Lesson 4

The purpose of this warm-up is to elicit the relationship between multiplication and division, which will be useful when students identify missing dividends and divisors in a later activity. While students may notice and wonder many things about this equation, possible numbers to fill in the blanks are the important discussion points.

• Groups of 2
• Display the equation.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”

• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “¿Qué números podrían ir en los espacios en blanco? ¿Cómo lo saben?” // “What numbers could go in the blanks? How do you know?” (I could put in 136 and 1 or 272 and 2. The first number has to be 136 times the second number.)

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 them to revisit this algorithm in the next lesson.

• Groups of 2

• 5–10 minutes: independent work time
• 5 minutes: partner discussion

• “¿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 ten and use place value understanding.
• can explain the relationship between multiplication and division.

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

• Groups of 2

• 3–5 minutes: independent work time
• “Compartan sus respuestas con su compañero. Si tienen ecuaciones que sean la misma, escriban una ecuación nueva que sea diferente. Juntos, encuentren 10 ecuaciones diferentes” // “Share your responses with your partner. If you have any equations that are the same, write a new equation that is different. Together, work to find 10 different equations.”
• 3–5 minutes: partner discussion
• Give each group tools for creating a visual display.

MLR7 Compare and Connect

• “Con su compañero, creen una presentación visual que muestre cómo pensaron en los problemas 1 y 2” // “Work with your partner to create a visual display that shows your thinking about problems 1 and 2.”
• 2–5 minutes: independent or group work
• 3–5 minutes: gallery walk

• Display: \(\underline{\hspace{1cm}} \div \underline{\hspace{1cm}} = 700\)
• Invite students to share the numbers they used to make the equation true.
• “¿Cómo encontraron 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: \(\underline{\hspace{1cm}} \div \underline{\hspace{1cm}} = 78\)
• “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, 1 worked and 2 and 10, but it was harder to find a variety of numbers.)