The purpose of this activity is for students to find the sum of 2 two-digit numbers in a way that makes sense to them.

Monitor for and select students with the following approaches to share in the Activity Synthesis:

• Break both addends into tens and ones, add tens and tens, and then add ones and ones.
• Start with one of the addends, add the tens from the second addend, and then add the ones from the second addend.
• Decompose the ones from 36 into 3 and 3, make a new ten with 17 and 3, and then add the remaining 3 ones and 3 tens.

When sequencing student approaches, consider inviting students to share from the most common approach to the least common approach used during the activity. This will help students make sense of different approaches to find the sum of 2 two-digit numbers when it is possible to compose a new ten. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

In the Activity Synthesis, student approaches are represented with drawings and numbers so the new ten is visible to all students.

• Invite previously selected students to share in order from the most common approach to the least common approach. Record or display their work for all to see.
• If students have not done so, record student thinking with drawings and numbers as they explain their approach.
• Connect students’ approaches by asking:
  • “How are they alike? How are they different?” (They all got 53. They all used tens and ones. The first person broke both numbers apart into tens and ones, and the other two only broke apart one number. The last way is the only one that makes a new ten.)
• If no students mentions making a ten, display the last approach and connect it to the learning goal by asking:
  • “How does the drawing of the last way show making a ten?” (They made a new ten when they combined the 3 ones from 36 to the 7 ones from 17. In the drawing, the 7 ones from 17 and 3 of the ones from 36 are circled to show the ones used to make a new ten.)

The purpose of this activity is for students to add 2 two-digit numbers represented as towers of 10 and single connecting cubes. In this activity, each student grabs a handful of towers of 10 and a handful of single cubes. They add their handfuls to a partner's handfuls. When using connecting cubes in this way, students may recall activities from prior lessons where they counted collections, and organize their addends into like units (tens and ones), make new tens, and count the result. Students may also add on ones to make a new ten so that one student has only tens and the other has some tens and ones to add on. Other students may represent their thinking with equations to show making a ten or adding tens and tens and ones and ones.

During the Activity Synthesis, students discuss adding onto a two-digit number to compose a ten and adding tens and tens and ones and ones. The teacher records students' thinking using base-ten drawings and equations and encourages students to explain how each representation shows the method used to determine the sum. For example, when finding the sum of 45 and 37, if the students add tens and tens and ones and ones by counting all the ones without making a new tower of 10, the teacher represents their thinking as:

Students should have opportunities to connect and compare this method and representation with those that do show physically making a new ten with connecting cubes or drawing to group 10 ones to make a unit of ten. Students will interpret base-ten drawings in the next lesson.

• Invite previously identified students to share.
• Record student thinking as base-ten drawings and equations.
• “How does this drawing show how they found the sum?” (The picture shows the tens with the tens and the ones with the ones to find the total.)