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Tab 0 -- BVD - Chapter 11
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BVD Chapter 11 - Understanding Randomness
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Lesson Plans
These activities are designed to be completed in 2 - 90 minute block periods.
First Activity: Show the numbers 1 2 3 4 and ask class to pick their favorite. Assign one of the numbers to each of the 4 corners of the classroom and have them go to the corner that represents their number choice. Most of the students will go to corner number 3. If everyone were choosing randomly, then there should be roughly equal number students at each corner. We don't pick randomly. This sets up the reason why we need to learn randomization techniques.
Second Activity: Randomization Activity - Work through the Simple Random Sample Worksheet with students. This worksheet is available for download by clicking on the link in blue above titled randomization activity. Type in the names of your students at the bottom of the second page of the worksheet before copying. The front page of the handout provides a definition of simple random sample with several scenarios for them to apply the definition. Only the last scenario is an SRS. The second page of the worksheet prompts students to explain three methods of randomization, by drawing slips of paper, using the randInt function on the TI graphing calculator, and by using the random number generator. We do this as a class.
- Draw Names Out of a Hat: Prior to class cut slips of paper with each student's name on it. I use a copy of my seating chart and just cut out the squares. We then draw names to sort into three different groups. We can either sort them like we deal cards, 1st person drawn is in group 1, second person drawn is in group two, thrd person drawn is in group three, fourth person drawn is in group 1, etc. Or, we can select names for the first group until 1/3 of the class has been drawn, the complete the second group, etc. After names have been drawn allow students a chance to write in the space provided how the groups were sorted.
- Use a Graphing Calculator: Have the students number the roster at the bottom of the page. Use the randInt( function to sort students according to their number. The RandInt( function is located in Math>Prb>5:RandInt(. Following the parentheses, type in 1 comma followed by the number of students on your roster. Example: If there are 33 students in the class, they command would be RandInt(1, 33). Press enter to draw your first student. Continue pressing enter, ignoring repeats until class is sorted or until the method becomes obvious. Give students an opportunity to describe the procedure in writing.
- Use a Random Digit Table: This method is probably the most important one for the AP Exam. If students are asked to do a simulation, then they will have to be proficient at using the table. The roster is already numbered, however, all numbers will need to be in two digit format. Have students add a 0 in front of the 1 through 9 digits. Demonstrate how to select the first student by reading the first line of the table left to right, two numbers at a time. The first student selected will be the one numbered 07, we will ignore the number 51, select 11, and so on. Keep reading the table until all three groups are formed. Again, provide students a chance to record this method in writing.
- Extra (not on page) Flip a Coin: It might be a good idea to sort class into two groups by flipping a coin. This is not a good randomization procedure if equal groups are desired. Place students in 1st group if heads is shown and second group if tails is shown. The class will easily see that it is possible for more students to be in one group over the other. What if we toss a coin until the 1st group is filled, then place all others in the second group? Also not good because those students at the end of the line did not get an equal opportunity to be in the first group.
Third Activity: Have students work in partners to complete Chapter 11 Quiz provided in the supplementary materials in Stats Modeling the World. This is just a class activity and not graded as a quiz. It takes about 20 minutes to complete and go over.
Fourth Activity: Vietnam Draft Simulation. This activity was obtained from Penny Smeltzer at a Two Day AP Workshop. I do not have this in electronic format. I will scan in and post later. Meanwhile, I have created a subtab at the top for websites that are the source of Penny's activity. In this activity, students find their draft number. Students who are drafted, numbers 1 through 195 come to the front of the room. I then have them sit down by their birth month. It should be noticed that out of those selected, the majority of them have fall birthdays. The landscaper website contains the draft numbers in order of month. Ideally, each month should contain about the same number of draft numbers from those that are called, 195/12 about 16 numbers per month. In actuality, the numbers in the fall months were as follows: December had 26, November had 22, October had 14, September had 19. The birthdays in these months made of 42% of the draft numbers, while it should have been closer to 33%. A quarter of the draft numbers occurred in November and December. The randomization procedure used was not a well designed procedure.
Fifth Activity: Let's Make A Deal Simulation. Read the letters to Marilyn Vos Savant located in the link above. Simulate the game with the class. Have the class try Marilyn's strategy of always switching to see how often the prize is one. Pool the class data so that there are at least 100 games played. The proportion of wins should be pretty close to 2/3.
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| http://farm4.static.flickr.com/3198/2827035854_602a8b2c1f.jpg |
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Subtab 0 -- Randomization Activity
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| http://www.livebinder.com/media/get/MTc0NDA=
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Subtab 1 -- http://www.landscaper.net/draft.htm
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| http://www.landscaper.net/draft.htm |
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Subtab 2 -- Selective Service System: History and Records
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| http://www.sss.gov/LOTTER8.HTM |
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Subtab 3 -- Marilyn letters
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| http://www.marilynvossavant.com/articles/gameshow.html |
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Subtab 4 -- Let's Make A Deal Applet
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| http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html |
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Tab 1 -- BVD - Chapter 12
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BVD - Chapter 12 - Surveys
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Lesson PlansThe activities for this chapter will take more than one 90 minute class period. The objective is to identify bias in surveys as well as to know various sampling methods.
First Activity: Count the g's in a frog story. This activity is designed to show the ineffectiveness of a census. Demonstrate to students what a typed g looks like. Then give them 3 minutes (plenty of time) to read a brief story counting the g's, both lower and upper case. At the end of the time allowed ask how many g's they found. Record responses on the board. There will be a variety of numbers. Ask the students if they understood the directions. If so, why are there so many different answers? A census does not always yield the actual numbers. The actual number of g's is 83.
Second Activity: Cartoon Survey. Divide the group up systematically into three groups by having them number off 1, 2, 3, 1, 2, 3, etc. Select one person from each group to ask one of the following questions and tally the yes answers.
- Question for 1st group: Do you watch cartoons? Yes or No
- Question for 2nd group: Do you still watch cartoons? Yes or No
- Question for 3rd group: Studies show that watching cartoons lowers IQ. Do you watch cartoons? Yes or No.
At the end of the activity show the class the questions and the results and discuss wording bias. This activity came from a post on the AP Statistics list serv. I can not remember the individual teacher's name who posted, but it is a great activity.
Third Activity: Give students a few notes on the different biases that occur in surveys. Provide each student with a copy of the Evaluating Bias in Surveys handout. Have students work in partners to determine bias in surveys and go over.
Fourth Activity: Use Random Rectangles activity to demonstrate sampling procedures. Random Rectangles is from Richard Schaeffer's book Activity Based Statistics.
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| http://farm4.static.flickr.com/3520/3925909976_8a11c1caed.jpg |
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Subtab 0 -- Evaluating Bias in Surveys
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| http://www.livebinder.com/media/get/MTc0NTQ=
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Subtab 1 -- Random Rectangles
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| http://www.livebinder.com/media/get/MTc0NTg=
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Tab 2 -- BVD - Chapter 13
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BVD - Chapter 13 Experiments and Observational Studies
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Introduction to Experiments & Observational Studies Overview & List of activities - Experiment on Memory from AP Statistics Reading 2009 by Adam Schrager. See tab above for activity
- Dan Ariely TED Talk on Predictably Irrational. See tab above for video.
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Blocking
- Matched Pairs Demo - Pepsi Challenge Activity - Students will simulate the Pepsi Challenge to see if they can identify which is coke and which is Pepsi. Supplies: 2 Dixie Cups for each student, a 2 Liter Bottle of Pepsi (chilled), a 2 Liter Bottle of Coke (chilled), a coin. Mark half of the dixie cups with an H and the other half with a T. Have a student decide if the H's will be filled with Coke or Pepsi, the T's will be filled with the other soda. The study should be blind to the class and to the students. Students will need to sample each cup. The choice of which to sample first should be made randomly by flipping a coin. If heads are tossed, then sample the cup marked H first. The student determines which cup is Pepsi or Coke and gives choice to student assistant.
- Malcolm Gladwell TED Talk on spaghetti sauces
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Subtab 0 -- Memory Experiment
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| http://www.livebinder.com/media/get/MTc0NjQ=
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Subtab 1 -- Predictably Irrational
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| http://www.ted.com/talks/lang/eng/dan_ariely_on_our_buggy_moral_code.html |
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Subtab 2 -- TED Talk Malcom Gladwell
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| http://www.ted.com/index.php/talks/malcolm_gladwell_on_spaghetti_sauce.html |
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Subtab 3 -- Swim with the Dolphins
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| http://www.livebinder.com/media/get/MTc0NjI=
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Subtab 4 -- www.rossmanchance.com/applets/Dolphins/Dolphins.html
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| http://www.rossmanchance.com/applets/Dolphins/Dolphins.html |
BVD - Chapter 11
