Lesson 10

The purpose of this Number Talk is to elicit strategies and understandings students have for mentally adding a multiple of 10 to a number. Building on their understanding of place value, students add tens to tens. When students notice that only the digit in the tens place is changing and make connections between the tens in each expression, they look for and make use of structure and express regularity in repeated reasoning (MP7, MP8). These understandings help students develop fluency and will be helpful in later lessons when students will add using strategies based on place value.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How could the first expression help you find the value of the second one?” (46 is 10 more than 36, and 30 is 10 less than 40, so the answer is the same. They have the same number of tens.)

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 when comparing numbers in which one number has more hundreds than the other, it is not necessary to consider the tens and ones.

• Groups of 2
• Display the image.
• “Who has more? How do you know?” (Tyler has 2 hundreds, but Mai only has 1. He has more.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Today you will compare quantities represented by base-ten diagrams.”
• “Compare the diagrams. Write the value of each quantity as a three-digit number and use the greater than, less than, or equal to symbols to compare the numbers.”
• 8 minutes: independent work time
• “Compare with a partner.”
• 2 minutes: partner discussion

• “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 new 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?”
• Display the images for \(224 = 224\).
• “Which value is greater? How do you know?” (The two quantities are equal. Both diagrams represent 224. One had 2 hundreds, but the other had 1 hundred and 12 tens.)
• Record \(224 = 224\).
• “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, they 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.

• Groups of 2

• “In the last activity we saw that if one number has more hundreds than another number it has the greater value.”
• “You will compare more quantities represented by base-ten diagrams.”
• “Compare the diagrams. Write the value of each quantity as a three-digit number and use the greater than, less than, or equal to symbols to compare the numbers.”
• “Work with your partner to compare numbers and discuss your thinking for each problem.”
• 15 minutes: partner work time
• Monitor for students who use precise language to explain how they knew that \(338 > 336\) based on comparing the value of each digit.

• 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.)