displaying numerical data using box plots 1. 2 lesson objective swbat display and analyze numerical...

Displaying Numerical Data Using Box Plots

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Lesson Objective SWBAT display and analyze numerical data using box plots.

Lesson Description The lesson begins with students engaging in a whole-class review of how to find the median, range, and IQR, with the IQR being the main focus. Following the review of the warm-up, students are introduced to the five-number summary of a data set. They then use that information to create a box plot. During the explore time, students continue to build on their understanding of how to create box plots by creating a poster-sized box plot in small groups using data generated from a class activity. After creating their box plots in small groups, students then assess the box plots of their peers. This provides an opportunity to clear up misconceptions related to the creation of box plots. The summary at the end of the small group activity focuses on the purpose of box plots. During the practice time, students move from creating box plots to analyzing box plots. The practice consists of a game of Four Corners where students are given a particular interval (less than the median, for example) and have to decide what percent of the data values fall within that interval. They move to the corner of the room that corresponds to their choice. Following the practice, students will be assessed on their understanding of box plots through an activity that utilizes paper plates. Throughout this portion of the lesson, students will be asked multiple choice questions (and T/F) and they will answer the questions by holding up a paper plate with the letter of their answer choice written on it. This allows the teacher to visually see which students have mastered the goals of the lesson and which need additional practice.

Lesson Overview (1 of 6)

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Lesson Vocabulary Box Plot: A graph that uses a rectangle to represent the middle50% of a set of data and “whiskers” at both ends to represent theremainder of the data.

Five-Number Summary:MinimumLower Quartile (Q1)MedianUpper Quartile (Q3)Maximum

Materials 1) Box plot class work handout 5) Colored Pencils/Markers

2) Notes handout 6) Chart Paper

3) Box plot homework 7) Post-Its

4) Steps to make a Box plot 8) Index cards

handout 9) Paper plates


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Scaffolding Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections.Handout on how to read and create box plots is provided for struggling students.

Enrichment Advanced Objective:SWBAT identify real world situations where one would use a box plot.

Ask students to brainstorm real life applications of this concept.

To support students in doing this, a copy of a newspaper or magazine may provide some ideas.


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Online Resources for Absent Students

http://www.purplemath.com/modules/boxwhisk.htm

http://nlvm.usu.edu/en/nav/frames_asid_200_g_3_t_5.html

http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html http://illuminations.nctm.org/ActivityDetail.aspx?ID=77


Common Core State Standard

6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

http://www.purplemath.com/modules/boxwhisk.htm

http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html

http://illuminations.nctm.org/ActivityDetail.aspx?ID=77

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Before and After Box plots, or box-and-whisker plots, are traditionally an eighth grade concept. As a result, this is most likely the first time that students at the sixth grade level will see box plots. While it is a new concept, students do come into the lesson with prior knowledge that will help them to create and analyze box plots. In the previous two lessons, students learned about the range and interquartile range. Through these lessons, students built an understanding of maximum, minimum, Q1 and Q3. Throughout the unit students have also been learning about the median. These are the five components of the five-number summary that is required to create a box plot. Knowing these five vocabulary words will serve very useful as students learn about box plots.Going forward, students will continue to work with box plots as they use them to compare multiple sets of data. It is important that students have a firm grasp on box plots by the end of this lesson, as the next lesson requires students to create double box plots.

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Topic Background Turn and Talk/Think-Pair-Share: “Various researchers (e.g. Douglas Reeves, Richard Allington, Vygotsky) have linked academic success with the capacity to engage in conversation and to ask and answer questions in full sentences.

One of the most powerful and easy to implement moves is called: Turn and talk, or think, pair, share, or partner talk. All of these are variations of a practice that has far reaching benefits for students. Simply defined, “turn and talk” is a teacher offered opportunity for students to turn to another student and talk something through for a very brief period of time before whole group discussion or lecture resumes.”-Lucy West & Antonia CameronMetamorphosis Teaching Learning Communities

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.

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Hint

34 40 52 57 57 60 60 63 67 69 69 71 71 89

A group of taste testers reviewed a brand of natural peanut butter. They gave the peanut butter a rating of 0-100 points depending on its quality. The ratings are below:

Find the minimum, maximum, median, range, and interquartile range (IQR) for this set of data.

Challenge: What would the 15th score have to be in order for the peanut butter to have a mean rating of 63 points? 86 points

Min = 34 points Max = 89 points Median = 61.5 points Range = 55 points Interquartile range (IQR) = 12 points

Agenda

Agenda:

1) Warm Up – Review of median, range, and IQR (Individual)2) Launch – Intro to Box Plots (Whole Class)3) Explore – Box Plots & Electronics Usage (Small Group)4) Summary – Why Use Box Plots? (Whole Class)5) Practice – Four Corners ( Whole Class)6) Assessment –Paper Plates Discussion (Partner)

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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.

Launch Think-Pair-Share

Agenda

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List some of the ways this information could be displayed visually.

34 40 52 57 57 60 60 63 67 69 69 71 71 89

Line Plot?

Bar Graph?

Circle Graph?Table?

Launch Whole Class

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A box plot is one of the ways this data can be displayed.

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Agenda

Launch Whole Class

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Example of a box plot:

Agenda

Launch Vocabulary

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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.

Agenda

Launch Turn-and-talk

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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?

Hint Agenda

Launch Notes

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Five-Number SummaryMinimumLower Quartile (Q1)MedianUpper Quartile (Q3)Maximum

34 40 52 57 57 60 60 63 67 69 69 71 71 89

Median = 61.5

Minimum Lower Quartile (Q1)

Upper Quartile (Q3)

Maximum

Agenda

Launch Think-Pair-Share

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The box plot below shows how the five-number summary corresponds to the box and whiskers of the box plot.

Based on the figures above, how do you make a box plot using the five-number summary?

Agenda

Launch Notes

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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 greatest2. Draw a number line that can show the data in equal intervals3. Mark the median4. 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 quartile9. Draw a vertical line through the median inside the box10. Draw two horizontal lines ("whiskers") from the rectangle to the extremes (minimum and maximum)

Agenda

Launch Check Your Work!

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Agenda

Explore – Class Challenge!

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1) In your head, estimate the NUMBER OF HOURS you spend using electronics in ONE WEEK .

-TV-Computer-Video Games, etc.

2) On the paper in front of you, in large writing, write your estimate.

3) Without talking, form a line from least to greatest in the front of the room. Hold your estimates in front of you for people to see.

Agenda

Explore

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Number of hours per week 6th graders spend using electronics.

To Do:1) Quietly return to your seat2) Record the information above in your notes

Agenda

Explore

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Next Steps:

1) Using the data, independently find the five-number summary in your notes2)Compare your five-number summary with those of your group members3) As a group, construct one poster that has the following:

a) Data ordered from least to greatestb) Five-number summaryc) Box Plot

You have 12 minutes!

Agenda

http://www.online-stopwatch.com/

Explore Small Group

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How does your box plot compare?

Quietly walk around the room to view the box plots made by other groups.

Questions to think about: -What is great about the mathematics you see? -What suggestions do you have for the other groups?

You have 3 minutes!

Agenda

http://www.online-stopwatch.com/

Summary Whole Class

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Questions to discuss:

-What is great about the mathematics you saw? -What suggestions do you have for the other groups?

-Based on the data that we collected, how much time does the typical student spend using electronics weekly?

-When are box plots useful? For example, why would someone choose to create a box plot instead of a bar graph?

Agenda

Explore Whole Class

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Let’s compare your box plot with a box plot that was created using an applet!

Online Tool Agenda



Practice Four Corners

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The five-number summary divides a data distribution into four parts.

In this activity you will have to decide what percent of the data values fall in given intervals.

1 2 3

4

Agenda


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About what percent of the data values fall in the following interval?

• after the upper quartile 25%

Agenda


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• before the median 50%

Agenda


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• after the median 50%

Agenda


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•in the box (between the upper and lower quartiles)

50%

Agenda


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• before the upper quartile 75%

Agenda


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• before the lower quartile 25%

Agenda


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• after the lower quartile 75%

Agenda


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• between the median and the upper quartile 25%

Agenda


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• between the median and the lower quartile 25%

Agenda

Assessment – Paper Plate Discussion!

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At your seats, you and your partner have four paper plates. Each plate has a letter on it: a, b, c, or d.

Each of the following slides has a multiple choice question on it. The possible answers are a, b, c, or d.

For each question, think about the answer in your head. Then turn to your partner and explain your answer. After your discussion, you or your partner should put the plate in your hand that represents what you believe is the correct answer.

When you hear two claps, raise your plate in the air.

Agenda


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Ms. Simmons made the box-and-whisker plot below to show some statistics about the ages of the students in her class at a community college.

Which of the following best represents the median age of the students in her class? A. 25 B. 27 C. 29 D. 31

Agenda


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The box-and-whisker plot below shows the distribution of the daily high temperatures, in degrees Fahrenheit, in the town of Clifton during the year 2004.

Based on the box-and-whisker plot, in which of the following intervals of temperatures is it most likely that exactly 50% of the daily high temperatures are located? A. 38°F to 54°F B. 38°F to 81°F C. 54°F to 72°F D. 54°F to 81°F

Agenda


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Ms. Dumont kept a record of the numbers of students enrolled in foreign language classes at Central High School during the past 20 years. She used her data to make the box-and-whisker plot shown below.

Based on Ms. Dumont’s plot, what is the interquartile range of the numbers of students enrolled in foreign language classes?

A. 5 C. 30 B. 15 D. 50

Agenda


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A community center offers classes for students. The range of the number of students in each class is 13. The median number of students in each class is 9. Which of the following box-and-whisker plots could represent the numbers of students in the classes?

Agenda


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At your seats, you have two paper plates in front of you. Each plate has a word on it: True or False.

Each of the following slides has a statement that is either true or false.

For each statement, determine if it is true or false. Then turn to a neighbor and explain your answer. After your discussion, put the plate in your hand that represents what you believe is the correct answer.

When you hear two claps, raise your plate in the air.

Agenda


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The class median is less than 80.

True or False?

True

Agenda


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Half the class scored between 60 and 80.

True or False?

True

Agenda


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At least one student earned a score of 100.

True or False?

True

Agenda


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The class mean is probably less than the median.

True or False?

True

Agenda


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If there are 30 students in the class, at least 10 scored above 80.

True or False?

False

Agenda

displaying numerical data using box plots 1. 2 lesson objective swbat display and analyze numerical...

Documents

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purpose of box plots

creation of box plots

lesson overview

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afterbox plots

whisker plots

lesson descriptionthe