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.

• “How did you figure out that Kiran has more than Elena?”
• “How can you use connecting cubes to show both collections?”

• 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.)

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).

• 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.)