# Probability and statistical thinking

This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any apocalyptic events that may occur during the semester.

### 1:

Mon

Class preparation

* n/a #### Introductions 1. assign groups 1. introductions and discuss Day 1 handout 1. Q&AExtra practice

* try NRICH: Which spinners? to begin exploring random outcomesWed

Class preparation

* finish Day 1 handout * (optional) answer the "off topic" question in this week's discussion board #### How do experiments lead to probability? 1. teams need: online dice roller or 2d6 in different colors, d4, d8; Roller derby board 1. notation for probabilityP(event) = (# event)/(total # outcomes) 1. Law of large numbers: As number of trials increase, the closer the experimental probability reflects the actual (theoretical) probability (Excel)

Extra practice

* try next problem on WeBWorK homework * Read Chapter 16.1### 2:

Mon

Class preparation

* Monte Carlo simulation using Excel * (optional) answer the "off topic" question in this week's discussion board #### How can we determine probability without experiments? 1. compare Monte Carlo simulation using Excel 1. represent sample space for 2d6 using: list, grid, tree diagram; then compute theoretical probabilities 1. compute theoretical probabilities for 2d4 using a sample space (hint: P(5) = 1/4) 1. group work: CA 16F, CA 16GExtra practice

* try next problem on WeBWorK homework * 16.1 problems: 1 (3/8, 4/8, 6/8), 2 (various, 5/12, various) * Read Chapter 16.2 * Supplemental Instructor's extra practiceWed

Class preparation

* finish CA 16G * watch clever combinations, e.g., the counting principle (CC version) * Try Technology practice for online quizzes/exams before Friday #### How can tree diagrams be used in different contexts? 1. formative quiz (~10 mins) 1. discuss: CA 16G.2 1. introduce weighted tree diagrams for compound probabilities Reminder: Next class online using ZoomExtra practice

* try next problem on WeBWorK homework * Chapter 16.2 practice exercises: 1, 2 * 16.2 practice exercises: 4 * 16.3 problems: 5 (9/16), 6 (1/64) * Supplemental Instructor's extra practice### 3:

Mon

Class preparation

* finish Hlas grid and with/without replacement on compound probabilities * (optional) answer the "off topic" question in this week's discussion boarddiscuss expectations for online classes

#### How can two-way tables be used to compute probabilities? 1. two-way frequency tables with experimental data 1. two-way frequency tables with theoretical dataExtra practice

* try next problem on WeBWorK homework * extra practice and challenges on conditional probability handout * NRICH: Odds and Evens * Supplemental Instructor's extra practiceWed

Class preparation

* try problems from "conditional probability" in WeBWorK homework * try Free Throws Challenge on compound probabilities #### How do values influence probability situations? 1. formative quiz (~10 mins) 1. expected value = value1 * probability1 + value2 * probability2 + … 1. use expected value to analyze fair gamesExtra practice

* try next problem on WeBWorK homework * Read Chapter 16.3 * Read Expected value * Supplemental Instructor's extra practice### 4:

Mon

Class preparation

* next problem fair games * (optional) answer the "off topic" question in this week's discussion board #### How do values influence probability situations? (continued) 1. finish fair games 1. CA 16K (expected earnings: ~29 prizes, $92-$93) 1. if time, challenge problems on fair gamesDiscuss online version of graded quiz & virtual review sessions with SI

Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * 16.3 problems: 14 (1/10, 20, $30) * Watch Dan Gilbert's discussion on decision makingWed

Class preparation

* if needed, email instructor to request online version of graded quiz (strict time limit, available before class, due before end of class) * try spinners #### What are examples of probability misconceptions? 1. groups: CA 16B (probability misconceptions), CA 16J (more probability misconceptions) 1. graded quiz (last 20 mins)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * CA 16A (both 2/3, both 1/4, various) * Lost key puzzle * (optional) possible tool for future teaching, pickerwheel.com### 5:

Mon

Class preparation

* read Chapter 9.5 * (optional) answer the "off topic" question in this week's discussion boardDiscuss graded quiz

#### How can story problems be modeled different ways? 1. CA 9U (strip diagrams and algebra)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * read Using a Model Approach to Enhance Algebraic Thinking in the Elementary School Mathematics ClassroomWed

Class preparation

* try next problem on CA 9U #### How can story problems be modeled different ways? (continued) 1. formative quiz (~10 mins) 1. continue CA 9U (strip diagrams and algebra)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * CA 9W ($750, $1200, 8.5L)### 6:

Mon

Class preparation

* try next problem on CA 9U * (optional) answer the "off topic" question in this week's discussion board #### How can (polynomial) formulas be developed from tables? 1. create functions from tables (tutorial)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceWed

Class preparation

* if needed, email instructor to request online version of graded quiz (strict time limit, available before class, due before end of class) * try next problem on functions from tables #### How can linear equations be identified? 1. finish functions from tables (tutorial) 1. graded quiz (last 20 mins)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice### 7:

Mon

Class preparation

* start note sheet for exam (1-sided, handwritten) * (optional) answer the "off topic" question in this week's discussion boardSchedule reminders: SI review, drop-in, next week

#### Review 1. review topics * creating practice problemsExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceWed

Class preparation

* if needed, email instructor to request online version of Exam I (strict time limit, available during class time) * finish note sheet for exam (1-sided, handwritten) * check batteries in calculator ;-) #### Exam I 1. approved calculators allowed 1. one pages notes (1-sided, handwritten) 1. manipulativesExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice### 8:

Mon

Class preparation

* n/a #### Exam I make-ups 1. No class except for make-up exams (sign-up required).Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceWed

Class preparation

* n/a #### Return exam 1. Exams will be return and discussedExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice### 9:

Mon

Class preparation

* Read Chapter 15.2: Displaying Data and Interpreting Data Displays * (optional) answer the "off topic" question in this week's discussion board #### How can data be displayed different ways? 1. revisit first class 1. types of displays: pictographs, dot plot, bar graph, pie chart, histogram, steam-and-leaf, line graph, scatterplot 1. CA 15E (data display errors)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Chapter 15.1 practice: 1, 3 * Chapter 15.2 practice exercises: 1a, 2, 3 * Misleading graphsWed

Class preparation

* Read Chapter 15.3: The Center of Data: Mean, Median, and Mode #### How can we measure the "center" of data? 1. formative quiz (~10 mins)"note sheet" (1 page, 1 sided, handwritten) now allowed on all quizzes! 1. arithmetic mean with leveling: CA 15K, CA 15L

Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Chapter 15.3 practice exercises: 1, 2, 3 * Chapter 15.3 problems: 3 (32), 4 ($83,333)### 10:

Mon

Class preparation

* finish CA 15L * try CA 15P * (optional) answer the "off topic" question in this week's discussion board #### How can we measure variability of data? (IQR) 1. formative quiz (~10 mins) 1. review preparation activities 1. define quartiles (exclusive), five-number summary, IQR 1. CA 15TExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Chapter 15.4 practice exercises: 3 * read Quartiles in Elementary Statistics (Langford, 2006)Wed

Class preparation

* if needed, email instructor to request online version of graded quiz (strict time limit, available before class, due before end of class) * finish CA 15T * read Chapter 15.4 Summarizing Distributions with Median and Interquartile Range and with Box Plots #### How can we measure variability of data? (box plots and outliers) 1. definitions: mode, bimodal, multimodal, outliers, and box plots 1. CA 15U (box plots) 1. graded quiz (last 20 mins)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice### 11:

Mon

Class preparation

* finish CA 15U * Read Chapter 15.4 "Summarizing distributions with mean and MAD" * (optional) answer the "off topic" question in this week's discussion board #### How can we measure variability of data? (MAD) 1. discuss graded quiz 1. CA 15W (compute MAD) 1. stats variability practice (mean, IQR, MAD)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Chapter 15.4 practice exercises: 4Wed

Class preparation

* n/a #### How can we measure variability of data? (var, SD) 1. formative quiz (~10 mins) 1. stats variability practice (var, SD) 1. CA 15W (compute variance, standard deviation)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Desmos: compute measures of variability * Read alternate variance computation### 12:

Mon

Class preparation

* Read Chapter 15.4 "Normal curves and standardized test results" #### How can we compare different scores? (normal distribution) 1. formative quiz (~10 mins) 1. introduce normal distribution (see student sample)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceWed

#### Class cancelled for Math RetreatThurs

Class preparation

* Read Math is Fun: Normal Distribution #### How can we compare different scores? (z-scores) 1. formative quiz (~10 mins) 1. introduce standard scores (aka. z-scores) 1. start scatterplotsExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice### 13:

Mon

Class preparation

* Read Math is Fun: Normal Distribution #### How can we compare different scores? (z-scores) 1. formative quiz (~10 mins) 1. introduce standard scores (aka. z-scores) 1. start scatterplotsExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceTues/Wed

Class preparation

* if needed, email instructor to request online version of graded quiz (strict time limit, available before class, due before end of class) #### How can we analyze bivariate data? 1. introduce quartile-quartile lines (with linear review) 1. graded quiz (last 20 mins)Extra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice * Desmos: quartile-quartile line and interpretationsThursday

#### Class cancelled for "wellness" day### 14:

Mon

Class preparation

* prepare for final exam #### Review 1. discuss graded quiz 1. discuss take-home part of final 1. sequels practiceExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practiceWed

Class preparation

* prepare for final exam #### Review 1. formative quiz (~10 mins) 1. Review topics 1. Q&AExtra practice

* try next problem on WeBWorK homework * Supplemental Instructor's extra practice