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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

To Gather

Connecting cubes in towers of 10 and singles

Activity 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 alike? How are they different? How do the different representations show tens and ones?”
Advances: Representing, Conversing

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 and .

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

to access Student Response.

Advancing Student Thinking

If students determine that Kiran has more than Elena, consider asking:

“How did you figure out that Kiran has more than Elena?”
“How can 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

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

To Gather

Connecting cubes in towers of 10 and singles

Activity 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. Students may find the total number of each representation and compare using the numbers. 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 2-digit numbers and circle the representation that is greater. Then you write them as 2-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 .

Activity

“First you will compare on your own. Then you will work with a partner.”
6 minutes: independent work time
6 minutes: partner discussion

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. That representation has 3 tens and the other has 4 so I know the other is greater.)