Lesson 3

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 1,000, particularly around adjusting numbers in a sum to make them easier to add. These understandings help students develop fluency for adding within 1,000.

When students notice that the same value is being removed from one addend and added to the other and the value of the sum does not change, they look for and make use of structure (MP7).

• 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.

• “¿Por qué creen que todas estas expresiones tienen el mismo valor?” // ”Why do you think all of these expressions have the same value?” (Even though each number is changing, the same amount is being added to one number and subtracted from the other number, so the total is the same.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy 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 a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is for students to physically represent the difference between making 2 groups and making groups of 2. Ten students will put themselves into 2 groups and then groups of 2. The rest of the students observe how the groups were made to highlight the difference between “how many groups?” problems and “how many in each group?” problems.

• Groups of 2
• Invite 10 students to come to the front of the class.
• “Estos estudiantes se van a organizar en grupos y lo harán de diferentes maneras. Si están observando, anoten sus observaciones acerca de cómo forman los grupos” // “These students are going to put themselves into groups in different ways. If you are observing, take notes on what you notice about how they make the groups.”

• Ask the 10 students to put themselves into groups of 2.
• Give observers a chance to take notes.
• Ask the 10 students to put themselves into 2 groups.
• Give observers a chance to take notes.
• Ask the students to return to their seats.
• “Hablen con un compañero sobre sus observaciones acerca de cómo los estudiantes se organizan en grupos de 2 y en 2 grupos” // “Talk with a partner about what you noticed about how the students put themselves into groups of 2 and 2 groups.”
• 2–3 minutes: partner discussion

• Ask students who observed to share what they noticed.
• Highlight ideas that help clarify differences between “how many groups?” and “how many in each group?”

The purpose of this activity is for students to match a division situation to a drawing of equal groups. Students should be able to explain why the situation matches drawing A, which shows 2 groups of 6, and why it does not match drawing B, which shows 6 groups of 2.

This activity uses MLR1 Stronger and Clearer Each Time.
Advances: reading, writing

• Groups of 2
• “Hoy vamos a examinar dibujos que representan situaciones de división. Tómense un minuto para leer esta situación” // “Today we are going to look at drawings to represent division situations. Take a minute to read this situation.”
• 1 minute: independent work time

• “Individualmente, decidan cuál dibujo corresponde a esta situación y luego expliquen su razonamiento” // “Work independently to decide which drawing matches this situation and explain your reasoning.”
• 2–3 minutes: independent work time

• “Compartan su respuesta con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta el momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 2–3 minutes: structured partner discussion
• Repeat with 2 different partners.
• “¿Cuál dibujo decidieron que corresponde? ¿Cómo lo saben?” // “Which drawing did you decide matches? How do you know?”
• “¿Cómo saben que el otro dibujo no corresponde a esta situación?” // “How do you know the other drawing does not match this situation?” (Drawing B is 6 groups of 2 colored pencils. That would be like if she had 6 boxes, not 2 boxes.)

The purpose of this activity is for students to relate division situations and drawings of equal groups (MP2). Each given drawing matches two different situations. Students learn that the same drawing can represent both a “how many groups?” problem and a “how many in each group?” problem because the drawing shows the end result, not how the groups were made. When students interpret one diagram as representing two different story types they state clearly how each part of the diagram corresponds to the story, including what corresponds to the unknown in the story (MP6). 

• Groups of 2
• “Vamos a examinar algunas situaciones que incluyen herramientas para escribir o dibujar. ¿Qué cosas usamos para escribir o dibujar?” // “We’re going to look at some situations that involve writing or drawing tools. What are some things we use to write or draw?”
• 30 seconds: quiet think time
• Share and record responses.

• “Van a asociar seis situaciones con dibujos que podrían representarlas. Tómense unos minutos para decidir cuál dibujo corresponde a cada situación” // “You are going to match six situations and drawings that could represent them. Take a few minutes to decide which drawing matches each situation.”
• 3-5 minutes: independent work time
• “Compartan sus ideas con su compañero” // “Share your ideas with your partner.”
• 2-3 minutes: partner discussion

If students say that the drawing can’t match both situations, consider asking:

• “¿Cómo podrías hacer un dibujo para cada situación?” // “How could we make a drawing for each situation?”
• “¿Qué podrías dibujar primero para representar la primera situación en la que hay 8 objetos? ¿Y para la segunda situación en la que hay 8 objetos?” // “What might we draw first to represent the first situation with 8 objects? What about with the second situation with 8 objects?”

• Invite students to share which drawing matches each situation.

• Focus on one drawing and the two situations it can represent, such as:

  

  

  Mai has 8 markers. She puts 4 markers in each box. How many boxes of markers are there?

  Lin has 8 colored pencils. She puts them into 2 bags. Each bag has the same number of colored pencils. How many colored pencils will be in each bag?

• “¿Cómo puede el mismo dibujo representar ambas situaciones?” // “How can the same drawing represent both situations?” (We didn’t see how the groups were made, but in the end, the same number and size of groups were made in both situations. The drawing can represent putting 8 markers into boxes with 4 markers in each box and finding that they fit into 2 boxes. It can also represent putting 8 pencils into 2 bags with the same number of pencils in each bag and finding that you can put 4 pencils in each bag.)