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
• “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.

• “Did anyone see the same number of dots in a different way?”
• Consider asking:
  • “Who can restate the way _____ saw the dots in different words?”
  • “Did anyone see the dots the same way but would explain it differently?”
  • “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.
• “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.
• “Think about which is your favorite and take one connecting cube.”
• Collect and display the connecting cubes in a scattered arrangement. 

• “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.)
• “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.
• “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.
• “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

• “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:
  • “Which category is this? What can you do so others can tell what each category is on your paper?”
  • “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.

• “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

• “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
• “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.
• “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.)
• “There are different ways to represent our data, but no matter the representation, the data should tell the same story.”