Lesson 9

The purpose of this How Many Do You See is for students to use their ability to know without counting (subitize) the number of dots. Students may recognize quantities up to four without having to count. They may recognize larger quantities when seen in a standard configuration, such as those seen on dot cubes. 

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see and how do you see them?”

• Flash the image.
• 10 seconds: quiet think time
• Display the image.
• Record responses.
• Repeat for each arrangement.

• “¿Alguien vio el mismo número de puntos, pero lo vio de otra forma?” // “Did anyone see the same number of dots in a different way?”
• Consider asking:
  • “¿Alguien puede expresar con otras palabras la forma en la que _____ vio los puntos?” // “Who can restate the way _____ saw the dots in different words?”
  • “¿Alguien vio los puntos de la misma forma, pero lo explicaría de otra manera?” // “Did anyone see the dots the same way but would explain it differently?”
  • “¿Alguien quiere compartir otra observación sobre la manera en la 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 collect information, or data, about their class and discuss how to organize it in a way that others will understand. Students learn how to conduct a survey and use connecting cubes to physically represent their vote which builds on their sorting work from previous lessons. During the activity synthesis, students discuss how to organize the cubes so they can easily determine how many are in each category.

Students need access to the data represented by connecting cubes in the next activity. Leave the cubes in a location where students can easily access them.

• Each group of 2 needs access to red, blue, and yellow connecting cubes.

• Groups of 2
• Give each group access to red, blue, and yellow connecting cubes.
• “Hoy vamos a hacer una encuesta. Una encuesta es una forma de recolectar información sobre las respuestas de un grupo de personas a la misma pregunta. La información que recolectamos sobre las cosas o las personas en el grupo se llama datos. Hagamos una encuesta y recolectemos datos sobre nuestro _____ favorito” // “Today we are going to take a survey. A survey is a way to collect information about a group of people's answers to the same question. The information we collect about the things or people in the group is called data. Let’s take a survey and collect data about our favorite _____.”
• Make sure there are three clear choices for students to choose from when answering the survey question. 
• Display the student book.
• Together, record the question and the answer that will be represented by each color.
• “Piensen cuál es su favorito y cojan un cubo encajable” // “Think about which is your favorite and take one connecting cube.”
• Collect and display the connecting cubes in a scattered arrangement. 

• “¿Qué observan sobre los datos que recolectamos?” // “What do you notice about the data that we collected?” (There are a lot of cubes and it’s hard to know how many of each there are.)
• “¿Qué podemos hacer para organizar los datos?” // “What could we do to organize the data?” (Organize the cubes by color, put the cubes in towers by color.)
• 30 seconds: quiet think time
• 1 minute: partner discussion

• Share responses.
• Group the cubes the ways students suggest.
• “¿De qué nos sirve organizar los cubos para mostrar los datos de nuestra encuesta?” // “How does organizing the cubes help us show the data from our class survey?” (When we organized, it was easier to see how many people voted for each.)

The purpose of this activity is for students to represent on paper the class data collected during the previous activity. Students determine how they want to represent their data which was represented by cubes in the previous activity. Representations may include squares (as cubes), tally marks, or number symbols. Students also label their representations.

• Have extra copies of the three-column table from a previous lesson available for students. 

• Groups of 2
• Give each group access to colored pencils or crayons and copies of the three-column table.
• “Tenemos que guardar los cubos al final de la clase de matemáticas, pero mañana vamos a querer ver los datos de nuestra clase. Con su pareja, piensen en un plan para mostrar nuestros datos en una hoja” // “We have to put the cubes away at the end of math, but we want to be able to see our class data tomorrow. With your partner, come up with a plan to show our data on paper.”
• 3 minutes: partner discussion

• “Ahora cada uno mostrará los datos de nuestra clase en una hoja” // “Now each of you will show our class data on paper.”
• 10 minutes: independent work time
• As students work, consider asking questions to help clarify representations:
  • “¿Cuál es esta categoría? ¿Qué pueden hacer para que otros entiendan qué es cada categoría que hay en la hoja?” // “Which category is this? What can you do so others can tell what each category is on your paper?”
  • “¿Cuál es el título de su representación de los datos?” // “What is the title of your data representation?”
• Monitor for different representations that use squares, tally marks, and numbers to share during the synthesis of the next activity.

• “Ahora veamos qué podemos aprender sobre las representaciones de los datos de nuestra clase” // “Now let’s see what we can learn about the representations of our class data.”

The purpose of this activity is for students to interpret the representations created in Activity 2. As the data is the same for each representation, students discuss how the representations they see are the same or different (MP3). This activity allows teachers to observe how students build on their work describing how objects were sorted while working with a new data context. Students may notice there are similarities in the number of votes for each category and make connections between representations. Students may notice that the representations are different as some use drawings and others use tally marks or numbers. They may also notice that the categories are in a different order. 

• Students need their representations from the previous activity.

• Groups of 2

• “Con su pareja, busquen un grupo que haya representado los datos de una forma distinta a ustedes. Una persona de su grupo intercambia hojas de trabajo con alguien del otro grupo. Hablen con su pareja sobre lo que observan que es parecido y lo que es diferente en cada representación” // “With your partner, find a group that represented the data in a different way from how you represented it. One person from each group switch papers with someone from the other group. With your partner, talk about what you notice is the same about each representation and what you notice is different.”
• 3 minutes: partner discussion
• “Compartan con el otro grupo cómo pensaron. ¿En qué están de acuerdo?” // “Share your thinking with the other group. What do you agree about?” (We agree that each representation shows the same number of votes in each category and the same total number of votes.)
• 3 minutes: small group discussion

• Display selected student representations from the previous activity.
• “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “What is the same about these representations? What is different?” (The way that groups represented the number of votes is different. The number of votes under each category is the same.)
• “Hay distintas formas de representar nuestros datos, pero, sin importar cuál sea la representación, los datos deben contar la misma historia” // “There are different ways to represent our data, but no matter the representation, the data should tell the same story.”