Lesson 7

This warm-up prompts students to compare four expressions. It gives the teacher an opportunity to hear how students talk about the characteristics of addends and use terminology related to the digits, the values of the addends, and the value of the sum.

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to use place value reasoning and properties of operations to determine whether they would compose a ten when adding a two-digit and a one-digit number.

Students write equations to show how they solved such as:

It is not important that students write their equations in this way, but it is important that they can relate each part of the equation to how they found the sum.

Students may write \(63 + 7 = 70 + 2 = 72\). Since this equation is not true, it is important to remind students that the equal sign means “the same amount as” and that it is necessary to use two separate equations.

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

• Read the task statement.
• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
  • can explain why the expression does or doesn’t make a new ten, without finding the sum.
  • use connecting cubes to show why there are or are not enough ones to make a new ten without representing the entire sum.

If students write equations that do not match their method for finding the sum, consider asking:

• “How did you find the sum?”
• “What equation could we write to represent your first step? Next step?”

• Invite previously identified students to share.
• “Let’s think some more about how we know whether or not we will make a new ten.”

The purpose of this activity is for students to deepen their understanding of place value and properties of operations when adding one-digit numbers and two-digit numbers. Students find an unknown addend that fits a specific rule for each expression. Some expressions have more than one number that fits the rule. As students complete each expression, they look for and make use of structure (MP7) as they think about whether or not the ones in the two numbers will combine to make a new 10.

During the activity synthesis, students look at different one-digit numbers that would make or not make a new ten when added to 16. In the lesson synthesis, students share their answers to the last problem in the task which encourages them to make generalizations (MP8).

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Read the task statement.
• Display:

  

  

• “Lin wrote a one-digit number where the smudge is. She said you can not make a new ten when you find the value of the sum. What number could she have written?” (0, 1, 2, 3, 4, or 5)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “Are there other numbers she could have written?”
• Record responses.

• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students with a range of responses for the last two questions.

If students choose numbers that do not follow Lin's rule or show they believe that only one number could follow the rule for a problem, consider asking:

• “What needs to be true about Lin's number for this sum?”
• “How do you know your number works? How could you prove your thinking with the connecting cubes?”
• “Are there other numbers Lin could have written? How could you prove it with the connecting cubes or a drawing?”

• Display

  

  

• “What two-digit numbers can she add that will make a new ten?” (12, 35, 49)
• “What two-digit numbers can she add that will not make a new ten?” (11, 30, 41)
• “What do you notice about each list of numbers?” (If she doesn't make a new ten, the number can only have 0 or 1 in the ones place, but it can have any number in the tens place. If she does make a new ten, the number can have 2, 3, 4, 5, 6, 7, 8, or 9 in the ones place.)