Lesson 16

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. These understandings help students develop fluency and will be helpful later in this lesson when students will develop their own number talk activity.

• Display one problem.
• “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 problems and work displayed.
• Repeat with each problem.

• “¿A qué cosas tuvo que prestarle atención el autor de esta actividad cuando la diseñaba?” // “What did the writer of this activity have to pay attention to when they designed this activity?” (The expressions need to be done mentally so they can't be too complex.)
• “¿Dónde ven estas cosas en la manera en la que cambian las expresiones durante la actividad?” // “Where do we see those things in how the expressions change during the Number Talk?” (The first problem helps to do the second one and the first 3 help to do the last one.)
• “Imaginemos que esta ‘Conversación numérica’ tuviera una quinta expresión. ¿Por qué \(700 \div 28\) sería una buena opción?” // “Imagine this number talk continued with a fifth expression. How does \(700 \div 28\) fit in with this number talk?” (It doubles the dividend and the divisor from the previous expression, which means the quotient is the same, 25.)

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add one expression to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

• Groups of 2 or 4
• “Ahora completen con su grupo una actividad tipo ‘Conversación numérica’. A esta actividad le falta una expresión. Decidan qué expresión podría completar la actividad y escríbanla en el espacio en blanco” // “Now you will work with your group to complete a Number Talk activity. This activity has one expression missing. Decide on an expression that would complete the Number Talk and write it on the blank line.”

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design an expression based on some of the following:
  • They keep the same divisor.
  • They add the dividends, but keep the same divisor.
  • They subtract the dividends and keep the same divisor.
  • They make the dividend smaller to get \(15 \div 15\) or \(3 \div 15\).
  • They use a combination of multiples, half, double, or triple the dividend and divisor to change both the dividend and divisor. For example, \(15 \div 60\).

• Choose small groups to share who had different reasons for their fourth expression.
• Ask students to share their completed Number Talk and ask the class to share reasons for the last expression.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add two expressions to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

• Groups of 2 or 4
• “Ahora completen con su grupo una actividad tipo ‘Conversación numérica’. Hay dos opciones y a cada una de ellas le faltan dos expresiones. Decidan qué expresiones completarían la ‘Conversación numérica’ y escríbanlas en los espacios en blanco” // “Now you will work with your group to complete a Number Talk activity. This activity has two options that each have two expressions missing. Decide on expressions that would complete the Number Talk and write them in the blank lines.”

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design expressions based on some of the following:
  • They adjust the dividend but keep the divisor.
  • They adjust the divisor and keep the dividend.
  • Use partial quotients either through addition or subtraction.
  • Use multiplicative relationships such as halving and doubling and reason how that impacts the quotient.
  • Use multiplicative relationships such as multiplying by 2 or 10 and dividing by 2 or 10 and reason how that impacts the quotient.

• Choose small groups to share that had different reasons for their expressions. 
• Ask students to share their completed Number Talk and ask the class to share reasons for their expressions. 
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why. 

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add three expressions to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

• Groups of 2 or 4
• “Ahora completen con su grupo una actividad tipo ‘Conversación numérica’. A esta actividad le faltan tres expresiones. Decidan qué expresiones completarían la ‘Conversación numérica’ y escríbanlas en los espacios en blanco” // “Now you will work with your group to complete a Number Talk activity. This activity has three expressions missing. Decide on expressions that would complete the Number Talk and write them in the blank lines.”

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design expressions based on some of the following:
  • They adjust the dividend but keep the divisor.
  • They adjust the divisor and keep the dividend.
  • Use partial quotients either through addition or subtraction.
  • Use multiplicative relationships such as multiplying by 2 or 10 and dividing by 2 or 10 and reason how that impacts the quotient.

• Choose small groups to share that had different reasons for their expressions. 
• Ask students to share their completed Number Talk and ask the class to share reasons for their expressions. 
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.