The purpose of this activity is for students to find sums that require composing a ten or a hundred when adding by place. The numbers in the expressions share the same digits, but one expression requires composing a ten and the other requires composing a hundred when adding by place. Students may use the methods that make sense to them when finding the value of each sum. Monitor for students who use base-ten blocks, base-ten diagrams, or equations to show adding by place and composing new units. The Activity Synthesis focuses on representations that show composing a ten and a hundred.

• “Will you explain your representation to me?”
• “Can you use base-ten blocks to show me the total, using as few blocks as possible? What is the value of the sum?”

• “How was finding the value of each expression the same? How was finding each value different?” (I made a unit in both of them. In the first expression, I made a ten with 10 ones, and in the second expression, I made a hundred with 10 tens.)
• Invite previously identified students to share their methods.
• “How did _____ represent composing a ten to find the value of ?”
• “How did _____ represent composing a hundred to find the value of ?”
• Consider asking, “When did you notice that you would need to compose a unit?” (I could tell because I knew that there would be more than 10 ones once I started adding. I knew when I got the blocks that there were more than 10 tens.)

The purpose of this activity is for students to practice adding a two-digit number and a three-digit number in sums that require composing a ten or a hundred when adding by place. Students are given a card with a three-digit number or a two-digit number. Students with three-digit numbers find a partner with a two-digit number. When students first discuss whether they need to compose a ten or a hundred when adding their numbers, they look for and make use of place value structure and construct viable arguments (MP3, MP7).

This activity uses MLR8 Discussion Supports. Advances: conversing.

• “What do you notice about the hundreds, tens, and ones?”
• “How could you represent your numbers with base-ten blocks and show where you would compose a unit?”

• Invite 2 or 3 previously identified groups to share how they decided if a ten or a hundred would be composed.
• Invite 1 or 2 previously identified groups to share an expression that resulted in the composition of a hundred. Have them share their method for finding the sum.