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Unit 1, Lesson 1

Human Box Plot

Extra Support Materials for Algebra 1

1.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Math Talk MLR8: Discussion Supports

Materials

None

Activity Narrative

This Math Talk focuses on mental subtraction. It encourages students to think about patterns and to rely on structure to mentally solve problems. The strategies elicited here will be helpful when students compute the interquartile range.

To solve each expression, students need to look for and make use of structure (MP7).

This is the first Math Talk activity in the course. See the Launch for extended instructions for facilitating this activity successfully.

Launch

This is the first time students do the Math Talk instructional routine in this course, so it is important to explain how it works before starting.

Explain that a Math Talk has four problems, revealed one at a time. For each problem, students have a minute to quietly think and are to give a signal when they have an answer and a strategy. The teacher then selects students to share different strategies (likely 2–3, given limited time), and might ask questions such as “Who thought about it in a different way?” The teacher then records the responses for all to see, and might ask clarifying questions about the strategies before revealing the next problem.

Consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. Signals may include a thumbs-up or a certain number of fingers that tells the number of responses they have. Using signals is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Activity

None

Evaluate mentally.

Activity Synthesis

The goal of this discussion is to review students’ strategies for subtracting mentally.

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

“Who can restate ’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to earlier problems do you see?”

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. Examples:

“First, I because .”
“I noticed , so I .”

Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

1.2

Activity

Instructional Routines

Poll the Class

Materials

To Gather

Index cards Masking tape Slips of paper

Activity Narrative

In a previous course, students learned to find the five-number summary of data sets (minimum, maximum, quartile 1, median, and quartile 3) and construct box plots from this data. They also calculated the range and interquartile range of distributions. In this activity, students recall the meaning of the values in the five-number summary and construct a box plot. This will be useful when students analyze data in a later lesson. They explore this new representation of data by creating a human box plot to represent class data. Students reason abstractly and quantitatively (MP2) as they interpret the box plot that relates to data about their classmates.

1.3

Activity

Instructional Routines

MLR2: Collect and Display

Materials

To Gather

Tools for creating a visual display

Activity Narrative

To construct their box plots, students calculate the five-number summary: minimum, maximum, median, first quartile, and third quartile. At this stage, students’ drawings of the box plot may be considered rough drafts that are needed only to demonstrate understanding of the five-number summary and the range. Although some students may mention the interquartile range, a deep understanding is not needed at this stage.

As the groups display their box plots for the class to see, students observe the different box plots to answer the questions.

This is the first time Math Language Routine 2: Collect and Display is suggested in this course. In this routine, the teacher circulates and listens to student talk while jotting 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.

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.

Launch

Before the lesson, use thin masking tape to make a number line on the ground. If the floor is tiled with equal-sized tiles, consider using the tiles for the intervals of the number line. Otherwise, mark off equal intervals on the tape. The number line should cover at least the distance between the least data value (the least number of pockets) to the greatest (the greatest number of pockets).

Distribute a slip of paper to each student, and ask students to write down the number of pockets or sections in their backpack. (Another metric could be used if there is one more appropriate for students. Examples may include the number of letters in their first and last names or the number of minutes it takes them to travel to school.)

Poll the class to create a list of these numbers for all to see. It is recommended that these numbers are not put in order.

Ask students to stand up, holding their slip of paper in front of them, and place themselves on the point on the number line that corresponds to their number. (Consider asking students to do so without speaking at all.) Students who have the same numbers should stand one in front of the other. Inquire about each component of the five-number summary in regard to the class’s data set. Ask students, “What are the maximum and minimum values? What value splits the group in half?” Remind students that the value that splits the group in half is called the "median" of the data set. Ask students, “If we split the class into quarters (or fourths), how many students would be in each group? What value splits the lower half of the data in half again?” Students should understand that splitting the lower half of the data in half gives the first quartile (Q1), and splitting the upper half of the data in half gives the third quartile (Q3).

Record and display the five-number summary for all to see.

Hold up the index card that has been labeled with “minimum.” Ask students who should claim the card, then hand the card to the appropriate student. Do the same for the other labels of the five-number summary. If any of the quartiles falls between two students’ numbers, write that number on the index card, and ask both students to hold that card together.

Now that the five numbers are identified and each is associated with one or more students, use wide masking tape to construct a box plot.

Form a rectangle on the ground by attaching the tape around the group of students between Q1 and Q3. If a quartile is between two people, put the tape down between them. If a quartile has the value of a student’s number, put the tape down at that value and ask the student to stand on it.
Put a tape segment at Q2, from the top side of the rectangle to the bottom side, to subdivide the rectangle into two smaller rectangles. If Q2 is a student’s number, ask the student to stand on the tape.
For the left whisker, attach the end of the tape to the Q1 end of the rectangle, then extend it to where the student holding the “minimum” card is standing. Do the same for the right whisker, from Q3 to the maximum.
Tape the five-number summary cards and students’ cards that correspond to them in the right locations. This image shows an example of a completed human box plot.

Explain to students that they have made a human box plot. Consider taking a photo of the box plot for reference and discussion later.

Activity

None

Using the list of data, find the lower quartile, median, upper quartile, lowest value, and highest value of the data set. Follow your teacher’s directions to create a human box plot.

Student Response

to access Student Response.

Building on Student Thinking

If students struggle to get started finding the 5 values in the task, consider asking:

“What are the meanings of the 5 values you are identifying?”
“How could you organize the numbers to make it easier to find the values you are looking for?”

Launch

Arrange students in groups of 2–4. Give each group tools for creating a visual display. Assign each group a data set:

Data set A: The height, in inches, of each plant in a garden: 7, 3, 4, 1, 7, 10, 3
Data set B: The age of each dancer at a dance camp: 3, 3, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 11, 13
Data set C: The number of points a player scored in each of their basketball games: 19, 16, 15, 21, 13, 16, 17, 19
Data set D: A student’s score, as a percentage, on each of several quizzes: 81, 81, 82, 83, 83, 83, 84, 86, 86
Data set E: The temperature, in degrees Fahrenheit, in each sauna at the spa: 132, 126, 129, 130, 132, 137, 134, 128
Data set F: The high temperature, in degrees Fahrenheit, each day during a family vacation: 50, 70, 70, 73, 75, 75, 80

Encourage each group to make a rough draft of their box plot and then create a visual display of their box plot. As each group finishes its box plot, post them around the room. Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language students use to create their box plots. Display words and phrases, such as: “minimum,” “maximum,” “median,” “Q1,” “Q3,” “first quartile,” “third quartile,” “middle,” “quarter,” and “find the middle of the first half.” Once all the displays are ready, invite students to observe each posted box plot and answer the questions in the Task Statement.

Activity

None

With a partner, calculate the five-number summary and create a box plot of your data set. When you are done, write the name of your data set, and display your box plot for the class to see. Then, find the answers to the questions below from your classmates’ box plots.

Which data set’s greatest value is 10?
Which data set has the largest range?
Which data set has a median of 16.5?
Which data set has the greatest upper quartile value?
Which data set’s least value is 3?
Which data set has the smallest range?

Student Response

to access Student Response.

Building on Student Thinking

Students may not remember how to find the five-number summary. Consider asking:

"How did we find the five-number summary of the human box plot?"
"What is another tool you can use to find the information you need?"

Activity Synthesis

The goal of this activity is for students to remember how to construct and interpret a box plot by creating one and then interpreting several. Direct students’ attention to the reference created using Collect and Display. Ask students to share how they identified each part of the five-number summary in their classmates' box plots. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Ask students questions to prompt discussion about their experiences constructing box plots:

“There is a Q1 and Q3. Why do you think there is no Q2?” (The median is a quartile itself. There are three quartiles that divide the data set into four groups, and the median of the data set is Q2.)
“What was the most difficult part to plot? Why?” (The quartiles were most difficult, because the highest and lowest values of the data set are straightforward to find no matter the order of the data. However, to calculate the quartiles, we need to list the data set in order and know which values to look for.)
“Does it make sense that the range for the temperature on the family vacation is greater than the range for the temperatures in the saunas? Explain your reasoning.” (Yes. The high temperature can vary from day to day, but saunas are generally kept at around the same temperature.)

The goal of the lesson is for students to connect components of a box plot to interpretations of the data set. For example, the box plot shows the median and quartiles, which helps us to calculate the interquartile range and determine how spread out the data is. Discuss how to construct box plots and when they are useful. Here are sample questions to prompt a class discussion:

“How do box plots help to analyze data?” (They show variability of a data set. By glancing at a box plot, the range is straightforward to observe, and the interquartile range is the distance between the upper and lower quartiles. Also, the median is a center of the data set.)
“When are box plots useful?” (Box plots are useful for visualizing some characteristics of large data sets and comparing two data sets.)
“What are other ways to represent data?” (We can represent data with tables, histograms, and dot plots.)
“What are some strategies you found useful when creating a box plot?” (It was easier for me to find the median first, and then each quartile.)

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Lesson 1

Human Box Plot

Warm-up

Standards Alignment

Building On

Addressing

2.NBT.B.5

Building Toward

HSS-ID.A.2

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity

Instructional Routines

Materials

To Gather

Activity Narrative

Activity

Instructional Routines

Materials

To Gather

Activity Narrative

Student Response

Building on Student Thinking

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

6.SP.B.4

Addressing

Building Toward

HSS-ID.A.1

Standards Alignment

Building On

6.SP.B.4

Addressing

Building Toward

HSS-ID.A.1