Lesson 4

The purpose of this activity is for students to subitize or use grouping strategies to describe the number of dots they see. Although the dots have been deliberately grouped by 5 to elicit counting by 5 as a strategy, students may see 2 groups of 5 as 10. Grouping strategies and skip-counting by 2, 5, and 10 offer a review of grade 2 work and build toward multiplication in future lessons. 

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash the image.
• 30 seconds: quiet think time

• Display the image. 
• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

• “¿Qué patrón vieron primero y cómo les ayudó a averiguar el total?” // “What pattern did you see first and how did this help you figure out the total?” (I saw that the dots were in groups of 5. This helped me because I know how to count by 5.)
• Consider asking:
  • “¿Alguien vio los puntos de la misma manera, pero lo explicaría de otra forma?” // “Did anyone see the dots the same way but would explain it differently?”
  • “¿Alguien quiere compartir otra observación sobre la manera en que _____ vio los puntos?” // “Does anyone want to add an observation to the way _____ saw the dots?”

The purpose of this activity is for students to gather and organize categorical data about their classmates. Students record their classmates’ preferred way to travel and discuss advantages and disadvantages of displaying categorical data in a table.

To make the data collection process faster, students can collect their responses within their group first and then each group can share out how many students chose each way of travel. Their names can be pre-printed in a table for them or they could only write the person’s first name and way of travel abbreviation (given in the task statement) in the table. In the next activity, students create a scaled picture graph for this categorical data.

• Groups of 4 

• “Hoy van a encuestar a sus compañeros. Van a empezar con su grupo y luego recolectaremos los datos de toda la clase” // “Today you will survey your classmates. You will start with your group and then we will collect the group data as a class.”
• Give directions for how students should collect the categorical data (see suggestions in the narrative).
• 10 minutes: students record classmate responses

• “¿En qué nos ayuda tener estos datos en forma de lista? ¿En qué no nos ayuda?” // “What’s helpful about having this data in the form of a list? What's not helpful?” (We know the way each person would like to travel. It’s hard to see how many people would like to travel each way.)
• Math Community: Ask students to reflect on both individual and group actions while considering the question “¿Qué normas o expectativas tuvimos en mente cuando hicimos matemáticas juntos en nuestra comunidad matemática?” // “What norms, or expectations, were we mindful of as we did math together in our math community?”
• Record and display their responses under the “Norms”​ ​header.

The purpose of this activity is for students to apply understandings from previous lessons to create a picture graph with a scale of 2 from the categorical data they gathered. Students are guided to use a scale of 2 but can choose their own symbol. Depending on the data, students may need to use a half symbol in order to represent an odd number of students choosing a specific method of travel. This idea is discussed in the synthesis.

Students will use their scaled picture graphs again in the next lesson.

• Groups of 2
• “Queremos representar los datos que recogimos en la encuesta en una gráfica de dibujos. ¿Cómo lo podemos hacer sin tener que hacer un dibujo por cada estudiante de la clase?” // “How can we represent our survey data in a picture graph without having to draw a picture for each student in our class?” (We can make each symbol represent more than one student so we don’t have to draw as much.)

• “Representen los datos que recolectaron en su propia gráfica de dibujos con escala. Cada dibujo debe representar 2 estudiantes” // “Represent the data that you collected in your own scaled picture graph where each picture represents 2 students.”
• 10 minutes: independent work time
• Circulate as students work:
  • Encourage them to include a title, category labels, and key.
  • Pay attention to how students are grouping by 2.
  • Support students with questions they may have (especially around representing odd number amounts).
• “Comparen su gráfica con la de su pareja” // “Compare your graph with your partner.”
• 2 minutes: partner discussion
• Monitor for a graph that uses a half picture to show an odd number of students in one of the categories to share during the activity synthesis.

If students choose symbols that are time-consuming to draw, consider asking:

• “¿Cómo escogiste qué símbolo usar en tu gráfica?” // “How did you choose the symbol to use on your graph?”
• “¿Cómo puedes hacer que el símbolo sea más fácil de dibujar?” // “How could you make your symbol easier to draw?”

• Display selected student work.
• “¿De qué manera esta gráfica representa los datos de la encuesta de nuestra clase? (Es decir, los datos recolectados a partir de la encuesta)” // “How does this graph represent the survey data from our class?”
• “¿De qué manera _____ representó el número de estudiantes que escogieron una forma de viajar cuando el número era impar?” // “How did _____ represent the number of students who picked a way of travel when it was an odd number?”
• “¿Qué preguntas tienen sobre cómo hacer una gráfica de dibujos con escala?” // “What questions do you have about creating a scaled picture graph?” (Could a face represent 3 students or 5 students? Can you use whatever picture you want to represent 2 students?)