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The New Illinois Learning Standards for Seventh Grade Statistics and Probability

The New Illinois Learning Standards for Seventh Grade Statistics and Probability. Julia Brenson. The Four Components of a Statistical Investigation*. 1) Formulate a question 2) Design and implement a plan to collect data 3) Analyze the data by measures and graphs

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The New Illinois Learning Standards for Seventh Grade Statistics and Probability

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  1. The New Illinois Learning Standards for Seventh GradeStatistics and Probability Julia Brenson

  2. The Four Components of a Statistical Investigation* 1) Formulate a question 2) Design and implement a plan to collect data 3) Analyze the data by measures and graphs 4) Interpret the results in the context of the original question *Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report American Statistical Association http://www.amstat.org/education/gaise/GAISEPreK-12_Full.pdf

  3. The New Illinois Learning Standards Seventh Grade

  4. Statistics Standards for 7th Grade * See Evidence Statement 7.D.3 Micro-models from the PARCC Evidence Table – Grade 7 PBA

  5. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Suppose we wish to know something about a population. For example we might want to know the average height of a 12 year old boy, the proportion of Americans over 70 who send text messages, or the typical number of kittens in a litter. It is often not possible or practical to collect data from the entire population, so instead, we collect data from a sample of the population. If our sample is representative of the population, we can make inferences, or in other words, draw conclusions about the population.

  6. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Identify the population and the sample: 1. George wants to know how many hours of TV his classmates watch each week. He asks five of his classmates. 2. A newspaper, after interviewing 250 registered voters, predicted that 43% of voters favor Bruce Rauner for Illinois governor.

  7. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Activity: Gettysburg Address Part I Judgment Sample Part II Simple Random Sample  Sampling Distribution

  8. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Gettysburg Address Judgment Sample First ask students to take a quick look at the population of 268 words and select 10 words that they think form a representative sample of the length of words found in the Gettysburg Address. This is a judgment sample. Students record the ten words and the number of letters in each word in the table provided. After calculating the mean of the sample, each student records his mean on the class dot plot on the chalkboard.

  9. Statistics Standards for 7th Grade Random Sampling to Draw Inferences About a Population How do we ensure that we select a sample that is representative of the population? We choose a method that eliminates the possibility that our own preferences, favoritism or biases impact who (or what) is selected. We want to give all individuals an equal chance to be chosen. We do not want the method of picking the sample to exclude certain individuals or favors others. One method that helps us to avoid biases is to select a simple random sample. If we want a sample to have n individuals, we use a method that will ensure that every possible sample from the population of size n has an equal chance of being selected.

  10. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Which of the following would produce a simple random sample of size 6 from the population of all students in our classroom? A. Select the first 6 students that enter the classroom. B. Put every student’s name in a hat, mix and draw 6 names. C. The classroom has 6 tables with three students per table. Randomly select two tables. The students at these two tables are the sample. D. The classroom has 6 tables of students. Randomly select one student from each table.

  11. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Back to Gettysburg Address Simple Random Sample Use a random number generator or a random digits table to select a simple random sample of size 10 from the population of 268 words.

  12. Statistics Standards for 7th Grade Random Sampling to Draw Inferences About a Population Random Digits Table Suppose, for example that we wanted a sample of size 5. There are 268 words. First select a row to use in the table. Select three digits at a time, letting 001 represent 1, 002 represents 2, and so on. Skip 000 and numbers that are greater than 268. Skip repeats. Our Sample: 32, 148, 238, 128, 104

  13. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Random Number Generator Random sample of 5 numbers representing the 5 words to be selected. The random number generator above is shared with permission from Beth Chance and Allan Rossman. This applet can be found at http://www.rossmanchance.com/applets/RandomGen/GenRandom01.htm

  14. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Gettysburg Address Sampling Words – Permission to share this applet was given by Beth Chance and Allan Rossman. Number of Letters for all Words in the Population Population Mean Last random sample of size 5 that was selected. Sample Mean http://www.rossmanchance.com/applets/GettysburgSampleE/GettysburgSample.html

  15. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Gettysburg Address 100 random samples of size 5 mean = 4.46

  16. Statistics Standards for 7th GradeRandom Sampling to Draw Inferences About a Population Gettysburg Address 500 random samples of size 5 Sampling Distribution mean = 4.313

  17. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations Why are some breakfast cereals placed on the top shelf at the grocery, some on the middle shelf, and others on the bottom shelf?

  18. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations The Healthy Breakfast Story data file was retrieved from http://lib.stat.cmu.edu/DASL/.

  19. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations Activity: Hot Dogs! Consumer Reports, In June, 1983, reported on the sodium content of major hot dog brands. The table and box plots below compare the calories for 20 beef hot dogs and 17 poultry hot dogs.

  20. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations Activity: Hot Dogs! Find the mean and the MAD for each type of hot dog.

  21. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations Activity: Hot Dogs! 1 MAD + 1 MAD mean mean

  22. Statistics Standards for 7th GradeDraw Informal Comparative Inferences About Two Populations Activity: Hot Dogs! The center of the distribution for poultry hot dogs is almost 2 MAD (2 X 18.5 or 2 x 20.3) below the center of the distribution for beef hot dogs. If the two samples of hot dogs are representative samples of beef and poultry hot dogs, then there is evidence that poultry hot dogs tend to have fewer calories than beef hot dogs.

  23. Statistics Standards for 7th GradeChance Processes and Probability Models Big Ideas: • Probability has a value from 0 to 1. • If it is impossible for an event to happen, then the probability of that event occurring is 0. • If an event is certain to happen, then the probability of that event occurring is 1. Equally likely to occur or not to occur Impossible Certain Less likely More likely

  24. Statistics Standards for 7th GradeChance Processes and Probability Models Example: A coin is tossed. What is the probability of the coin landing heads up? Sample space (possible outcomes): Heads (H) or Tails (T) We are interested in the outcome of Heads. We say we are interested in the event that a coin lands heads up. This event, which has only one outcome (heads), is a simple event. A compound event has more than one outcome from the sample space. For example, a coin is tossed twice. The outcomes are: HH, TT, HT, or TH.

  25. Statistics Standards for 7th GradeChance Processes and Probability Models When a coin is tossed, all the outcomes (H or T) have an equal chance of occurring. This is a uniform probability model. If we toss a tack, or a paper cup, or a stack of 10 pennies that are taped together, the outcomes no longer have an equal chance of occurring. These events all have non-uniform distributions.

  26. Statistics Standards for 7th GradeChance Processes and Probability Models Activity: Tack Tossing (non-uniform distribution) When a thumb tack is tossed, is it more likely to land point up or point down? What is the probability of a tossed tack landing point up? When 10 tacks are tossed, how many tacks will usually land point up? Place 10 tacks in a Dixie cup. Cover the cup with your hand, shake, and pour the tacks on to your desk. Count the number of tacks that land point up? Repeat 10 times. Place tally marks on the class chart to represent the counts for each of your ten tosses. Create a class dot plot.

  27. Statistics Standards for 7th GradeChance Processes and Probability Models Activity: Tack Tossing (non-uniform distribution) ? ? On average, how many of the ten tacks land point up? What is the probability of a tack landing point up?

  28. Statistics Standards for 7th GradeChance Processes and Probability Models Example: Tree Diagram Michael and Gita would like to have three children. What is the probability that all three children will be boys? Third Child Possible Outcomes BBB (0.5)(0.5)(0.5) = 0.125 BBG BGB BGG GBBGBGGGBGGG Second Child First Child B 0.5 B 0.5 0.5 G B 0.5 0.5 B 0.5 G 0.5 G 0.5 B 0.5 B 0.5 0.5 G G 0.5 0.5 B G 0.5 G

  29. Statistics Standards for 7th GradeChance Processes and Probability Models Three Children Continued… Another way to look at this problem is to create a list of all possible outcomes (the sample space). (B, B, B) (G, B, B) (B, B, G) (G, B, G) (B, G, B) (G, G, B) (B, G, G) (G, G, G) This is a uniform distribution in which every outcome has an equal chance of occurring. There are 8 outcomes and each outcome has a 1/8 chance of occurring. We can now answer questions like: What is the probability of the couple having 3 boys? What is the probability of having one boy?

  30. Statistics Standards for 7th GradeChance Processes and Probability Models Activity: Blood Type A If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

  31. Statistics Standards for 7th GradeChance Processes and Probability Models Activity: Example Given in 7.SP.C.8c • Using a random digits table, let 1, 2, 3, 4 represent having type A blood. 0,5,6,7,8,9 represent not having type A blood. • Select a row. • Count how many digits it takes to reach a 1,2,3, or 4. • Record this count with a tally mark in a table. • Repeat many times to determine the long-run behavior.

  32. Statistics Standards for 7th GradeChance Processes and Probability Models Row 14 58842 81316 30021 29902 35106 87744 89832 15 89104 07798 63824 84546 52699 12394 59894 16 32161 26081 81678 46319 40588 24581 51397 17 43757 41089 36430 92049 88555 90515 64921 18 56847 26072 30263 70043 29892 48430 11287 12341 12111 21231 11234 11212 34561 12341 Continue on to simulate the long run behavior or combine results with classmates.

  33. Statistics Standards for 7th GradeChance Processes and Probability Models Blood Type A - Part II Tree Diagram Let A = the event that a donor has blood type A Let O = the event that a donor has some other blood type.

  34. OOOA (0.6)(0.6)(0.6)(0.4) = 0.0864

  35. Statistics Standards for 7th Grade Activities: • Gettysburg Address (A sampling activity) • This activity is adapted from the Sampling Words activity by Beth Chance and Allan Rossman. • Beth Chance and Allan Rossman have given permission for their Sampling Words applet to be shared with Illinois math teachers. (http://www.rossmanchance.com/applets/GettysburgSampleE/GettysburgSample.html ) • Hot Dogs! • Blood Type A • 7.SP.2 Valentine Marbles (http://www.illustrativemathematics.org/illustrations/1339) • Census at School ( http://www.amstat.org/censusatschool/)

  36. Statistics Standards for 7th Grade Census at School (http://www.amstat.org/censusatschool/) Statistics Education Web (http://www.amstat.org/education/stew/)

  37. Acknowledgements and Resources Chance, B. & Rossman, A. (Preliminary Edition). Investigating Statistical Concepts, Application and Methods. Duxbury Press. Chance, B., et al. Rossman/Chance Applet Collection. Retrieved from http://www.rossmanchance.com/. Chicago Tribune. (2014, April). Chicago Bears. Retrieved from http://chicagosports.sportsdirectinc.com/football/nfl-teams.aspx?page=/data/nfl/teams/rosters/roster16.html Daily Mail. (2012, December 2). What are the odds? New study shows how guessing heads or trails isn’t really a 50-50 game. Retrieved from http://www.dailymail.co.uk/news/article-2241854/What-odds-New-study-shows-guessing-heads-tails-isnt-really-50-50-game.html. Duggan, M. & Brenner, J. (2013, February 14). The Demographics of Social Media Users – 2012. Retrieved from http://www.pewinternet.org/2013/02/14/the-demographics-of-social-media-users-2012/. Focht, D., Spicer, C, and Fairchok, M. (2002). The Efficacy of Duct Tape vs Cryotherapy in the Treatment of Verruca Vulgaris (the Common Wart). 156 (10) pp. 971-974. Retrieved from http://archpedi.jamanetwork.com/article.aspx?articleid=203979&resultClick=1.

  38. Acknowledgements and Resources Franklin, C., Kader, G., Mewborn, J. M., Peck, R., Perry, M. & Schaeffer, R. (2007) Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework. Alexandria, VA: American Statistical Association. McCallum, B., et al. (2011, December 26). Progressions for the Common Core State Standards in Mathematics (draft) 6-8 Statistics and Probability. Retrieved from http://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf. McCallum, B., et al. (2012, April 21). Progressions for the Common Core State Standards in Mathematics (draft) High School Statistics and Probability. Retrieved from http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_sp_hs_2012_04_21_bis.pdf. Moore, D. & McCabe, P. (1989). Introduction to the Practice of Statistics. New York, NY: W. H. Freeman. Oakes, J. “Causation verses Correlation” Grossmont. Retrieved July 7, 2013, from www.grossmont.edu/johnoakes/s110online/Causation%20versus%20Correlation.pdf Peck, R., Gould, R., & Miller, S. (2013). Developing Essential Understand of Statistics for Teaching Mathematics in Grades 9-12. Reston, VA: The National Council of Teachers of Mathematics, Inc.

  39. Acknowledgements and Resources Peck, R., Olsen C. & Devore J. (2005). Introduction to Statistics and Data Analysis. Belmont, CA: Brooks/Cole. Peck, R. & Starnes, D. (2009). Making Sense of Statistical Studies. Alexandria, VA: American Statistical Association. Ramsey, F. & Schafer, D. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis. Boston, MA: Brooks/Cole, Cengage Learning. Rossen, J. (2014, January 15). Taste Test Pits Fine Chocolate Against Cheaper Brands. Retrieved from http://www.today.com/video/today/54076112#54301611. Rossen, J. (2014, February 26). Underage Alcohol Buys. Retrieved from http://www.today.com/video/today/54076112#54515111. Rossman, A. (2012). Interview With Roxy Peck. Journal of Statistics Education, 20(2). pp. 1 – 14. Retrieved from http://www.amstat.org/publications/jse/v20n2/rossmanint.pdf. Rossman, A., Chance, B., & Von Oehsen, J. (2002). Workshop Statistics Discovery With Data and the Graphing Calculator. New York: Key College Publishing.

  40. Acknowledgements and Resources Scheaffer, R., Gnanadesikan, M., Watkins, A., & Witmer, J. (1996). Activity-Based Statistics. New York: Springer-Verlag. Stickgold, R., James, L. & Hobson, J. (2000). Visual discrimination learning requires sleep after training. 3(12) pp. 1237-1238. Retrieved from http://www.nature.com/neuro/journal/v3/n12/pdf/nn1200_1237.pdf. Strayer, D. and Johnston, W. (2001, November 6) 12(6). Driven to Distraction: Dual-Task Studies of Simulated Driving and Conversing on a Cellular Telephone. Pp. 462-466Retrieved from http://www.psych.utah.edu/AppliedCognitionLab/PS-Reprint.pdf.

  41. Online Resources Census at School. http://www.amstat.org/censusatschool/ Consortium for the Advancement of Undergraduate Statistics Education. http://causeweb.org/ Engage NY. http://www.engageny.org/mathematics Illustrative Mathematics. http://www.illustrativemathematics.org/ Inside Mathematics. http://www.insidemathematics.org Mathematics Assessment Project. http://map.mathshell.org/ Math Vision Project. http://www.mathematicsvisionproject.org/ NCSSM Statistics Institutes. http://courses.ncssm.edu/math/Stat_Inst/links_to_all_stats_institutes.htm

  42. Online Resources PARCC Model Content Frameworks. http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember2012V3_FINAL.pdf PARCC Mathematics Evidence Tables. https://www.parcconline.org/assessment-blueprints-test-specs Smarter Balanced Assessment Consortium. http://www.smarterbalanced.org/ Statistics Education Web (STEW).  http://www.amstat.org/education/STEW/ The Data and Story Library (DASL). http://lib.stat.cmu.edu/DASL/ The High School Flip Book Common Core State Standards for Mathematics. http://www.azed.gov/azcommoncore/files/2012/11/high-school-ccss-flip-book-usd-259-2012.pdf

  43. The New Illinois Learning Standards for Seventh GradeStatistics and Probability Julia Brenson Lyons Township High School jbrenson@lths.net

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