Lesson 13

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for dividing a three-digit number by a two-digit number. These understandings help students develop fluency and will be helpful later in this lesson when students use an algorithm that uses partial quotients to divide larger three-digit numbers by two-digit numbers.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Qué sigue siendo lo mismo en cada problema? ¿Qué cambia?” // “What stays the same with each problem? What changes?” (The quotient is always 11. There are always 11 groups of the divisor. The dividend and the divisor change.)

The purpose of this activity is for students to explain the steps for using an algorithm that uses partial quotients to divide a three-digit number by a two-digit number. Because the size of the dividends is larger and the numbers are less friendly, the problems encourage students to reflect about which partial quotients will be most efficient for making the calculations. Monitor for students who begin with partial quotients that are multiples of 10. This strategy helps make the calculations simpler and students have seen and used multiples of 10 for these calculations throughout the last several lessons. 

When students share and compare their methods with their partner and with other groups, they explain and improve their calculations (MP3).

• Groups of 2, then 4
• “Van a usar el algoritmo de cocientes parciales para resolver algunos problemas. Luego, van a comparar los pasos que usaron con los pasos de otros estudiantes” // “You are going to use the partial quotients algorithm to solve some problems and compare the steps you used with other students.”

• “Ahora decidan quién va a resolver cada problema. Resuelvan su problema y explíquenselo a su compañero” // “Now, decide who will solve each problem, solve your problem, and explain it to your partner.”
• 3–5 minutes: independent work time
• 1–3 minutes: partner discussion
• “Ahora busquen otra pareja y comparen sus soluciones. ¿En qué se parecen? ¿En qué son diferentes?” // “Now, find another group of 2 and compare your solutions. How are they the same? How are they different?”
• 3–5 minutes: small group work time
• Monitor for students who use different multiples for the quotients.

• Ask selected students who used different strategies to divide.
• “¿Qué preguntas tienen sobre los algoritmos en los que se usan cocientes parciales?” // “What questions do you have about algorithms that use partial quotients?”
• Display solutions from student solutions for the quotient \(589 \div 19\).
• “¿En qué se parecen estas estrategias? ¿En qué son diferentes?” // “How are the strategies the same? How are they different?” (They all subtract 1 group of 19 at the end. Before that, they all subtract multiples of 10.)
• “¿Cómo está representado el 30 de la solución C en los cocientes parciales de las soluciones A y B?” // “How is the 30 in the solution C represented in the partial quotients in solutions A and B?” (Solution A uses 20 and 10 and solution B uses 10, 10, and 10 more. These add up to 30.)

The purpose of this activity is for students to practice using an algorithm that uses partial quotients to divide multi-digit numbers by two-digit divisors. Before finding the quotient, students estimate the value of the quotient which both helps students decide which partial quotients to use and helps them evaluate the reasonableness of their solution (MP8).  For example, if students estimate that the value of \(529 \div 23\) is a little more than 20, that means that a good choice for first partial quotient is 20. Whenever possible, ask students to explain the steps they are taking.

To add movement to the activity, after students have solved each problem, they can partner with other students who used different partial quotients or got a different solution. This gives students the opportunity to explain their reasoning to one another and make adjustments to their work, as needed.

• Groups of 2

• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who use different sets of partial quotients for the same problem.

• Ask 2–3 students to share their work for the same problem that shows different partial quotients.
• “¿Cómo pueden asegurarse de que el cociente entero que obtuvieron al final es razonable?” //  “How can you make sure that the whole number quotient you got at the end is reasonable?” (It should be close to my estimate. I can multiply the quotient and divisor and that should give me the dividend.)
• If students pair and share with other partners, ask, “¿Cómo les ayudó hoy explicarle su trabajo a otros?” // “How did explaining your work to others help you today?” or “¿Qué dijo alguien hoy que les ayudó a comprender mejor la división?” // “What did someone say today that helped you in your understanding of division?” (I learned that it’s ok to take more steps because I was comfortable with the multiples I used.)