Lesson 3

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to add up the total number of students represented in a picture graph. When students use strategies based on place value to add 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.

• “¿Cómo les ayudó el valor posicional cuando sumaron estos números?” // “How was place value helpful as you added these numbers?” (I was able to use tens and ones to help me find the sum.)
• Consider asking:
  • “¿Quién puede expresar el razonamiento de _____ de una forma diferente?” // “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 read a scaled picture graph. A scale of 5 is used to encourage skip-counting because students skip-counted by 5 in grade 2. The questions in the task focus on the structure of a scaled picture graph and strategies for reading them.

• Groups of 2
• “¿Cuál es su deporte o actividad favorita afuera de la escuela?” // “What is your favorite sport or activity outside of school?”
• Share responses.
• Display the first image of the single-unit scale picture graph.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (Students may notice: The graph is about students’ favorite sports. There are a lot of smiley faces. Each smiley face represents 1 student. It takes a lot of time to count up the students in each category. Students may wonder: How many student responses are shown in the whole graph? How could we make the graph take up less space?)
• 1 minute: quiet think time
• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Con su pareja, encuentren cuántos estudiantes están representados en la gráfica” // “Work with your partner to find how many students are represented in the graph.”
• 3–5 minutes: partner work time
• Monitor for students who group the smiley faces by 2, 5, or 10 to make them easier to count. 
• Have students who grouped the smiley faces share their strategies for how they found the total number of students represented in the graph. 
• If no students use this strategy ask, “¿Cómo puede ayudarnos agrupar los dibujos de la gráfica a contar más fácilmente?” // “How could grouping the pictures in the graph make them easier to count?” (We could circle tens so we could count by ten. It would be easier to keep track of your count than by counting by ones.)
• Display the second image of the scaled picture graph. 
• “¿Cómo podríamos contar el número total de estudiantes en esta gráfica?” // “How could we count the total number of students in this graph?”
• 2 minutes: partner work time
• Math Community: As students work, monitor for examples of the “Doing Math” actions.

If students count the students in the scaled picture graph and get a total other than 65, consider asking:

• “¿Cómo encontraste el número total de estudiantes representados en la gráfica?” // “How did you find the total number of students represented in the graph?”
• “¿Cómo te ayudaría contar de 5 en 5 a encontrar el número total de estudiantes representados en la gráfica?” // “How could you use counting by 5 to find the total number of students represented in the graph?”

• “Cuando una gráfica tiene muchos datos, podemos ajustar la escala para que cada dibujo represente más de 1 objeto. Si cada dibujo representa algo que no es 1, decimos que la gráfica es una gráfica de dibujos con escala. La leyenda nos dice que, en esta gráfica, cada carita feliz representa 5 estudiantes” // “In a graph where there’s a lot of data we can adjust the scale so each picture represents more than 1 object. When each picture represents something other than 1, we say that it’s a scaled picture graph. The key tells us that in this graph, each smiley face represents 5 students.”

The purpose of this activity is for students to interpret a scaled picture graph and write questions that can be asked based on the data represented in a scaled picture graph.

• Groups of 2
• Display the graphs for all to see.
• “¿Qué estrategias podrían usar para leer estas gráficas?” // “What are some strategies you could use to read the graphs?” (In the Flowers I Saw on the Way Home graph I could count each category by 5 since each picture represents 5 flowers.)
• 1 minute: quiet think time
• Share and record responses.

• “Ahora, vamos a responder preguntas sobre las gráficas de dibujos con escala. También tendrán la oportunidad de escribir sus propias preguntas basándose en cada gráfica” // “Now, we’re going to answer some questions about the scaled picture graphs. You will also have a chance to write your own question that can be asked based on each graph.”
• 8–10 minutes: partner work time
• If there is time, have groups trade books and answer each other’s questions.
• Math Community: As students work, monitor for examples of the “Doing Math” actions.

If students answer questions about the graph with numbers that don’t match the graph, consider asking:

• “¿Cómo hiciste para responder las preguntas sobre la gráfica?” // “How did you answer the questions about the graph?”
• “¿Qué nos dice la leyenda sobre cada dibujo en la gráfica?” // “What does the key tell us about each picture in the graph?”

• Have students share responses to the questions they answered and explain their reasoning.
• Consider asking:
  • “¿Cómo usaron la escala para responder las preguntas?” // “How did you use the scale to answer the questions?” (I counted by the number that each picture represented, like by 5 for the flowers and by 2 for the students.)
• Share a variety of student written questions.
• Consider asking:
  • “¿Cómo supieron que su pregunta se podía contestar con la gráfica?” // “How did you know your question could be answered with the graph?” (The data you needed to answer the question was in the graph.)
  • If time ask, “¿Qué preguntas no se pueden contestar con esta gráfica?” // “What questions cannot be answered by this graph?” (How many students' favorite type of book is graphic novels?)