Lesson 13

The purpose of this Number Talk is to elicit strategies and understandings students have for adding or subtracting 1 or 2. When students add or subtract 1 or 2 and see that the result is 1 or 2 more or less in the count sequence, they are looking for and making sense 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 podemos sumar o restar 1 o 2 rápidamente?” // “How can we add or subtract 1 or 2 quickly?” (It’s like counting. \(+1\) is the number right after, \(- 2\) is two numbers before.)

The purpose of this activity is for students to determine whether or not questions about data can be answered with a given data representation. Students explain why questions can or cannot be answered with the representation. When students explain why some questions can not be answered, they think carefully about the meaning of the data representation, what it allows them to conclude, and what it does not allow them to conclude (MP6).

• Groups of 2

• Read the task statement. 
• “Si la pregunta se puede responder, marquen 'pulgar arriba'. Si no se puede responder, marquen 'pulgar abajo'” // “If the question can be answered, circle ‘thumbs up’. If it can’t be answered, circle ‘thumbs down’.”
• 3 minutes: independent work time
• 3 minutes: partner work time

• “¿Qué pregunta encontraron que no se puede responder? ¿Por qué no se puede responder?” // “What question did you find that cannot be answered? Why can’t it be answered?”
• “¿Cómo podemos cambiar la pregunta para que se pueda responder usando esta representación?” // “How can we change the question so that it can be answered using this representation?”

The purpose of this activity is for students to think of questions that can be answered using the data representation they create as they collect data from the class. Although there are two different sets of data, all of the questions students ask should be able to be answered using either data set. Questions are compiled during the synthesis and will be used in the following activity.

If necessary, use the provided blackline master instead of collecting data from the class. Cut the blackline master in half and give half the class data from Group A and the other half data from Group B.

• Groups of 2
• “Vamos a responder otra encuesta y a hacer preguntas sobre los datos” // “We are going to take another survey and ask questions about the data.”
• Decide on a survey question the class would like to answer and three possible responses.
• “Anoten el título de la representación de los datos y el nombre de cada categoría” // “Record the title of the data representation and each category.”
• Demonstrate recording the titles. 
• Divide the class into Group A and Group B. Each partnership should have one person from each group.
• “El grupo A va a responder la encuesta primero. Si están en el grupo B, anoten los datos en sus cuadernos mientras yo los anoto para que todos los vean” // “Group A is going to take the survey first. If you are in Group B, record the data in your book as I record it for all to see.”
• Ask students in Group A the survey question and record the data on the table using tally marks and numbers.
• “Ahora el grupo B va a responder la encuesta y el grupo A va a anotar los datos” // “Now Group B is going to take the survey and Group A will record the data.”
• Ask students in Group B the survey question and record the data on the table using tally marks and numbers.

• “Ahora, piensen en todas las preguntas que se pueden responder si usamos su representación de los datos. Si quieren, anoten sus preguntas en sus cuadernos” // “Now, think of as many questions as you can that can be answered using your data representation. Record your questions in your book if you would like.”
• 5 minutes: independent work time

If students make statements instead of questions, consider asking:

• “¿Cuál es la pregunta que quieres que tu compañero responda?” // “What is the question you want your partner to answer?”
• “Cómo podrías terminar esta pregunta: ’¿Cuántos estudiantes escogieron _____?’” // “How could you finish this question, ‘How many students chose _____?’”

• Share and record the students’ questions about their data.
• “Ahora le haremos algunas de estas preguntas a nuestro compañero” // “Now we will ask our partner some of these questions.”

The purpose of this activity is for students to ask and answer questions about data. Students ask each other questions about the data collected in the previous activity. Most of the questions should be able to be answered using the data representation, however if a question can’t be answered, the students should explain to their partner why they can’t answer the question using the data representation. Connecting cubes should be available to all students, since some questions may require adding within 20.

Required preparation:

• Display the list of questions from the synthesis in the previous activity.

• Groups of 2
• Give students access to connecting cubes.

• “Ahora van jugar por turnos a hacer y responder preguntas sobre sus datos. La persona que tenga el primer turno le muestra su representación de los datos a su compañero y le hace una pregunta sobre los datos. Su compañero responde la pregunta y explica cómo encontró la respuesta. Hagan lo mismo con otra pregunta y luego intercambien roles. Si su compañero les hace una pregunta que no se puede responder usando la representación de los datos, expliquen por qué no se puede responder” // “Now you will take turns asking and answering questions about your data. The person who goes first shows their data representation to their partner and asks a question about the data. Their partner answers the question and explains how they found the answer. Repeat with another question, then switch roles. If your partner asks you a question that can’t be answered using the data representation, explain why it can’t be answered."
• 7 minutes: partner work time

• Choose one of the questions from the list created in Activity 2.
• “Usen su representación de los datos para responder la pregunta” // “Use your data representation to answer the question.”
• Share responses.
• “¿Por qué tenemos dos respuestas diferentes para las preguntas?” // “Why do we have two different answers to the questions?” (We have two different sets of data.)