Lesson 21
Compare TwoDigit Numbers Shown in Different Ways
Warmup: Number Talk: Addition Within 20 (10 minutes)
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 20, in which one of the addends is close to 10. These understandings help students develop fluency with addition within 20.
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(10 + 6\)
 \(9 + 6\)
 \(10 + 7\)
 \(8 + 7\)
Student Response
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Activity Synthesis
 “Did anyone approach the problem in a different way?”
 “How did you use \(10 + 6\) to help you solve \(9 + 6\)?“ (I know that \(10 + 6\) is 16. Since 9 is one less than 10, and the six stays the same, the sum is one less.)
 "How did you use \(10 + 7\) to help you solve \(8 + 7\)?” (I know that \(10 + 7 = 17\), so I subtracted 2 from 17 because 8 is 2 less than 10.)
Activity 1: Elena and Kiran Compare Collections (15 minutes)
Narrative
The purpose of this activity is for students to compare two collections represented with tens and ones in different ways. Students are given access to connecting cubes in towers of 10 and singles to make sense of the problem and compare the quantities. In the activity synthesis, students discuss methods for comparing the collections.
Advances: Representing, Conversing
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to connecting cubes in towers of 10 and singles.
Activity
 Read the task statement.
 7 minutes: partner work time
 Monitor for a student who:
 uses towers of 10 and singles, puts the singles together to make new tens
 writes addition equations such as \(50 + 32 = 82\) and \(70 + 2 = 72\)
Student Facing
Elena and Kiran are comparing their collections.
Elena says, “I have 5 tens 32 ones.”
Kiran says, “I have 7 tens 2 ones.”
Who has more in their collection?
Show your thinking using drawings, numbers, words, or expressions.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students compare the tens and determine that Kiran has more than Elena, consider asking:
 “How did you figure out that Kiran has more than Elena?”
 “Could you use connecting cubes to show both collections?”
Activity Synthesis
 Invite previously identified students to share.
 “How do these representations help us compare the collections?” (Making as many tens as possible helps because then we can compare the tens to see who has more. Writing an equation helps because then we can just compare the totals.)
 “Why might Kiran think he has more?” (He has 7 tens. He didn’t think about Elena’s ones and how many tens those could make.)
Activity 2: BaseTen Representation Compare (20 minutes)
Narrative
The purpose of this activity is for students to compare twodigit numbers represented with different amounts of tens and ones, and shown with baseten diagrams, ___ tens _____ ones, and addition expressions. Students apply what they have learned about representing numbers with tens and ones to compare each representation. Some students may find the total number of each representation and compare using the numbers. Other students may consider the number of tens in each representation to compare. Students record each comparison using the symbols <, >, or =. Students reason abstractly and quantitatively when they move fluently between different representations in order to make comparisons (MP2).
Supports accessibility for: Organization, Attention, SocialEmotional Functioning
Required Materials
Materials to Gather
Launch
 Groups of 2
 Display the baseten diagrams to compare 3 tens 8 ones to 2 tens 8 ones.
 “What do you notice?” (One has 3 tens and the other has 2 tens. They both have 8 ones. One is 38 and the other is 28.)
 Share responses.
 “You are going to look at different representations of twodigit numbers and circle the representation that is greater. Then you write them as twodigit numbers and write a comparison. Let's do this one together.”
 “Which is greater? How do you know?” (The first one is greater because there are more tens and they have the same number of ones. 38 is greater than 28.)
 30 seconds: quiet think time
 Share responses.
 “Since the first representation is greater, we circle that representation. Then we write the comparison below.”
 Demonstrate circling the representation of 38 and writing \(38 > 28\).
Activity
 “First you will compare on your own. Then you will work with a partner.”
 6 minutes: independent work time
 6 minutes: partner discussion
Student Facing
 What do you notice?
\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

Circle the representation that shows the greater number.
Write a number to match each representation.
Then write a comparison statement using <, >, or =.
\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

5 tens 2 ones
12 ones 3 tens
\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

1 ten 25 ones
\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

7 tens 29 ones
\(50 + 39\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} \,\, \underline{\phantom{\frac{aaai}{aaa_{p_{p_a}}}}} \,\, \boxed{\phantom{\frac{aaai}{aaai}}}\)

Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Display 3 towers of ten and 2 ones, and 2 towers of ten and 12 ones.
 “How can we compare without finding the value of each representation?” (I can see that I can make one more 10 with 10 ones in the second representation. That tells me they are equal because they both have 3 tens and 2 ones.)
 Display 2 towers of ten and 15 ones, and 4 tens.
 “How can we compare without finding the value of each representation?” (I see that they both have 2 tens. Then one only has ones left and I can tell there are not 20 ones so that representation is less than the other. I imagine circling two columns of ones and that makes another 10. So that representation has 3 tens and the other has 4 so I know the other is greater.)
Lesson Synthesis
Lesson Synthesis
“We have done a lot of work with twodigit numbers in this unit. What have you learned about twodigit numbers?” (They have tens and ones. You can make a number with different amounts of tens and ones. When you write a twodigit number the first digit tells how many tens and the second digit tells how many ones. You can compare twodigit numbers by comparing the tens, but if they have the same number of tens then you need to look at the ones. When you add 10 to a twodigit number, the tens digit changes and the ones digits stays the same.)
Cooldown: Compare 2 Collections (5 minutes)
CoolDown
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Student Section Summary
Student Facing
We made twodigit numbers with different amounts of tens and ones.
Each of these representations shows 37.
We compared twodigit numbers that were made with tens and ones in different ways.
5 tens 2 ones and 12 ones 3 tens
\(52 > 42\)