Percentile –  a value of a variable below which a certain percent of observation fall

Median –  the number that lies in the middle when a set of numbers is arranged in order. If there  are two middle values, the median is the mean of these values.

Range – the difference between the maximum and minimum values

Maximum – the highest value that occurs in a data set

Minimum – the lowest value that occurs in a data set

Outlier – values that stand by themselves away from most of the data

Quartile – those percentiles that divide the data into fourths

First Quartile –  25th percentile

Second Quartile – 50^th  percentile or median

Third Quartile – 75^th percentile

Interquartile  Range –  difference between third and first quartile

 Five Number Summary – Lowest value, Q1, median,  Q3, and highest value

Students will use a box and whisker plot to represent and analyze data.

The student will be able to create a box whisker plot using data generated by the class.

The student will be able to create a box whisker plot using data generated by a survey the students design and gather.

1+ Class Periods

A computer per student or one computer per group of two

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

Scoring Rubric:  Student Presentation Rubric.doc

Google form or wikispace that allows for the compilation of studenet survey data

WHERETO
W	=	The teacher will introduce the lesson by reviewing with the students the vocabulary and skills that they had learned previously in regards to percentiles, quartiles, etc.  Today’s lesson is looking at a graphic representation of this information.  The Box Whisker Plot is a quick method to display the five number summary.  Students will be told that they will be evaluated on their mastery of this lesson through the creation, implementation, and summary of a survey they create and their report of their findings to the class.
H	=	The use of real world data tied in with use of technology will hook and hold the students’ interest.  Students will analyze the quartile creation based on input from the number of songs in their ipods/mp3 players.  Additionally, students will be able to create their own box and whisker plot to analyze the change that occurs in relationship to data input.
E	=	The teacher will first model the behavior that is expected for the remainder of the lesson.  Students will then have the opportunity to create their own box and whisker plots based on their own data input.  The summative assessment will be a student presentation scored on a rubric. Student Presentation Rubric.doc
R	=	Questions at the transition point in the lesson will guide the students through the types of questions that they should be able to answer in their presentation of their survey.
E	=	Students will present a box whisker plot that summarizes their findings from a survey that they created.  They will also analyze this plot to express their understanding. Students will use the presentation rubrice to guide the development of their learning.
T	=	If need be, students can be paired with another student to assist with this activity. Additional practice via challenge opportunities or opportunities for remediation/additional practice will be available through different website activities.
O	=	The teacher will first model the activity by guiding the students through the first example.  Students then will work independently on their project.

The teacher will introduce the lesson by reviewing with the students the vocabulary and skills that have been presented previously in regards to percentiles, quartiles, etc.  The teacher will use student responses as a formative assessment to adjust instruction accordingly.

The student will be directed to log on to the computer either individually or in groups of two.  Each user will answer the two question survey.  Student data can be displayed either from a wikispace or google.doc form that the teacher has previous prepared.

                1.             How many songs do you have on your iPod, mp3 player, etc.

                2.             Are you male or female?

The teacher will then share the real-time date with the class. 

The teacher will demonstrate, with the use of a projection unit, each of the following steps as the students do the same step at their computer.

1. Go to the following website:  http://illuminations.nctm.org/ActivityDetail.aspx?ID=77
2. Choose My Data under Select a Data Set.  Under Describe your Data, type a title such as
   Period  3 Songs on our iPods.
3. Clear the data by highlighting the existing data and click delete. 
4. Enter the data we gather as a class entering the number of songs, a comma, and then either a M for male or F or female for each student in the class.
5. Click on update Boxplot.  First view graph all data and then graph by category.

While the students are entering the data, the teacher will need to monitor student progress via informal observation as a formative assessment.  Teacher can adjust instructional practice as necessary. 

The teacher will lead a discussion on what information can be generated when looking at these Box Whisker plots.  Questions should include ones like:  How does the number of songs compare between males and females?  What the sample bias?  Which quartile do you belong to in the overall data?  Which quartile do you belong to based on your gender?

The teacher will ask the class what would happen if we enter some more data that was extremely low or extremely high.  The students should then add this type of data to this list.  The teacher may want to have part of the room add several students with no songs (implying that they don’t have an iPod or MP3 player) and some to add several students with a lot of songs (more than the maximum from the actual data).  As the students add the data, they should update the Boxplot and see what differences they notice.

After the demonstration,  students will indepenently create a box and whisker plot on the website.  The students will be instructed on how to conduct their own survey and enter the data on the Box-Whisker plot.  The teacher will review the presentation rubric to guide student work.  During the remainder of the period, the students will work independently or in groups of two to design their survey which needs to include categories and how they are going to gather the data in an unbiased method. Results will be required to be displayed in a box and whisker plot.

After ongoing informal observation by the teacher to determine mastery, the students will then report their findings to the class.  Student presentations will be scored based on the following rubric: Student Presentation Rubric.doc

At the beginning of the lesson, as the teacher reviews vocabulary, student responses will serve as a formative assessment to adjust instruction accordingly.  As students are working individually or in small groups the instructor will progress monitor by observation in order to differentiate and make adjustments to instructional practice.

For challenge opportunities the following link may be used:

https://www.pdesas.org/module/content/resources/3184/view.ashx

For review or remediation purposes, the following links provide additional materials and resources:

https://www.pdesas.org/module/content/resources/3171/view.ashx

Box Whisker Plot, quartiles, saslesson, sastf

March 29, 2010