Lesson 9

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting multi-digit numbers when the minuend is a multiple of 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to interpret student work and solve word problems that involve multi-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.

• “¿Siempre usaron una de las primeras expresiones como ayuda para encontrar el valor de una nueva expresión? ¿En algunos casos cambiaron de estrategia?” // “Did you find yourself always using an earlier expression to help you find the value of a new expression? Did you find yourself switching strategies at times?”
• “¿Sobre cuál expresión les pareció más retador razonar?” // “Which expression did you find most challenging to reason about?” (Sample response: \(26,\!000-1,\!493\) because there were many zeros in the number being subtracted from.)

In this activity, students analyze a situation and given solutions and think about what questions were asked. They also write their own question that can be answered with the quantities in the situation. As they connect equations to a context, students reason quantitatively and abstractly (MP2) and engage in aspects of modeling (MP4). 

• Groups of 2
• “¿Alguna vez han hecho una caminata larga? ¿Cuál es la mayor distancia que han recorrido caminando?” // “Have you ever gone on a long hike? What is the longest distance you ever traveled just by walking?”
• “Examinemos el trabajo que hizo un estudiante para responder unas preguntas sobre dos hombres que establecieron récords mundiales de viajes a pie” // “Let’s look at the work a student did to answer questions about two men who set world records for traveling by walking.”

• 5 minutes: independent work time
• 5 minutes: partner work
• “Compartan sus soluciones con su compañero y compartan estrategias para resolver la tarea” // “Share solutions with your partner and share strategies for solving the task.”
• 5 minutes: Trade problems with a partner, solve, and review strategies for solving.

• “Con solo mirar las ecuaciones, ¿cómo averiguaron cuál era la pregunta que se estaba haciendo?” // “How did you figure out the question that was asked just by looking at the equations?” (We can look at the numbers they used and look back at the story to see what they meant. For example, subtracting the years lets us know something about the difference between the years. Dividing 12 by 6 lets us know that the years and the pairs of boots were used to find an answer.)

In this task, students create their own word problems that must have a specific answer and follow additional constraints involving the type of operations that could be used to solve the problem or the size of the numbers they can use (MP2, MP4). 

• Groups of 2

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

• Select 1–2 students to share the problem they created for each constraint.
• Consider asking:
  • “¿Cómo empezaron?” // “How did you start?”
  • “¿Cómo se aseguraron de que la respuesta fuera 1,564? ¿Cómo se aseguraron de que su problema coincidiera con lo que usó cada estudiante?” // “How did you make sure 1,564 would be the answer? How did you make sure your problem would match what each student used?”