The purpose of this activity is for students to find the sum of a two-digit and a three-digit number when both a ten and a hundred are composed when adding by place. They find the value of each sum in a string of expressions, in which the first addend remains the same but the second addend changes. These variations result in composing a ten, composing a hundred, and composing both a ten and a hundred.

Although the number choices encourage students to consider adding by place, they may use any method that makes sense to them when finding the value of each sum. Students share their thinking with a partner and explain why their method works (MP3). The Lesson Synthesis focuses on students sharing and making sense of strategies based on place value and using place-value language to describe what they noticed about the sums and composing greater units (MP7).

This activity uses MLR8 Discussion Supports. Advances: conversing

• Invite previously identified students to share their work for .
• “How did _____ find the sum?”
• “What was the same and what was different about what you did to find the value of each sum?” (We had to make a ten and a hundred to find the last sum. To find the first two sums, we just had to make a ten or a hundred.)

The purpose of this activity is for students to make sense of different representations of adding a three-digit number and a two-digit number. First, students analyze base-ten diagrams and corresponding equations that represent the sum that requires composing a ten and a hundred when adding by place. They make connections between the methods and discuss how they are the same and how they are different. In the Activity Synthesis, students compare and connect their own methods for adding within 1,000, using their understanding of place value.

If students create diagrams or other representations to show how they added by place, but it is unclear how they composed hundreds or tens, consider asking:

• “Can you explain your representation to me?”
• “How can you show others that you composed a ten or a hundred here?”

• Invite previously identified students to share their work.
• “What’s the same across these representations? What's different?” (They all show the same answer. They all made a ten and a hundred. Some use words, some use diagrams, and some use only numbers.)