The purpose of this activity is for students to analyze a common error when using the standard algorithm to add decimals. The standard addition algorithm requires students to add digits with the same place value. In the given example the two numbers are “right aligned” as when adding whole numbers, but this leads to the error of adding tenths from one number to hundredths of the other number. When students analyze the incorrect calculation, explain why it is incorrect, and correct it, they critique the reasoning of others (MP3).

This activity uses MLR3 Critique, Correct, Clarify. Advances: reading, writing, representing

• Display Elena’s partially correct answer and explanation for students to consider.
• Read the explanation aloud.
• “What parts of this response are unclear, incorrect, or incomplete?” (She says the answer will be more than 621, but she doesn’t say how much more. The answer will be a lot more than 628.68.)
• 1 minute: quiet think time
• 2 minute: partner discussion
• Invite 2–3 groups share what they discussed. Record for all to see.
• “With your partner, work together to write a revised solution and explanation.”
• Display and review the following criteria:
  • Explain each step.
  • Use “decimal point,” “tenths,” “hundredths,” or other place value words.
  • Label your work with details that help your explanation.
• 3–5 minutes: partner work time
• Select 1–2 groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each group shares. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.
• “What is the same and different about the revised solutions and explanations?”

The purpose of this activity is for students to find the value of various decimal sums with no scaffold. Most of the numbers do not have the same number of decimal digits so students need to add carefully if they make vertical calculations, making sure to align place values correctly (MP6).

• “Can you explain how you found the value of the expression?”
• “Which 2 whole numbers will the value of the sum be between?”

• Invite previously selected students to share.
• Display:
• “How do you add these using the standard algorithm?” (I made sure that the 3 in 463 lines up with the 3 in 3.14 so I am adding numbers with the same place value. I added 0’s in the tenths and hundredths places of 463 to help add the numbers.)
• “Did anyone use a different strategy to add these numbers?” (I knew that 463 and 3 is 466. Then I also have 14 hundredths so it's 466.14.)