Unit 3, Lesson 1
Getting to Know You
Integrated Math 1
1.1
Warm-up
Standards Alignment
Building On
6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages.
Addressing
Building Toward
HSS-ID.A.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
Instructional Routines
NoneMaterials
NoneActivity Narrative
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.
Launch
Arrange students in groups of 2–4. Display the questions for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, tell each student to share the items in their group and the property that those items share that any other items do not.
Activity
NoneUse the four questions to make a group of two related questions. What property do the items in the group share that the others do not?
- Question A: How many potato chips are in this bag of chips?
- Question B: What is the typical number of chips in a bag of chips?
- Question C: What type of chips are these?
- Question D: What type of chips do students in this class prefer?
Student Response
Loading...
Building on Student Thinking
Activity Synthesis
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?”
1.2
Activity
Instructional Routines
MLR2: Collect and DisplayMaterials
NoneActivity Narrative
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 activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.
Lesson Synthesis
To promote student understanding of the differences between statistical and non-statistical questions and classifying data as numerical or categorical, ask:
- “What makes a question statistical?” (There is variability in the data collected.)
- “What is an example of a non-statistical question?” (What value for makes the equation true?)
- “What is an example of a statistical question that we have not used in class?” (On average, how many people eat breakfast every day?)
- “What type of data are collected to answer the statistical question, ‘Would the class rather have pizza or donuts?’” (Categorical)
- “What is an example of a statistical question that results in numerical data?” (What is the typical surface area of styrofoam pellets?)
To help prepare students for the next lesson, ask:
- “What are some different ways to represent data graphically?” (Bar graphs, dot plots, box plots, pie charts, and histograms.)
Student Lesson Summary
Statistics is about using data to solve problems or make decisions. There are two types of data:
- Numerical data are expressed using numbers that can be put in order. For example, the question “How tall are the students in this class?” would involve measuring the height of each student, resulting in numerical data.
- Categorical data are expressed using characteristics. For example, the question “What brand of phones do people use?” would involve surveying several people, with their answers resulting in categorical data.
The question that you ask determines the type of data that you collect and whether or not there is variability in the data collected. In earlier grades, you learned that there is variability in a data set if not all of the values in the data set are the same. These are examples of statistical questions because they are answered by collecting data that have variability:
- “What is the average class size at this school?” would produce numerical data with some variability.
- “What are the favorite colors of students in this class?” would produce categorical data with some variability.
These are examples of non-statistical questions because they are answered by collecting data that does not vary:
- “How many students are on the roster for this class?” has only one possible answer. There is only one value in the data set, so there is no variability.
- “What color is this marker?” has only one answer. There is only one value in the data set, so there is no variability.