Lesson 9

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to add 2 two-digit numbers within 100 with composing a ten. When students describe methods based on making a ten, adding tens and tens and ones and ones, and using known or previously found sums, they are looking for and making use of the base-ten structure and properties of operations (MP7).

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “Who can restate _______ 's reasoning in a different way?”
• “How could the expressions \(38 + 2\) and \(40 + 3\) help you to find the value of \(38 + 5\)?” (The first one shows us adding part of 5 to get to 40 and then adding the rest in the second expression.)

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 and select students with the following methods, all of which use an understanding of place value in the two addends (MP7), to share in the synthesis:

• Start with 17, add 30, then add 6 ones (\(17 + 30 = 47\), \(47 + 6 = 53\))
• Start with 36, count on 1 ten, add 7 ones (\(36 + 10 = 46\), \(46 + 7 = 53\))
• Start with 36, add 4 ones to make a ten, add ten, add leftover ones (\(36 + 4 = 40\), \(40 + 10 + 3 = 53\))
• Combine the tens (\(30 + 10 = 40\)), combine the ones (\(6 + 7 = 13\)), then add the sums together (\(40 + 13 = 53\))

Students may represent these methods in different ways, including using connecting cubes in towers of 10 and singles. Monitor for students who use connecting cubes or base-ten drawings to show making a new unit of ten as part of their method (MP5). In the activity synthesis, students compare different methods for finding the sum and make connections between them.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

• Read the task statement.
• 5 minutes: independent work time
• As students work, consider asking:
  • “How did you determine which parts to add first?”
  • “What did you do next?”
  • “What other way can you find the value of the sum?”
• “Share your thinking with your partner.”
• 2 minutes: partner discussion

If students find the value mentally, consider asking:

• “Can you explain how you found the value of the sum?”
• “How could you represent each step with an equation?”

• Invite previously identified students to share in the order in the activity narrative.
• As each student shares, record their thinking with drawings and numbers.
• After each student shares, ask:
  • “How did _____ find value of \(17 + 36\)?”
  • “Does anyone have any questions for _____?”

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: \(45 + 37 = \boxed{\phantom{3}}\)

\(70 + 12 = \boxed{82}\)

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.

• Groups of 4
• Give students access to connecting cubes in towers of 10 and singles.
• “We are going to play a game called Grab and Add. Each partner grabs a handful of towers and a handful of single cubes. You don’t need to grab huge handfuls. First you each determine how many cubes you have, then determine how many cubes you and your partner have altogether. Show your thinking using drawings, numbers, or words.”

• 10 minutes: partner work time
• Monitor for students who:
  • add on to a two-digit number to compose a new ten.
  • add tens and tens and ones and ones.

• 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.)