# Lesson 21

Compare Two-Digit Numbers Shown in Different Ways

## Warm-up: 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

• 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

For access, consult one of our IM Certified Partners.

### 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.

MLR7 Compare and Connect. Synthesis: After all representations have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “How are the representations the same? How are they different? How do the different representations show tens and ones?”

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

### Activity

• 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.

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: Base-Ten Representation Compare (20 minutes)

### Narrative

The purpose of this activity is for students to compare two-digit numbers represented with different amounts of tens and ones, and shown with base-ten 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).

Engagement: Provide Access by Recruiting Interest. Leverage choice around perceived challenge. Invite students to select at least 4 of the 6 problems to complete.
Supports accessibility for: Organization, Attention, Social-Emotional Functioning

### Launch

• Groups of 2
• Display the base-ten 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 two-digit numbers and circle the representation that is greater. Then you write them as two-digit 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

1. What do you notice?

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

2. Circle the representation that shows the greater number.
Write a number to match each representation.
Then write a comparison statement using <, >, or =.

1.

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

2.

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

3. 5 tens 2 ones

12 ones 3 tens

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

4. 1 ten 25 ones

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

5. 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 two-digit numbers in this unit. What have you learned about two-digit numbers?” (They have tens and ones. You can make a number with different amounts of tens and ones. When you write a two-digit number the first digit tells how many tens and the second digit tells how many ones. You can compare two-digit 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 two-digit number, the tens digit changes and the ones digits stays the same.)

## Cool-down: Compare 2 Collections (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

We made two-digit numbers with different amounts of tens and ones.

Each of these representations shows 37.

$$52 > 42$$