The purpose of this activity is for students to make sense of different approaches they can use to compare three-digit numbers. They analyze the thinking of others and make connections across representations (MP2, MP3).

Monitor for and select students with the following approaches to share in the Synthesis:

• Students reason that both numbers have the same number of hundreds, but 371 has more tens. They show their thinking with a base-ten diagram.
• Students reason that both numbers have the same number of hundreds, but 371 has more tens. They show their thinking with words, numbers, or symbols.
• Students reason that 371 is further from 0 on the number line.

The approaches will later be displayed side by side to help students make sense of the different methods they can use to compare three-digit numbers. It is also an opportunity for students to consider ways they can use the number line to compare three-digit numbers. If no student uses the number line, draw or display a number line with 317 and 371 labeled (see Required Preparation for an example). Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

• Invite previously selected students to display their work side by side without sharing their thinking.
• As needed, draw or display a number line with 317 and 371 labeled.
• “Take a minute to look at each of these ways of thinking about 371 and 317.”
• Connect students’ approaches by asking:
  • “What is the same about the different ways of thinking about 371 and 317? What is different?” (They all show that 371 is greater. Some ways show thinking about hundreds and tens. One way shows thinking about which number is further from 0.)
• Display and or highlight these statements in the displayed student work.
• Connect students' approaches to the learning goal by asking:
  • "How does the number line show that 371 is greater than 317?" (You can see that 371 is further to the right. It's a longer distance from 0 than 317.)
  • "How does the number line show that 317 is less than 371?" (You can see that 317 is further to the left. It's closer to 0 than 371.)

The purpose of this activity is for students to compare three-digit numbers based on different representations. Students continue to make connections and deepen their understanding of place value as they compare numbers using base-ten diagrams and number lines. They have the opportunity to reflect and share about the representation that makes the most sense to them and how they can use it to justify their thinking (MP3). This understanding will be helpful in upcoming lessons when students choose their own ways to compare three-digit numbers.

• Display the images for 432 and 423.

• “What is the same about seeing these numbers on the number line compared to looking at a base-ten diagram? What is different?” (The one farthest to the right is greater. With the diagram you have to count to see which one has more. The number with more hundreds or tens is farther to the right on the number line.)