1. Displaying Numerical Data Using Box Plots

2. Warm Up OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to describe all parts of a box plot to a partner.
A group of taste testers reviewed a brand of natural peanut butter. They gave the peanut butter a rating of points depending on its quality. The ratings are below:
Find the minimum, maximum, median, range, and interquartile
range (IQR) for this set of data.
(5 min) 0 – 5
In-Class Notes
Anticipate that students may not know which data points to use to find the lower and upper quartile since there are an even number of data points (they may forget whether they should use 61.5 as a value when finding these values).
Review answers as a class before clicking to show answers.
Ensure that students report their answers with a label (points).
Scaffolding: Show how to find the IQR.
Follow-up questions: What does a median of 61.5 points mean? What does a range of 55 points mean? What does an interquartile range of 12 points mean?
Challenge question follow-up: After the 16th score, the mean falls to 60 points. What do you know has to be true about score #16?
Preparation Notes
This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them.
Min = 34 points Max = 89 points Median = 61.5 points Range = 55 points Interquartile range (IQR) = 12 points

3. Warm Up OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to describe all parts of a box plot to a partner.
A group of taste testers reviewed a brand of natural peanut butter. They gave the peanut butter a rating of points depending on its quality. The ratings are below:
IQR = Q3 – Q1
Find the minimum, maximum, median, range, and interquartile
range (IQR) for this set of data.
(5 min) 0 – 5
In-Class Notes
Anticipate that students may not know which data points to use to find the lower and upper quartile since there are an even number of data points (they may forget whether they should use 61.5 as a value when finding these values).
Review answers as a class before clicking to show answers.
Ensure that students report their answers with a label (points).
Scaffolding: Show how to find the IQR.
Follow-up questions: What does a median of 61.5 points mean? What does a range of 55 points mean? What does an interquartile range of 12 points mean?
Challenge question follow-up: After the 16th score, the mean falls to 60 points. What do you know has to be true about score #16?
Preparation Notes
This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them.
Min = 34 points Max = 89 points Median = 61.5 points Range = 55 points Interquartile range (IQR) = 12 points

4. Launch Think-Pair-Share
List some of the ways this information could be displayed visually.
Bar Graph?
Line Plot?
Circle Graph?
(2 min) 6 – 8
In-Class Notes
Poll students to see if they prefer to analyze data sets by just looking at the data (like it is presented on this slide) or if they prefer to use tables/graphs. This will help highlight the purpose of box plots.
Ask students, Would you prefer to analyze this data in table or graph form? Which visual display is more useful to you?
Ask students to brainstorm ways to display this information visually (tables, graphs, etc).
After students have shared out, click to show possible representations.
Ask students to assess each visual representation. For example, “Would it make sense to use a line plot to represent this set of data? Why/why not?”
Preparation Notes
Table?

5. Launch Whole Class
A box plot is one of the ways this data can be displayed.
(<1 min) 6 – 8
In-Class Notes
Inform students that today in class they will learn about constructing box plots, which allow readers to easily analyze a set of data.
Preparation Notes

6. Launch Whole Class Example of a box plot: (1 min) 8 – 9 In-Class Notes
Questions to ask: What is the box plot about? What is a quality rating? What do you notice about the box plot? Can you make any educated guesses about how to “translate” the box plot? Can you see why it is sometimes called a box-and-whisker plot?
Point out that like other graphs they have seen before, a box plot needs a title and a label along the x-axis
Preparation Notes
This slide is included to just show students what a box plot looks like before dissecting it. Students do not need to understand how to read this box plot. It is included to provide exposure before going into context.

7. Launch Vocabulary Box Plot:
A graph that uses a rectangle (box) to represent the middle 50% of a set of data and “whiskers” at both ends to represent the remainder of the data.
(3 min) 9 – 12
In-Class Notes
Inform students that box plots are also called box-and-whisker plots.
Before showing the definition, ask students to create a definition of a box plot in their groups (30 seconds). Keep in mind that this is the first time that they will have seen box plots.
Discuss ideas about the definition of box plots.
Click to show formal definition.
Students should write the definition down in their notes (preferably in a vocabulary section).
Ask a student to come up and point to the “rectangle” or the “box.”
Ask another student to come up and point to the “whiskers.”
Ask a student to point to where the middle 50% of the data lies. Follow-up questions: If the rectangle represents 50% of the data, how is that 50% broken down within the two areas of the box? If the box represents 50% of the data, where does the other 50% of the data lie?
Preparation Notes

8. Launch Turn-and-talk
A box plot is constructed from the five-number summary of a set of data.
Using the graph and what you know about range and interquartile range, what do you think the five-number summary consists of?
(2 min) 12 – 14
In-Class Notes
Ask students to talk about this question with a partner before discussing it as a class.
For students who are struggling, click on hint to show the yellow dots on the number line. Inform students that these yellow dots represent the values from the five-number summary. Remind them to use their understanding of quartiles (specifically Q1 and Q3) to help them.
Question to ask: Why is the graph drawn above the number line instead of on the number line?
Preparation Notes
This slide is connected to Math PS 6 – Attend to Precision: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning.

9. Launch Turn-and-talk
A box plot is constructed from the five-number summary of a set of data.
Using the graph and what you know about range and interquartile range, what do you think the five-number summary consists of?
(2 min) 12 – 14
In-Class Notes
Ask students to talk about this question with a partner before discussing it as a class.
For students who are struggling, click on hint to show the yellow dots on the number line. Inform students that these yellow dots represent the values from the five-number summary. Remind them to use their understanding of quartiles (specifically Q1 and Q3) to help them.
Question to ask: Why is the graph drawn above the number line instead of on the number line?
Preparation Notes
This slide is connected to Math PS 6 – Attend to Precision: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning.

10. Launch Notes Five-Number Summary Minimum Lower Quartile (Q1) Median
Upper Quartile (Q3)
Maximum
Median = 61.5
(2 min) 14 – 16
In-Class Notes
Begin by listing the five components of the five-number summary.
Students should write what the five-number summary is made up of and the set of data provided in their notebooks. Notes should be titled “Box Plots.”
Ask students to work with a partner to find each part of the five-number summary for this set of data. Refer them to their warm-up where they found the range and IQR if they need support.
Once students have finished and have shared out, click to show answers.
Anticipate the following misconception: Students will have trouble defining Q1 and Q3. The word quartile leads students to believe it will be a section on the graph. In reality, students should view Q1 and Q3 as medians. Instead of being the median of the whole set of data, they are the median of the lower and upper half of the data, respectively. Push students to explain in their own words what Q1 and Q3 represent before moving on. When a student has succinctly defined Q1 and Q3, ask a few other students to repeat or paraphrase that student’s ideas.
Preparation Notes
Minimum
Upper Quartile (Q3)
Lower Quartile (Q1)
Maximum

11. Launch Think-Pair-Share
The box plot below shows how the five-number summary corresponds to the box and whiskers of the box plot.
(2 min) 16 – 18
In-Class Notes
Students should think about this question independently for 30 seconds before talking to a peer. Once pairs have discussed the question for about 1 minute, review ideas as a class.
Questions to ask: Why is the graph drawn above the number line instead of on top of it? Does the number line for every box plot range from 0-100? Could the creator of this box plot have chosen a different range for the number line? How would this have affected the intervals, or scale, of the number line?
Inform students that typically the five-number summary is not included on a box plot (the words minimum value, lower quartile, etc.). They are included today just to reinforce what the values represent.
Preparation Notes
Based on the figures above, how do you make a box plot using the five-number summary?

12. Launch Notes
Once you have found the five-number summary, follow these steps to make a box plot: 1. Write the data in order from least to greatest 2. Draw a number line that can show the data in equal intervals 3. Mark the median 4. Mark the median of the upper half (the upper quartile, or Q3) 5. Mark the median of the lower half (the lower quartile, or Q1) 6. Mark the maximum (the greatest number) 7. Mark the minimum (the lowest number) 8. Draw a box between the lower quartile and the upper quartile 9. Draw a vertical line through the median inside the box 10. Draw two horizontal lines ("whiskers") from the rectangle to the extremes (minimum and maximum)
(3 min) 18 – 21
In-Class Notes
Distribute the hand out that includes these steps and the blank box plot.
Read through the steps as a class.
Ask students to use the steps to fill in the values on the box plot.
Preparation Notes
Before class, have these steps and a blank box plot drawn on paper for kids for the set of data from Slide 19. Hand out a copy of this to each student.
It may be helpful to have these steps written on chart paper so that they can be posted in the classroom.

13. Launch Check Your Work!
(<1 min) 18 – 21
In-Class Notes
Give students about 30 seconds to compare their box plot to what it should look like.
Poll students to see what they chose to use as the range and scale for their number lines.
Follow-Up Questions: Why are the whiskers longer than the box? What does that tell you about the range of the different quartiles? Why is one portion of the box bigger than the other?
Ask students to make statements about the peanut butter using the box plot. For example, 50% of the ratings were between roughly 57 points and 70 points. 75% of the ratings were below 70 points. If 75% of the ratings were below 70 points, how would you judge the quality of this peanut butter?
Anticipate that it may be difficult for some students to see that each “section” of the graph represents 25% of the data values, as students see 25% as one of four equal pieces, and in terms of actual size, the four “sections” are not equal.
Preparation Notes
This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them.

14. Practice Four Corners 25%
About what percent of the data values fall in the following interval?
after the upper quartile
25%
(5 min) 44 – 49
In-Class Notes
Use this question as an example before beginning the game.
Students should talk through this question in small groups.
Ask students to share out answers and ask for supporting explanations.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

15. Practice Four Corners 50%
About what percent of the data values fall in the following interval?
before the median
50%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

16. Practice Four Corners 50%
About what percent of the data values fall in the following interval?
after the median
50%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

17. Practice Four Corners 50%
About what percent of the data values fall in the following interval?
in the box (between the upper and lower quartiles)
50%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

18. Practice Four Corners 75%
About what percent of the data values fall in the following interval?
before the upper quartile
75%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

19. Practice Four Corners 25%
About what percent of the data values fall in the following interval?
before the lower quartile
25%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

20. Practice Four Corners 75%
About what percent of the data values fall in the following interval?
after the lower quartile
75%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

21. Practice Four Corners 25%
About what percent of the data values fall in the following interval?
between the median and the upper quartile
25%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

22. Practice Four Corners 25%
About what percent of the data values fall in the following interval?
between the median and the lower quartile
25%
(5 min) 44 – 49
In-Class Notes
Give students about 15 seconds to think about this question in their heads.
On a cue from the teacher, students should move to their chosen corners.
Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice.
Preparation Notes
This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments.