Lesson Plan I
by: Chris Povich

Macintosh Clarisworks Users: download the original lesson in Clarisworks 4.0 or higher.

Topic: Introduction to Descriptive Statistics with Mode, Median, Mean, and Range.

Grade Level: Six through ninth grade.

NCTM Standards: 2-3 Express mathematical ideas orally and in writing.
10-3 Understand and apply measures of central tendency, variability, and correlation.


Day One

Activity One: Students will work in groups of three and four members. Each group will visit the URL, http://www.mste.uiuc.edu/hill/dstat/dstatintro.html, and access, "Descriptive Statistics (Introduction to Mode, Median, and Mean)," by Jay Hill. The groups will access the pages dealing with mode, median, mean, and range.

Activity Two: Students will perform the dice game described by Jay Hill in their groups.
Part A) Each group member picks two numbers ranging from one to six. Students within the same group cannot pick the same two numbers. Students within each group take turns rolling a six-sided die fifty times. Each time a number comes up that matches one of a student's chosen numbers, that student receives a point. Students then are to make a bar graph on Claris Works that represents their group outcomes.

Example of a Group's Outcomes:



Activity Two: Jay Hill's Descriptive Statistics Activity.
Part B) The class will now pool all their scores together. Each group will put the class scores in order from lowest to highest. Each group will create a bar graph of the class data on Claris Works.

Example of Class Bar Graph:



Part C) Each group is to find the mode, median, mean, and range for the class results. Then the groups will discuss which central tendency best represents the scores of the class.

Assessment: Groups will turn in their histograms and results at the end of the period for a group grade.

Day Two

Activity One: "What's Your Average"

1. The teacher will write out questions which relate to a unit or chapter being taught in another subject on index cards. The teacher will then tape the cards on the back of students in the classroom. (Students may not look at the card on their back.)
   
2. Students will then go to eight other students and ask them to answer the question on their back using a number. They must also ask for a one word clue to help them figure out what their question might be. Students will record this information on their paper.
   
3. After soliciting the numbers and clue words, students return to their desks/tables and find the average of the numbers and attempt to write what the question is on their backs from the given data.
   
4. Each student will share their clue numbers, clue words, average, and suggested question with the class. Then the student will remove the question from their back so they can compare the suggested question with the actual question. Students are to answer if the numbers and/or average helped them figure their question out. They will also discuss with the class what the actual answer is. Furthermore, students will explain if the high and low scores were thrown out would their average be closer to the actual answer.
   
   

Example Question:

How many bone are in the human body?

Answers:

200 Vertebrae
500 Skeleton
260 Cast
256 Calcium
200 X-ray
100 Connections
206 Broken
200 Skull

Average: 240.25 (Actual answer is 206. If the high and low scores were thrown out, the average would then be 220.33. This is closer to the actual answer.)

Activity Two: "Water on a Penny"
Part A) Each group will get an eye dropper, a glass of water, and a penny. Each student in the group will make an estimate of how many drops of water they will be able to put on the penny. Each student in the group will take a turn and try to put as many drops as they can on the penny. Students will post their results on the board using a stem and leaf diagram. Each group is responsible for copying the diagram down.

Example of Class Stem and Leaf Diagram:

Prediction Leaf Stem Results Leaf

3,5,3,6,5,4,7 0 3,5,2,4 1 0,7,2 2 6,9 6,5 3 4,2,1,0,6,4,9,9,6,7,8,4,5 0,8 4 0,0,1,2,1,2 0 5 5 6 7 Part B) Each group will then use the TI-82 to come up with box plots for the prediction data and the results data. The groups will then sketch the box plots using Claris Works.

Example of Box Plots:



Part C) Students will attach the previous data in their journals. They are required to discuss in their groups and write in their journals about the mode, median, mean, and range for each set of data. They are to discuss why the ranges are different and what contributes to this.

Assessment: Students will turn in their journals for a journal grade at the end of the week.





Day Three

Activity One: Review Using "Open Eyes" Project
Part A) Each student in the group will get a stop watch. The student will close their eyes and start the stop watch. After they think a minute has passed they will stop the stop watch and open their eyes. The students in the class will pull their data together and create a stem and leaf diagram, histogram, and a box plot. Lastly, the students will discuss the mode, median, mean, and the range of their data.

Example of Stem and Leaf Diagram in Seconds:

Stem Leaf
3 4, 4 5,0,5,3, 5 0 6 5,9,4,8,2,5,6,8 7 0,5,3,1,7,
8 1

Example of Histogram:



Example of Box Plot:



The mode = 45, 65, 68 seconds.
The median = 65.5 seconds.
The mean = 61.55 seconds.
The range = 81-34 = 47 seconds.

Part B) Students are to discuss about the range and if most of the class estimated under or over a minute. How does the different graphical presentations demonstrate this? How does the different central tendencies demonstrate the estimations of the class. (This discussion can lead into variance and standard deviation.)

Activity Two: "Finger Snap" Quiz
Part A) Students will predict how many times they can snap their fingers in thirty seconds. The class data will be collected and listed in a chart on the board or overhead.
Part B) The teacher will run a stop watch for thirty seconds as students snap their fingers. After thirty seconds the teacher will collect and list the class results in another chart on the board or overhead.
Part C) Quiz - The students individually are to produce a stem and leaf diagram, histogram, and box plots for the given data. Students will then write about the advantages and disadvantages of each graphical representation. Then they will calculate the mode, median, mean, and range for each set of data. They are to choose a central tendency that best represents each set of data and explain why they chose these particular measurements. The ranges of the two data sets are to be compared and the students are to explain why or why not there is a variation in the ranges.

Assessment: The "Finger Snap" Quiz will be turned in and count as an individual quiz grade for each student.