This Warm-up prompts students to compare four survey questions. It gives students a reason to use language precisely (MP6) and gives you the opportunity to hear how they use terminology and talk about characteristics of the items in comparison to one another. 

Invite each group to share one reason why a particular set of two questions go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which questions go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any statistical terminology they use, such as “numerical data,” “categorical data,” or “average,” and to clarify their reasoning as needed. Consider asking:

• “How do you know . . . ?”
• “What do you mean by . . . ?”
• “Can you say that in another way?”

Math Community

After the Warm-up, tell students that today is the start of planning the type of mathematical community they want to be a part of for this school year. The start of this work will take several weeks as the class gets to know one another, reflects on past classroom experiences, and shares their hopes for the year.

Display and read aloud the question “What do you think it should look like and sound like to do math together as a mathematical community?” Give students 2 minutes of quiet think time and then 1–2 minutes to share with a partner. Ask students to record their thoughts on sticky notes and then place the notes on the sheet of chart paper. Thank students for sharing their thoughts and tell them that the sticky notes will be collected into a class chart and used at the start of the next discussion.

After the lesson is complete, review the sticky notes to identify themes. Make a Math Community Chart to display in the classroom. See the blackline master Blank Math Community Chart for one way to set up this chart. Depending on resources and wall space, this may look like a chart paper hung on the wall, a regular sheet of paper to display using a document camera, or a digital version that can be projected. Add the identified themes from the students’ sticky notes to the student section of the “Doing Math” column of the chart.

In this activity, students begin classifying questions as “statistical” or “non-statistical” and data as “numerical” or “categorical” while getting to know a little about their classmates.

Each group of four students is assigned three questions. One of the three they are assigned is a non-statistical question, one would generate numerical data, and one would generate categorical data. The questions could be changed to questions that are more relevant to students and would help students learn about each other, as long as each set of three  questions contains one question of each of the three types described. Groups also generate a fourth question of their own that can be answered with data. First, the group comes up with four survey questions that they can ask their classmates to collect data about their four questions of interest. Then, they collect data from their classmates by asking the survey questions. Finally, they summarize their results to answer the four questions of interest and reflect on the nature of the different questions they attempted to answer.

In a later lesson, students will represent the distribution of data collected in this activity graphically. If they record the data in their workbooks, it will be easy to retrieve later. If students record data some other way, be sure that your method allows them to easily retrieve the data later.

This is the first time Math Language Routine 2: Collect and Display is suggested in this course. In this routine, the teacher circulates, listens, and jots down words, phrases, drawings, or writing that students use. The language collected is displayed visually for the whole class to use throughout the lesson and unit. The purpose of this routine is to capture a variety of students’ words and phrases—including especially everyday or social language and non-English—in a display that students can refer to, build on, or make connections with during future discussions, and to increase students’ awareness of language used in mathematics conversations.

Display the numbered questions from all of the sets for all to see.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their responses. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond. (For example, “All of these questions require numerical data to find an answer.”)

Then tell students that we call data collected to answer questions of interest like those numbered  1 numerical data, and that we call data collected by questions like those numbered 2 categorical data. Questions like those numbered 3 are non-statistical questions because there will be no variability in the responses. Questions like those numbered 1 and 2 are called statistical questions because they require the collection of data and there is anticipated variability in the responses.

Ask students to sort the collected language from the display into either numerical or categorical data as well as either statistical or non-statistical questions. For example, “There is only 1 answer” would be categorized as “non-statistical.”