The purpose of this activity is for students to learn that when comparing three-digit numbers, it is helpful to start by comparing the value of the hundreds. In this activity, the base-ten diagrams are not organized by place and do not mirror the structure of a three-digit number. Students learn that to compare numbers in which one number has more hundreds than the other, it is not necessary to consider the tens and ones. We know there cannot be more than 9 tens and 9 ones which means those digits will always have a value less than 1 hundred.

• “How did you decide how to write each value as a three-digit number? How did you compare the numbers?”
• “Are there any units that have 10 or more? How did composing a unit change your answer?”

• Share responses for the first two comparisons.
• Consider asking:
  • “How did you know your statement is true?”
  • “What unit was most important in deciding which quantity was greater?”

  • “Why don’t you have to compare the other units?”

• Display the images for .
• “Which value is greater? How do you know?” (The two quantities are equal. Both diagrams represent 224. One has 2 hundreds, but the other has 1 hundred and 12 tens.)
• Record .
• “When comparing numbers based on base-ten diagrams, what do you think about to help you decide which quantity is greater? Explain.” (First, we need to find out how many hundreds each number has, but sometimes that means we have to count the tens to see if there are enough to make another hundred. If a number has more hundreds, we know that number is greater.)

The purpose of this activity is for students to extend their understanding of comparing three-digit numbers to include amounts in which the values in the hundreds place and tens place are the same in both numbers. In the last activity, students learned that by comparing the hundreds you can determine the greater value without considering the tens and ones. In this activity, students recognize the need to compare hundreds to hundreds, tens to tens, and ones to ones when the digits are the same in the numbers being compared.

• Invite previously selected students to share how they compared 338 and 336.
• Display 445 _____ 447.
• “Based on what you learned, how can you tell which number is larger without using the blocks?” (I can look at a number and see how many hundreds, tens, and ones there are without the diagrams.)