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By Carol Shields,
Andrew Lewis Middle School, Salem, VA
GRADE LEVELS 6-8th grade
TIME ALLOTMENT One class period - 55 minutes
OVERVIEW - This lesson shows the students how to relate collected data with a box and whiskers graph in a number of formats. The students will collect, organize, create, and interpret a box and whiskers graph. Students interpret the difference between sets of data using two different types of technology.
SUBJECT MATTER - Middle School Mathematics, data analysis and graphing.
STANDARDS
The objectives will in part meet the following State Standards.
Virginia 6th Grade Math Standards of Learning
6.18 The student, given a problem situation, will collect, analyze, display, and interpret data in a variety of graphical methods, including
a) line, bar, and circle graphs;
b) stem-and-leaf plots; and
c) box-and-whisker plots.
6.10 The student will estimate and then determine length, weight/mass, area, and liquid volume/capacity, using standard and nonstandard units of measure.
Standards can be found at
http://www.pen.k12.va.us/VDOE/Superintendent/Sols/home.shtml
MATERIALS
For the teacher:
Computer with projection capacity
TI interactive computer program from Texas Instruments
Computer file - box and whiskers.ti
TI-83 overhead calculator or Smart View program
Signs made for participants to wear to indicate the five main locations on box and whiskers graph. Signs can be made on 8x11 sheets of paper and worn around the neck by attaching string to one of the corners. The five signs should be: median, lower extreme, upper extreme, lower quartile, upper quartile.
Yarn
For the students:
TI-83 calculators (one per student)
One small bag of Scooby snacks per student
One ruler per student
One index card per student
PREP FOR TEACHERS
Load the computer file, boxandwhiskers.ti in the computer.
Test out each of the TI-83 calculators to make sure that the batteries are working.
Place the following on the students' desk ahead of time: index card, ruler, small bag of candy, calculators.
INTRODUCTORY ACTIVITY: SETTING THE STAGE
Say Today we are going to make a human box and whiskers graph like the ones that we have studied in class. On your desk you will find an index card and a ruler. Take the ruler and measure your hand span to the nearest centimeter. Then record your results on your index cards in large numbers.
Students will measure their hand span in centimeters and record their score on 3x5 index cards.
SayNow I want you to line up in the front of the room facing me in order from smallest to largest, smallest score on your right. Hold the card in front of you so that everyone can see what your number is.
Students form a line at the front of the room facing the instructor with the smallest score on the instructors left.
Ask: Who can tell me the five points on a box and whiskers graph? (Answer median, lower extreme, upper extreme, lower quartile, upper quartile)
Say Now we are going to find those five points. I want the persons at the ends of the line to raise their hands. Then in turn move one person over until the middle of the line is found.
Place the card with the word median on it around that persons neck.
SayNow we are going to find the lower extreme. The lower extreme is the lowest score in our list. Ask: Which person has the lower score in our line? (Answer the person at the end of the line to the left)
Place the card with the word lower extreme on it around that persons neck.
SayNow we are going to find the upper extreme. The upper extreme is the highest score in our list. Ask: Which person has the highest score in our line? (Answer the person at the end of the line to the right)
Place the card with the word upper extreme on it around that persons neck.
Say Now we are going to find the lower quartile. Using the hand raising method that we used to find the median, lets find the middle person between the median and the lower extreme.
Place the card labeled lower quartile around the neck of the person who is in the middle.
Say Now we are going to find the upper quartile. Using the hand raising method that we used to find the median, lets find the middle person between the median and the upper extreme.
Place the card labeled upper quartile around the neck of the person who is in the middle.
Say Now we need to form our box. Ask: Which people should be inside of our box? (Answer everyone from the lower quartile to the upper quartile.)
Hand the end of the yarn to the lower extreme. String it down the line to the upper extreme. Then run the yard behind the line until you reach the lower extreme. That person will hold the ball of yarn.
Say Now we have completed our human box and whiskers graph. Ask:What percent of our data is inside the box? (Answer 50 percent) Ask: What percent of our data is part of the lower whisker? (Answer 25 percent) Ask: What percent of our data is part of the upper whisker? (Answer 25 percent)
Collect the cards from the participants as they return to their seats.
LEARNING ACTIVITIES
Activity One.
Open the file Boxandwhiskers.ti on the computer which is connected to the overhead projector.
Say Now we are going to enter the data we just collected into this spreadsheet and observe the box and whiskers graph that it generates.
Using the data collected in the Introductory Activity, input this data into the Exercise one spreadsheet of the TI Interactive worksheet.
Ask: Where are each of the five points in this graph? (Answer point to the lower and upper extremes, median, upper and lower quartiles)
Ask: What are some general observations you can make about this graph? (Let participants respond orally)
Ask: What is different about the human graph and the computer version?
(Let participants respond orally)
Activity Two
Scroll up the screen until you are showing the box and whiskers graph in exercise two.
Say Now we are going to look at another box and whiskers graph and answer some questions about them Ask: What is the median of the graph? (Answer 42) Ask: What are the upper and lower quartiles of this graph? (Answer 14 and 53) Ask: What are the upper and lower extremes of this graph? (Answer 10 and 65) Ask: What do you predict will occur if I change the upper extreme to 75? (Let the participants respond with their opinions)
Move the upper extreme to 75.
Ask: Did the graph change as you thought it would? (Let the participants respond)
Activity Three
Scroll up so that the graph in activity three is at the top of the screen.
Say Now we are going to look at two box and whiskers graphs on side by side. These graphs are of two different math classes on a recent test
Ask: Which graph belongs with the data in L1? How do you know? (Answer the graph in L1 belongs with the red box and whiskers because it is the graph with that particular upper extreme)
Ask: What is the median of each class? The upper and lower extreme? (Answer medians is 42 and 48, upper extremes are 72 and 60, lower extremes are 2 and 15)
Say Now, look at the two graphs and decide which class performed better on the math test. Be prepared to defend your answer.
(Let participants respond orally)
Activity Four
Open up your internet browser to HYPERLINK "http://weather.unisys.com/hurricane/atlantic/2005/index.html" http://weather.unisys.com/hurricane/atlantic/2005/index.html
Say Now we are going to look at how to collect real data from the internet. I have opened up the official website for U.S. hurricane data.
Highlight the two columns for season 2004 and 2005. Copy this data to the spreadsheet on TI interactive. Delete all columns except wind speeds and names.
Say These two columns show the wind speeds for hurricane seasons 2004 and 2005. Compare the two graphs and make some general observations.
Ask: What did you notice? Did anything surprise you?
(Let participants respond)
Ask: What other factors may have had an impact on the graph? (Answer hurricanes this year landed near major cities, more hurricanes this year)
(Optional activity) Use this web site to instruct students on how to import data into TI interactive using the import feature.
Activity Five
In this part of the lesson, students will count the number of Scooby Snacks found in their bag. Scooby Snacks tend to have close to the exact number of snacks in each bag. This leads to the issue of quality control and to whom is quality control in a product important.
Say On your desk is a small bag of Scooby Snacks. Please open the bag and count how many Scooby Snacks are in the bag. Do not eat them at this time. When you are finished counting them, raise your hand and I will record your answer in this graph.
As people finish, record their answers in activity five list. When the last person has given their answer, double click on the list to create the graph.
Ask: How is this graph different from the other graphs? (Answer - this graph shows very little variability, and may even show a straight line.)
Ask: What might cause this graph to be different from the other graphs? (Answer the number of Scooby Snacks is almost the same in every single bag so there is a lack of variability)
Ask: Who in real life might be concerned about the number of items in a product of be sold? (Answer possible answers include a quality control person in a factory, consumer )
CULMINATING ACTIVITY
In this activity you will instruct the participants in the use of the TI-83s to construct a box and whiskers graph. Be sure to familiarize yourself thoroughly before trying this in class. I have put in screenshots to help you work through the instruction.
Turn on your overhead calculator or SmartView.
Say Today we are going to use TI-83's to construct box and whiskers graph. I will go through the steps with you slowly. Here is the data that we will use.
Given the data set (3, 15, 24, 25, 27, 30, 45, 55, 56, 70) create a box and whisker plot to represent this data.
Say. Turn the calculator on. Press the Y= button. Clear out any information left over in the calculator.
(this is what should be on your calculator)
Say. Press STAT key. You will see a list of choices. The words Edit and number 1 should be highlighted.
(this is what should be on your calculator)
Say Press the ENTER key.
Say Look in the column under L1. Use the DEL key to remove any left over data.
Say Enter each piece of data in the L1 column. Press enter after each entry.
(this is what should be on your calculator)
Say Press the 2nd Key
Say Press the Stat Plot Key (y=key)
Say Plot1 should be highlighted. Press the enter key.
(this is what should be on your calculator)
Say Using the arrow keys, move over until the SECOND box plot graphic is highlighted. See the figure on the screen.
Say. Press the zoom button followed by the number 9. You should now be able to view the box and whiskers graph.
Say Press the trace button. Locate the value of the median, lower and upper quartile, lower and upper extreme by moving the cursor over each of the points
(answer - median = 28.5 upper quartile=55 lower quartile=24 lower extreme=3, upper extreme=70)
Extension Activities
Name the 5 points on a box and whiskers graph
Explain why and how one graph might be different from another.
Demonstrate that you can create a box and whiskers graph on your calculator.
CROSS-CURRICULAR EXTENSIONS
Social Studies
Students can investigate the roll of surveys and polls in American history and government.
English
Students can develop presentations based on a chosen research topic for which a presentation might include a box and whiskers graph.
Science
Students can explore the internet to locate sources of real life data in the scientific areas.
COMMUNITY CONNECTIONS
Invite a pollster to speak to the class about what polls are, how they are collected and how they are used for a variety of purposes.
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