The purpose of this activity is for students to estimate quotients of multi-digit numbers and reason about multiplication expressions that are helpful when dividing. In previous units, students learned a partial-quotients algorithm to divide multi-digit whole numbers. This lesson prepares students to revisit the algorithm in the next lesson.

• “¿Cómo les ayudó la multiplicación a hacer sus estimaciones?” // “How did multiplication help you with your estimates?” (Multiplying by tens is easy to do in my head so I could find the product that was closest to the dividend.)
• “¿Cómo les ayudaron sus estimaciones a encontrar el cociente?” // “How did your estimates help you find the quotient?” (My estimates gave me a good idea what multiple of the divisor to subtract to begin my calculation. They helped me check that my answer was reasonable.)

The purpose of this activity is for students to use the relationship between multiplication and division to determine possible dividends and divisors that have a given value for their quotient (MP7). Monitor for students who:

• Multiply the quotient by friendly numbers such as 1, 2, or 5.
• Multiply the quotient by powers of 10 and use place-value understanding.
• Can explain the relationship between multiplication and division.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing

• Display:
• Invite students to share the numbers they used to make the equation true.
• “¿Cómo encontraron los números que hacen que la ecuación sea verdadera?” // “How did you find numbers that make the equation true?” (I multiplied 700 by different numbers. I chose simple quotients, like dividing by 1 or 2 or 10.)
• Display:
• “Para encontrar números que hacen que esta ecuación sea verdadera, ¿funcionaron las mismas estrategias?” // “Did the same strategies work to find numbers that make this equation true?” (Yes, but 78 is a more difficult number to multiply by in my head. So, the divisors 1, 2, and 10 worked, but it was harder to find a variety of numbers.)
• “¿En qué se parecen las estrategias que usaron para los dos problemas de división? ¿En qué son diferentes?” // "What is the same and what is different about the approaches used for the two division problems?" (For both, we multiplied the quotient by any number to get the dividend. The multiplication for the quotient 700 was easier to do mentally than for the quotient 78.)