Lesson 2

• Groups of 2
• Display the expression.
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”

• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.
• Monitor for students who estimate by using $10,\!000 \times 900$.

• Invite students to share estimates.
• “¿Por qué $10,\!000 \times 900$ es una buena estimación del producto?” // “Why is $10,\!000 \times 900$ a good estimate for the product?” (10,000 is just 1 more than 9,999 and 896 is close to 900.)
• “¿Cuál es el valor de $10,\!000 \times 900$? ¿Cómo lo saben?” // “What is the value of $10,\!000 \times 900$? How do you know?” (9,000,000 because the two numbers have 6 factors of 10 combined.)

• revise their answer after examining Kiran’s mistake.
• recognize that $650 \times 10 = 6,\!500$ so $650 \times 27$ has to be much greater than 5,850.
• can explain why Kiran should be multiplying $650 \times 2 \times 10$.
• recognize that $20 \times 50 = 1,\!000$ so there should be three zeros in the second partial product.

When students determine Kiran's error and make sense of his work, they interpret and critique the work of others (MP3).

• Display or write for all to see.

  $650 \times 27$

• Display each number in a different corner of the room:
  14,000
  18,000
  13,000
  19,000

• “Cuando yo diga ‘ya’, párense en la esquina que tenga el número que crean que es la estimación más razonable de $650 \times 27$. Prepárense para explicar cómo razonaron” // “When I say go, stand in the corner with the number that you think is the most reasonable estimate for $650 \times 27$. Be prepared to explain your reasoning.”
• 1 minute: quiet think time
• Ask a representative from each corner to explain their reasoning.
• “¿Alguien quiere cambiar de esquina?” // “Does anyone want to switch corners?”
• Ask a student who switched corners to explain their reasoning.
• “Ahora van a encontrar este producto y a analizar un trabajo” // “Now you are going to find this product and analyze some work.”

• Groups of 2
• 5–7 minutes: partner work time

• Ask previously identified students to share their thinking.
• Display Kiran's work.
• “¿Por qué 5,850 no tiene sentido?” // “Why doesn’t 5,850 make sense?” ($650 \times 10 = 6,\!500$ so $650 \times 27$ should be a lot larger than 6,500.)
• “¿Qué tiene sentido en el trabajo de Kiran?” // “What makes sense about Kiran’s work?” ($650 \times 2 =1,\!300$, but he needs to multiply $650\times2\times10$.)
• Display a student's solution or the image from the student solution.
• “¿Cómo sabemos que 17,550 es una estimación razonable del producto?” // “How do we know that 17,550 is a reasonable value for the product?” (Because $600 \times 30 =18,\!000$.)

The purpose of this activity is for students to practice multiplying multi-digit numbers that have one or more digits of 0 at the end. Monitor for students who:

• use the standard algorithm to evaluate $6,\!700 \times 89$.
• multiply the product $67 \times 89$ by 10 to find the value of the product $670 \times 89$.
• multiply the product of $670 \times 89$ by 10 to find the value of the product $6,\!700 \times 89$.

Students who observe that $670 = 10 \times 67$ and $6,\!700 = 10 \times 670$ and use these relationships to find the values of the products are observing regularity in repeated reasoning and using their knowledge of how to multiply a whole number by 10 (MP7, MP8).

• Groups of 2

• 5–7 minutes: independent work time
• 5–7 minutes: partner discussion

• Display the product $6,\!700 \times 89$:
• Ask previously identified students to share their solutions.
• Display student work or the image from the sample response:

  

  

• “¿Qué relación hay entre $670\times89$ y $6,\!700\times89$?” // “What is the relationship between $670\times89$ and $6,\!700\times89$?” (The product $6,\!700\times89$ is ten times larger because one of the factors is ten times greater.)
• “¿Qué relación hay entre $67 \times 89$ y $6,\!700 \times 89$?” // “What is the relationship between $67 \times 89$ and $6,\!700 \times 89$?” (The product $6,\!700 \times 89$ is 100 times as large as $67 \times 89$ since 6,700 is $100 \times 67$.)