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Fathom's Impact on Lesson Effectiveness and Data Sets in Probability and Statistics - Prof, Study notes of Mathematics

Various journal entry tasks related to probability and statistics. Students are required to write thorough responses to the given tasks, which involve analyzing the effectiveness of fathom technology in teaching statistics, identifying variables and observational units, creating graphs and stemplots, interpreting data, and solving problems using snap-cubes and the leveling-off procedure. Additionally, students will explore concepts such as mean, median, standard deviation, association between variables, and compound events.

Typology: Study notes

Pre 2010

Uploaded on 08/04/2009

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Probability and Statistics Journal Entries
1. Read the “Fathom” paper given to you and write a thorough response. Do not
summarize the article! Your response should include the following:
Your reaction to the content of the paper.
What would this lesson have looked like had Fathom not been used?
How might it have been different without the technology?
How did Fathom help to make this an effective lesson?
2. Suppose you randomly stopped school-aged children as they entered WalMart
and asked, “What grade are you in?” What type of variable does this question
represent? Explain your reasoning. What are the observational units? Suppose
you gathered the data below. Use this information to create a circle graph.
Grade K 1 2 3 4 5
Number 10 20 45 90 10 5
3. Recently, a researcher asked students to provide the number of minutes they
spent reading the night before. In addition, the students reported their grade
level. The data are reported below. Create a side-by-side stemplot for the data.
What statistical tendency is being exhibited? Why might this statistical tendency
exist? What is a statistical tendency?
Grade 5 5 7 7 7 5 5 7 7 7
Time 28 30 20 20 22 31 33 19 18 16
Grade 5 5 7 7 7 7 5 5 7 7
Time 34 32 24 29 22 18 28 32 17 23
4. Dr. Rivera believes that teachers who were taught as children using manipulative
are more inclined to use manipulatives in their own classrooms. To test this, she
surveyed 50 teachers and asked them the following:
When you were a child, did your teachers use manipulatives in order to
teach mathematical concepts to you?
Do you use manipulatives to teach mathematics concepts to your students?
Of the 40 teachers replying “yes” to question #1, 25 answered “yes” to question #2. Of
the remaining 10 teachers, 6 answered “yes” to question #2.
oUse the data provided to create a two-way table.
oUse the information to create and answer a question that represents marginal
information.
oUse the information to create and answer a question that represents conditional
information.
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Probability and Statistics Journal Entries

  1. Read the “Fathom” paper given to you and write a thorough response. Do not summarize the article! Your response should include the following:  Your reaction to the content of the paper.  What would this lesson have looked like had Fathom not been used?  How might it have been different without the technology?  How did Fathom help to make this an effective lesson?
  2. Suppose you randomly stopped school-aged children as they entered WalMart and asked, “What grade are you in?” What type of variable does this question represent? Explain your reasoning. What are the observational units? Suppose you gathered the data below. Use this information to create a circle graph. Grade K 1 2 3 4 5 Number 10 20 45 90 10 5
  3. Recently, a researcher asked students to provide the number of minutes they spent reading the night before. In addition, the students reported their grade level. The data are reported below. Create a side-by-side stemplot for the data. What statistical tendency is being exhibited? Why might this statistical tendency exist? What is a statistical tendency? Grade 5 5 7 7 7 5 5 7 7 7 Time 28 30 20 20 22 31 33 19 18 16 Grade 5 5 7 7 7 7 5 5 7 7 Time 34 32 24 29 22 18 28 32 17 23
  4. Dr. Rivera believes that teachers who were taught as children using manipulative are more inclined to use manipulatives in their own classrooms. To test this, she surveyed 50 teachers and asked them the following:  When you were a child, did your teachers use manipulatives in order to teach mathematical concepts to you?  Do you use manipulatives to teach mathematics concepts to your students? Of the 40 teachers replying “yes” to question #1, 25 answered “yes” to question #2. Of the remaining 10 teachers, 6 answered “yes” to question #2. o Use the data provided to create a two-way table. o Use the information to create and answer a question that represents marginal information. o Use the information to create and answer a question that represents conditional information.
  1. Explain how to use snap-cubes and the leveling-off procedure to solve the following problem: On the first three quizzes, Mary scored 6, 9, and 7 points. How many points must she score on the fourth quiz in order to have an average of 8 points?
  2. Explain in your own words what is meant by the phrase, “The mean is the balance point of a distribution.” Include with your explanation a sample data set, and an explanation of how the mean balances that particular data set.
  3. Suppose that you are given the following data set:  2, 1, 4, 2, 2, 5, 3, 3, 2, 1 Find two different numbers that can be added to the given data set that change the median but not the mean. Explain how you chose these two numbers. (Note: The two numbers do not have to be integers.)
  4. a) Create a box plot for the data set below. Describe the process you use in identifying the 5 numbers used in creating the box plot. Also, describe how these 5 numbers are identified on the box plot.  19, 50, 23, 5, 21, 23, 20, 4, 9, 7 b) Describe how you could use the length of the box in your box plot to estimate visually whether or not 50 represents an outlier.
  5. a) In your own words, describe what it means if a person’s test score is within one standard deviation of the mean. b) Suppose that for a set of test scores the mean is 78 and the standard deviation is 4.3. What would be the score of a person who scored 2.5 standard deviations above the mean? Explain your reasoning.
  6. a) In your own words, explain what it means for two variables to be positively associated. Provide an example of a pair of variables that would be positively associated. b) In your own words, explain what it means for two variables to be negatively associated. Provide an example of a pair of variable that would be negatively associated. Note: Your examples should be different from those used in the text or discussed in class.
  7. Suppose that your experiment is to flip a coin and then roll a die. When asked to provide an example of a compound event, Janie replied, “Getting heads on the coin and a 4 on the die. This is a compound even because it contains information on both the coin and the die.” Explain to Janie why this actually represents a simple event. Be sure to include an actual example of a compound event and why this event is a compound event.

Examine Sammy’s work below: P(both teachers) = P(1st^ teacher AND 2nd^ teacher) = (25/100) * (25/100) = (625/10000) Is Sammy’s work correct? If so, explain how you know this is correct. If not, explain where Sammy went wrong in his thinking and how to correct his work.

  1. Experiment: There are three bags and you are going to select a colored chip from each bag. Bag A has 2 red chips and 1 blue chip. Bag B has 3 green chips and 2 red chips. Bag C has 5 red chips and 4 blue chips. Suppose you want to know the probability of getting “at least one red chip.” In class, we worked this type of problem using the complement of the event “at least one red chip.” First, what is the complement of this event? Second, why is it beneficial or necessary to use the complement to solve this probability?