2.1: Notice and Wonder: Flipping Coins (5 minutes)
The purpose of this warm-up is to elicit the idea of how a frequency table and dot plot are connected, which will be useful when students create dot plots in a later activity. While students may notice and wonder many things about these representations, the connections between the summaries of the data are the important discussion points.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how the frequency for a value is related to the number of dots above the value in the number line on the dot plot.
Display the prompt, table, and dot plot for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
200 students flip a coin 100 times and record the number of heads that are flipped.
What do you notice? What do you wonder?
|number of heads flipped
|number of heads flipped
|number of heads flipped
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the representations. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If the connection between the representations does not come up during the conversation, ask students to discuss this idea.
2.2: Human Dot Plot (20 minutes)
In a previous course, students learned to construct dot plots and histograms. In this activity, students construct a human dot plot to represent class data, which provides a concrete way to interpret the meaning of this representation.
Questions for data collection aren’t printed in the task; they are suggested in the launch, to give you the flexibility to customize the questions for your class.
Before class begins, create a number line along one side of the classroom using painter’s tape on the floor or along the wall. Either align a row of desks to each whole number, or leave enough room for students to stand several students deep in front of the number line.
Ask all students to silently think of their answer to the same question. Choose a question that has an answer that is a whole number that you think will work best. Here are some suggestions:
- How many pets are in your household?
- How many siblings do you have?
- How many articles of clothing do you have on right now?
- How many days could you go without talking?
Draw students’ attention to the number line created ahead of time, and that sitting at a desk aligned with a certain value on the number line means that that number is true for them. Ask students to think about their answer to the question, and move to a seat that matches their answer.
Before students return to their original seats, make a list for all to see of the numbers in the data set. Tell students that aligning the elements of a data set to a number line creates a representation called a dot plot.
- Follow your teacher’s directions to create a human dot plot.
- Create a dot plot that represents the same data as the human dot plot.
Ask students questions to help them interpret the human dot plot they created. All answers vary, depending on the data collected from the class. For example, if students answered the question, “How many siblings do you have?”, here are sample questions for the data set:
- “How many students have no siblings?” (2)
- “How many students have more than 3 siblings?” (7)
- “How many siblings does [a certain student] have?” ( [the certain student] has 1 sibling.)
- “Can we figure out the median number of siblings?” (Yes, the median is _____.)
- “Who has the most siblings here?” ( _____ has the most siblings.)
- “Most of your classmates have _____ siblings.” (Most of my classmates have 3 siblings, because that is the number with the highest frequency.)
2.3: Constructing a Dot Plot (15 minutes)
Each student should work to create the dot plot from the data collected from the class. Students should collaborate with their partner when answering the questions about the data set. Monitor for students’ strategies for expressing the typical amount of sleep (some may calculate mean, and some may calculate median). Highlight that the two ideas of “typical” for a given data set will be emphasized in later lessons.
This activity will help students when they analyze data in a later lesson. It also gives them practice with collecting data from classmates, and representing it with a graph, which is a skill they will use throughout the unit.
Ask students to think about how many hours of sleep they get on a typical night. Poll the class and display this list of values for all to see. Arrange students in groups of 2 so that they can collaborate with a partner.
Using the class data, construct a dot plot.
Use your dot plot to answer the following questions:
- What is the largest value in the data set? The smallest? What do these numbers represent?
- What is a typical amount of sleep for a student in your class?
- It is recommended that teenagers get 8–10 hours of sleep each night to perform at their best the following day. Based on the data, how well do you think your class would perform on a test? Explain your reasoning.
- What would the dot plot look like for a class that has the same number of students, but those students tend to get less sleep than students in your class?
Students may think the dots should represent the amount of sleep instead of the number of people who got the amount of sleep as the corresponding number on the number line. For example, four dots over the number 5 means that four people got 5 hours of sleep. Students sometimes read this as 5 people getting four hours of sleep. The dots represent the frequency of the numbers on the number line. It may help students to label the number line before adding their dots for the data. In this case, the number line should be labeled “hours of sleep” to show that the numbers on the number line represent amount of sleep rather than number of people in a category. Students may need guidance on what interval to use in creating their number lines. Remind students of the previous task and how each dot represented a single student.
The goal of this activity is to ensure students understand the meaning of a dot plot. Here are some sample questions to promote a class discussion:
- “What are similarities and differences between dot plots and box plots?” (Dot plots and box plots both help you find the median, lowest value, and highest value. They are different because a dot plot provides enough information to find the mean, and the box plot does not.)
- “When is a dot plot more useful in representing data?” (A dot plot is more useful if you want to know about frequency of individual values or see the shape of the distribution. The box plot provides a range of points, so it is not possible to know how many data points are included in the data and how many times.)
The goal of the lesson discussion is for students to connect how dot plots are created with what they show about a data set, and contrast them with box plots. For example, students might notice that while a dot plot illustrates a distribution more precisely, a box plot shows the median without any further interpretation required. Discuss how to construct dot plots and when they are useful. Here are sample questions to promote a class discussion:
- “How do dot plots help to analyze data?” (Dot plots show each data point in a data set. They also show the shape of a data distribution.)
- “What are similarities and differences between dot plots and box plots?” (They both give us information about the the distribution of a data set. A dot plot shows where each data point lies along a number line, but a box plot only shows the values that split the data set into four quarters.)