Lesson 18

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting with 2 three-digit numbers. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to solve problems involving addition and subtraction on a bar graph.

• 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 strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien usó el mismo método, pero lo explicaría de otra forma?” // “Did anyone have the same method but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
  • “¿Alguien quiere agregar algo al método de _____?” // “Does anyone want to add on to _____’s method?”

The purpose of this activity is for students to analyze a given bar graph and answer questions involving addition and subtraction within 1,000 (MP2). Students may notice that some of the information for the grade 1 population on the bar graph has been hidden by a paint splatter.

In the last part of activity, students come up with their own mathematical question that can be answered using the graph. It is okay if some students come up with questions that require more than the given information. This is addressed in the next activity.

• Groups of 2

• “¡Oh, no! Cayó pintura sobre el póster de la gráfica de barras que hicieron Clare y Priya. Tómense un minuto para mirar la gráfica” // “Oh no! Paint fell on the poster of the bar graph Clare and Priya created. Take a minute to look at their graph.”
• 1 minute: quiet think time
• “Con su compañero, respondan las preguntas acerca de la gráfica de barras” // “Work with your partner on the questions about the bar graph.”
• 7 minutes: partner work time
• Monitor for students who:
  • write addition and subtraction equations.
  • are able to reason why there is not sufficient information to compare the number of grade 1 students to grade 2 students.
  • are able to use the features they can see in the graph to make assumptions about how many more students are in grade 2 than grade 1.
  • ask questions that can be answered by adding and subtracting.

• Invite previously identified students to share how they compared the number of students in each grade and what they noticed when comparing grade 2 and grade 1.
• Invite a few students to share one of their mathematical questions and give students a chance to discuss them with their partner.
• “En la siguiente actividad, cada uno de ustedes tendrá la oportunidad de hacerle una de sus preguntas a uno de sus compañeros” //  “You’ll each get a chance to ask your classmates one of your questions in the next activity.”

The purpose of this activity is for students to use information in a bar graph to answer their peers' mathematical questions.

In this activity, students exchange the questions they wrote in the previous activity and go through 3 rounds of answering new questions. Students may notice some questions require more than the given information and cannot be answered or cannot be answered precisely. For example, if students create a question that requires the grade 1 data, some students may argue that the question cannot be answered. However, others may decide to estimate based on the given information. Encourage students to justify their reasoning to convince others (MP3).

• Groups of 4

• “Intercambien con otro compañero una pregunta de las que se inventaron en la actividad anterior. Respondan la pregunta de su compañero” //  “Trade a question that you came up with in the last activity with another partner. Answer each others’ question.”
• “Si no pueden responder una pregunta, prepárense para explicar por qué no pueden responder la pregunta basándose en la información dada” // “If you cannot answer a question, be prepared to explain why you cannot answer the question based on the given information.”
• “Si les queda tiempo, intercambien otra pregunta con un compañero diferente” // “If you have time, trade another question with a different partner.”
• Give students 3–4 minutes with each partner.
• 9–12 minutes: partner work time
• Monitor for students who are able to reason why a question cannot be answered.
• Monitor for addition and subtraction expressions students write during the rounds and record a few on the board.

• Invite previously selected students to share their questions.
• “¿Cómo decidieron si tenían suficiente información para responder una pregunta?” // “How did you decide if you had enough information to answer a question?”
• Point to the expressions recorded earlier.
• Consider asking:
  • “¿Qué representa esta expresión?” // “What does this expression represent?”
  • “¿Cómo podrían encontrar su valor?” // “How might you solve it?”