Data Analysis Goal 4

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Data AnalysisGoal 4

• Grade 8
• NC SCOS objectives
• Sandra Davidson
• NBCT EA Math

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NC SCOS Objectives (4 wks.)

• 4.01 Collect, organize, analyze, and display data
  (including scatterplots) to solve problems.
• 4.02 Approximate a line of best fit, for a given
  scatterplot, explain the meaning of the line as
  it relates to the problem, and make predictions.
• 4.03 Identify misuses of statistical and
  numerical data.

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1. Name Exchange use mean, median, and mode to
analyze data on the names in your class.

• Write each letter of your first name on a
  different sheet of paper.
• In your group exchange just enough letters so
  that each person has the same number.

• Share with the class, did you find that some in
  your group did not need to exchange any letters?
  What did your group do with any extra letters?
• Record the mean length of names in your group.

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Line Plot with post-it notes

• Remove two names without changing the median?
• Remove two names so the median increases?
• Remove two names so the median decreases?
• Add two names so the median increases?
• Add two names so the median decreases?
• Add two names without changing the median?

• Each student should write their first name on a
  post-it note and put it on the number line on the
  board.
• Find the mean, median, mode, and range of name
  lengths in our class. Which of the measures do
  you think gives the best sense of what is typical
  for the class?

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2. Mystery Data If you know that a basketball
players mean score is 10 points, can you find
his/her individual scores?

• Tanya played 5 basketball games and kept track of
  how many points she scored in each game.
• Her mean score was 8 points.
• She never scored 0 points.
• What might each of her scores be? Find a data
  set to match all the clues. __, __, __, __, __
• Rule data sets like 8,8,8,8,8 are not allowed
  because they are too easy!

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Mystery Data create data sets that have
different relationships among means, medians, and
modes!

• Seven students kept track of how many hours they
  played lacrosse during September. Their mean was
  21 hours. How many hours might each of the
  students have played lacrosse?
• Choose four of the descriptions and make a
  different data set to match each one. All the
  data sets should have 7 values and a mean of 21.
  Circle the median and put a square around the
  mode.

• Mean is larger than median.
• Median is larger than mean.
• Mean is larger than mode.
• Mode is larger than mean.
• Median is larger than mode.
• Mode is larger than median.
• Mean, median, and mode are equal.
• Homework MAPS worksheet 16

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3. Mean, Median, Mode Bingo

• Run bingo call-cards on transparencies.
• Give each student a bingo card.
• Solve each problem to get bingo!

• Assessment!
• Using Measures of Central Tendency

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4. Misuses of statistical data group discussion
cards (NC DPI Strategies IV 17)
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(continued) Misuses of statistical data
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Scale Skewer- The graph below is a comparison of
sneaker prices at various mall stores.

• Redraw the graph on the grid below.
• Which graph shows a better picture of the price
  comparison?
• Explain.

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Scale Skewer the graph below shows the amount
of pollution from a certain factory has changed
over the years.

• Redraw the graph on the grid below.
• How do the two pictures differ?
• Which one is a more honest representation of the
  situation?
• Explain.

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5. Payday at Planet Adventure

• Make a table to show what pay she should receive
  for different numbers of hours worked each day.
• Draw a graph of the data for Rachels pay. Label
  and choose an appropriate scale for the graph.

• Rachel and Enrico have summer jobs at Planet
  Adventure, a local amusement park. Rachel works
  in the Hall of Mirrors. Her rate of pay is 5
  per hour, plus a daily bonus of 9 for wearing a
  costume.

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Enrico works at the Space Shot roller coaster.
His rate of pay is 6.50 an hour.

• Make a table to show what pay he receives for
  different numbers of hours worked each day.
• On the same grid you used for Rachels pay, draw
  a graph of the data for Enricos pay.
• Graph both on Excel.

• Compare the graphs, how are they alike and how
  are they different?
• When does Rachel make more? Enrico?
• Do Rachel and Enrico ever earn the same amount
  for the number of hours worked?

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6. Bouncing Tennis Balls

• Work in teams of three, a timer, a recorder and a
  ball bouncer.
• Each person will take turns bouncing a tennis
  ball in their right hand for 2 min.
• Next, each person will bounce the tennis ball in
  their left hand for 2 min.

• Compile the class data into a stem-and-leaf plot.
• Combine the class data into a box-and-whisker
  plot.
• What conclusions can you draw based on the data
  collected?

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Is there more sugar in a piece of pie or a candy
bar?

• Complete the sugar content data worksheet.
• Stack the box-and-whisker plot above on the same
  scale where you drew the box-and-whisker plot on
  your worksheet.
• Compare the medians of the two data sets. Which
  appears to have more sugar, candy bars or
  desserts? Explain.

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7. Solving an Archeological Mystery Connected
Math Samples and Populations 3.1

• Archaeologist dig and analyze their findings to
  gain information about ancient civilizations.
  Here you have data about Native American
  arrowheads that were unearthed at six sites.
• How could you use the data from the known sites
  to help you estimate the time period during which
  each of the two new sites was settled?
• Complete the box plots on Labsheets 3.1A-D to
  represent the data, and statistics such as means,
  medians, and ranges to analyze and write a
  comparison summary. Your conclusion should
  include a prediction of the time period during
  which the new sites may have been settled.

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8. Eighth Grade Jumping Event (work with a
partner)

• One person will jump rope for 60 seconds while
  the other counts, and records the data.
• Switch so the other person jump ropes.
• One person will do jumping jacks for 60 seconds
  while the other counts, and records the data.
• Switch so the other person does the jumping jacks.

• Record your results on the large class
  scatterplot.
• Analyze the data once everyone has put their
  results on the plot.
• Do you see a trend or correlation in the data.
  Explain your reasoning.

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9. Is there a Relationship?

• There are three possible relationships between
  the variables
• A positive correlation
• A negative correlation
• Or no correlation
• Draw a line of best fit for the scatterplot.

• Scatterplots are useful for showing the
  relationship between two variables, such as
  heights and weights.
• Measure your foot and forearm in cm.
• Collect data from the entire class and create a
  scatterplot.
• Is there a relationship?

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What types of relationships can two variables
have?

• Positive correlation one variable increases when
  the other increases.
• Negative correlation one variable increases when
  the other decreases.
• No correlation no relationship
• Which type of correlation do you think each pair
  has?

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Reading a Scatterplot Use the scatterplot on
the worksheet to compare the population and the
number of area codes for each state.

• How many states have five area codes? How did
  you determine this?
• What does the point labeled A represent?
• The population of Canada is approximately
  29,100,000. If a similar pattern exists there,
  predict how many area codes you think Canada has?
  Explain.
• The population of Great Britain is approximately
  58,600,000. If Great Britain used the same
  system how many area codes do you think it would
  need? Explain.
• Suppose that a state had fourteen area codes.
  What do you think the population of that state
  would be? Explain.
• Describe the relationship between a states
  population and the number of area codes assigned
  to it.

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10. Predict how high a typical eighth grade
student can jump. How high would someone your
age need to jump to be an amazing jumper?

• Make a table like the one above. Measure and
  record the height of each person in your group to
  the nearest inch.
• Make two standing jumps, placing a piece of tape
  as high on the wall as possible.
• Record your jump height. This is the distance
  from the floor to your higher piece of tape.

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Jump Heights

• Write your jump height on the board as an ordered
  pair like the one shown here.
• Record the results of the entire class.
• Make a scatterplot of the entire class data.
  Student heights will be along the x-axis. Jump
  heights will be along the y-axis.
• Be sure to label the x- and y-axis and give a
  title to your graph.
• Plot one point for each person in the class.

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Jump Heights

• What can you tell about the jump heights? What
  is the greatest height reached? The least
  reached? The range?
• What information does the graph show about the
  heights of the students?
• Is there a correlation between student heights
  and how high they could jump? Is this what you
  expected? Where there any exceptions?
• Will the scale on your graph change if a new
  student in your class is 6 ft. 1 in. and jumps 9
  ft. 4 in? Explain.

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11. Olympic Gold Times Computer Lab

• NCTM Navigating through Data Analysis in Grades
  6-8, Olympic Gold Times worksheet.
• Use the internet to compare your predicted
  winning time for the year 2000 with the actual
  winning time for the event in that year.

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12. Human Development and Life Expectancies
Connected Math Samples and Populations 4.3

• Explore the relationship between safe water and
  life expectancies for several different countries
  in the world.
• Use a world map to locate the various countries
  listed on the table.
• What is safe water?
• (drinkable water)
• Why might some countries have less access to safe
  water than other countries?
• (sanitation practices)
• With your partner explore the data and make two
  different kinds of representations. Write a
  summary that discusses the relationships you
  found and your solutions.

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13, 14. Review and Test

• Do the Chapter review for data analysis on pages
  214-216, problems 7-18.
• Data Analysis Assessment
• Business project Power Points and Excel.

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References

• Balanced Assessment Middle Grades
• Connected Mathematics Samples and Populations
• Exemplary Mathematics Assessments Tasks for
  Middle grades
• MAPS
• Mathematical Understanding
• Mathematics Learning
• Mathematics Teaching in the Middle School (March
  2001)
• Mathscapes
• Math Thematics (STEM project)
• NCDPI Strategies
• NCTM Navigating Through Geometry Grades 6-8
• The Regents of the University of California