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Analytically Speaking

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					LeAndrea Sanderfur 1                                                                M6D1

                              LeAndrea Sanderfur

                             Analytically Speaking

                                      Sixth Grade

           Georgia Performance Standards Covered:
M6D1. Students will pose questions, collect data, represent and analyze the data,
and interpret results.
       a. Formulate questions that can be answered by data.
       b. Using data, construct frequency distributions, frequency tables, and graphs.
       c. Choose appropriate graphs to be consistent with the nature of the data
       (categorical or numerical). Graphs should include pictographs, histograms,
       bar graphs, line graphs, circle graphs*, and line plots.
       d. Use tables and graphs to examine variation that occurs within a group and
       variation that occurs between groups.
       e. Relate the data analysis to the context of the questions posed.

M6P1. Students will solve problems (using appropriate technology).
      a. Build new mathematical knowledge through problem solving.
      b. Solve problems that arise in mathematics and in other contexts.
      c. Apply and adapt a variety of appropriate strategies to solve problems.
      d. Monitor and reflect on the process of mathematical problem solving.

M6P3. Students will communicate mathematically.
       a. Organize and consolidate their mathematical thinking through communication.
       b. Communicate their mathematical thinking coherently and clearly to peers, teachers,
and others.
       c. Analyze and evaluate the mathematical thinking and strategies of others.
M6P5. Students will represent mathematics in multiple ways.
       a. Create and use representations to organize, record, and communicate mathematical
ideas.
       b. Select, apply, and translate among mathematical representations to solve problems.
       c. Use representations to model and interpret physical, social, and mathematical
phenomena.
LeAndrea Sanderfur 2                                                                      M6D1

                                 Analytically Speaking
Question:
        How can you use data to describe different groups?
Launch:
According to Laura Griffith, a meteorologist with the National Weather Service, Atlanta is in
the midst of its seventh-driest year since records started being kept in 1880. Below is
rainfall data for Atlanta Georgia from 2000- 2007.
http://www.srh.noaa.gov/ffc/html/rainfall_scorecard.shtml

Year                          June                           January - June
2007                          3.66 inches                    15.39 inches
2006                          5.8 inches                     24.67 inches
2005                          2.91 inches                    24.74 inches
2004                          5.99 inches                    19.85 inches
2003                          7.34 inches                    33.32 inches
2002                          2.81 inches                    27.47 inches
2001                          6.69 inches                    28.76 inches
2000                          1.11 inches                    15.38 inches

1. What is the mean amount of rainfall for the month of June using the data above?

2. What is the mean amount of rainfall for the months January-June using the data above?

3. What is the median amount of rainfall for the month of June? The median for January to June?

4. How does 2007’s rainfall for Jan. – Jun. compare to the median rainfall amount for Jan. – Jun.?

5. Create a line graph that compares June’s rainfall amounts over the past eight years.




6. Does this graph support the fact that 2007 is one of the driest years?
  LeAndrea Sanderfur 3                                                                M6D1




  Investigation:
  Overview: We will display a data set using the most appropriate graphs and interpret and
  analyze the results.

  You are a recent college graduate looking for employment in the United States. You must select
  a state you would prefer to live in and tell why using and comparing information gained from
  population, income and housing. You will use the following website to collect your data
  http://quickfacts.census.gov/qfd/.

  7. Wikipedia suggests that there are approximately 30,000 cities in the United States. You must
  narrow your desired locations down to 5. List your top 5 cities in the chart below and use the
  website http://quickfacts.census.gov/qfd/ to find the population and median income for each city.

U. S. City                   Population                          Median Income




  8. Create a double bar graph for the population data and median income for your top five states.




  9. Based only on the data displayed in your graph, what two cities would you choose to live in
  and use your data to justify your answer?

  10. What other information would you need to narrow down your choices?
LeAndrea Sanderfur 4                                                                 M6D1

Your friend Solange is in the process of moving and she feels one of the most important factors
to her is the cost of living. She did research in the Atlanta area and found the price of 5 homes
using the following website http://realestate.yahoo.com. Below are her results

$138,490       $1,700,000     $546,900       $389,051       $259,900

11. What is the range according to Solange’s data?




12. Find the mean of Solange’s data? Find the mean?




13. Which measure of central tendency best describes the home prices?




14. Use the http://realestate.yahoo.com/ to find the price of 5 homes in your top two cities and
find the mean.


City: ________________                               City: ____________________

1st Cities Home Prices                            2nd Cities Home Prices




Mean:                                             Mean:
LeAndrea Sanderfur 5                                                               M6D1

15. Create a double bar graph comparing the median income to the mean home cost of your top
two cities.




16. Based only on the data displayed in your graph, what city would you choose to live in and
use your data to justify your answer?
LeAndrea Sanderfur 6                                                               M6D1

Using Data to Persuade
Misleading Graphs
The graphical display of data can be used to influence the opinion of others. A misleading graph
alters the top three rules for creating a graph to convey the message they want to be heard.



                                    Persuasive Graphs Alter

                              1) the scale and the intervals.
                              2) don’t begin with zero
                              3) use inappropriate titles and labels


Investigation 2
Two students created graphs to represent the data, but student # 1 wanted to convince the
cafeteria that hamburgers were being wasted and they would make more money if they only
served chicken.


                         Food                       Votes
                         Chicken Nuggets                    994
                         Hamburgers                         945
                         Pizza                              979



17. What is the range in student votes?




18. Based on the results do you believe the school should only serve chicken nuggets?




19. Can the first graph persuade the cafeteria to sell more chicken nuggets?
LeAndrea Sanderfur 7                     M6D1

20. Why is the first graph misleading?




 STUDENT 1




 STUDENT 2
LeAndrea Sanderfur 8                                                                 M6D1


Investigation:
Overview: We will display a data set using the most appropriate graphs and interpret and
analyze the results.

You are a recent college graduate looking for employment in the United States. You have
selected the city you would prefer, but you want your friends to move there as well.

21. First, survey four of your classmates and record their data in the chart below then add your
data to the bottom of the chart.
                                      Classmate City Data

                             POPULATION             MEDIAN INCOME               HOME COST
         CITY
                                                                                 (mean of 5)




Your city’s data

22. Second, create a graph using population, mean home cost, or median income to persuade
your peers to move to your favorite city.
LeAndrea Sanderfur 9                                                               M6D1



23. Using the data from your chart and the previous graph, write a paragraph that explains why
your friends should choose your state. Be sure to include reasons gathered from your data.




Conclusion:
Sometimes people alter graphs to persuade the opinion of others. These types of graphs are
considered to be ____________________________________.


What should people be aware of when interpreting graphs?
______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Homework
LeAndrea Sanderfur 10                                                              M6D1

Caleb conducted a survey of students at Blue River Middle School. He found that
9 students spent the following amounts of money on video games over the
summer.
              $105      $78   $91   $74    $82    $79     $83    $98    $82

1. Find the mean of Caleb’s data.




2. What is the median of Caleb’s data?




3. How does the mode compare to the median of the data?




Caleb bought 3 video games over the summer: Wii Fit, Super Paper Mario,
and ActRaiser.

4. Caleb spent $145.00 on games over the summer, what will happen to the mean (found in #1) if
you include Caleb’s spending?

       $105   $78       $91   $74   $82    $79    $83     $98    $82    $145


______________________________________________________________________________

______________________________________________________________________________

5. What is the median amount spent on video games when Caleb’s data is included?

______________________________________________________________________________
LeAndrea Sanderfur 11                                                           M6D1

6. Create a bar graph that emphasizes the amount of money Caleb spent on video games.




7. Create a graph that does not emphasize the amount of money Caleb spent on video games.




8. Which graph could be used to convince Caleb’s parents that his spending was normal?
Explain.
LeAndrea Sanderfur 12                                     M6D1

                                           Works Cited


http://score.kings.k12.ca.us/lessons/jfstate.report.htm