Lesson 12

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 add 2 two-digit numbers, with composing a ten, using methods based on place value and the properties of operations.

In this activity, students have an opportunity to look for and make use of structure (MP7) because they decompose addends to make a new ten.

• 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.

• “How could \(7 + 3\) help you solve \(37 + 3\)?” (I know 37 is 3 more tens than 7. Since I know \(3 + 7\) is 10, I need to add \(30 +10\).)
• “How could \(7 + 3\) help you solve \(7 + 8\)?” (\(7 + 3 = 10\). So far I have added 3 of the 8 and have 5 left. \(10 + 5 = 15\).)
• “How could \(7 + 8\) help you solve \(57 + 8\)?” (Since I know \(7 + 8 = 15\), I can add \(50 + 15 = 65\))

The purpose of this activity is for students to add 2 two-digit numbers within 100 and show their thinking with equations. Although some students may write each step of their thinking with equations, it is not required that they do so. Students can write one equation that shows the sum and represent their solution pathway in their drawings. In the activity synthesis, students present their method verbally to a new partner.

This activity uses MLR8 Discussion Supports. Advances: listening, speaking, conversing

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “We have been learning about different ways to add within 100. You are going to find sums using a method that makes most sense to you for each problem. Record equations to show your thinking.”

• 5 minutes: independent work time
• “Compare your work with your partner’s. Did you use the same method? Did you represent your method in the same way? How is your work the same? How is it different?"
• 5 minutes: partner work time
• Monitor for a student who wrote equations related to making ten and one who wrote equations related to adding by place.

• Display sentence frames to support students when they explain their method as equations:
  • “First, I _____ because . . .”
  • “I noticed _____ so I . . .”
• “You are going to explain your method to another student in the class. Practice what you will say with your partner. Use these sentence starters to help you.”
• 3 minutes: partner discussion
• “Find a new partner and explain your method.”
• 2 minutes: partner discussion

The purpose of this activity is for students to use what they know about the base-ten structure of numbers to create different expressions. Students use place value reasoning to create expressions with the smallest and largest values and expressions that may or may not require composing a ten when adding using methods based on place value (MP7). In the synthesis, students explain how they reasoned about whether or not a new ten could be composed just by looking at the addends (MP3). Although some students may complete the activity without finding any sums, others may need to find partial sums or complete sums in order to explain what happens when adding.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “Now we are going to use what we know about numbers and addition to think about what will happen when we add different numbers together. You may add the numbers if it is helpful, but you don’t have to.”

• 8 minutes: partner work time
• Monitor for students who write expressions without finding the value of the sums and can explain their reasoning.

• Invite a previously identified student to share their expression that does not require making a new ten.
• “Are there other numbers you could use? How do you know?"
• Invite a student who found two numbers that make a ten without finding the sums to share.
• “Are there other numbers you could use? How do you know?"

The purpose of this activity is for students to relate adding within 100 to real-world contexts. In previous lessons and activities, students have used different methods to add within 100. In this activity, students solve problems that help them see when this type of addition is used in people’s lives. This activity is optional because it is an opportunity for extra practice that not all classes may need.

When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2).

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “We recently discussed a story problem about a class that volunteered to clean up their local park. What are some other ways you can volunteer to help in your community?” (You can volunteer at an animal shelter. You can help by donating food or clothes.)
• 30 seconds: quiet think time
• Share responses.
• “We are going to solve some more problems about people volunteering in different ways.”

• 5 minutes: independent work time
• 5 minutes: partner discussion

• Invite students to share the methods used for each problem. Record equations to match each method.