# 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:

### Monday

Class preparation

- n/a #### Introductions #. assign groups #. introductions and discuss Day 1 handout #. Q&A

Extra practice

- try NRICH: Which spinners? to begin exploring random outcomes
### Wednesday

Class preparation

- finish Day 1 handout - (optional) answer the "off topic" question in this week's discussion board #### How do experiments lead to probability? #. teams need: online dice roller or 2d6 in different colors, d4, d8; Roller derby board #. notation for probability
P(event) = (# event)/(total # outcomes) #. 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:

### Monday

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? #. compare Monte Carlo simulation using Excel #. represent sample space for 2d6 using: list, grid, tree diagram; then compute theoretical probabilities #. compute theoretical probabilities for 2d4 using a sample space (hint: P(5) = 1/4) #. group work: CA 16F, CA 16G

Extra 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 practice
### Wednesday

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? #. formative quiz (~10 mins) #. discuss: CA 16G.2 #. introduce weighted tree diagrams for compound probabilities Reminder: Next class online using Zoom

Extra 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:

### Monday

Class preparation

- finish Hlas grid and with/without replacement on compound probabilities - (optional) answer the "off topic" question in this week's discussion board

discuss expectations for online classes

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

Extra practice

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

Class preparation

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

Extra practice

- try next problem on WeBWorK homework - Read Chapter 16.3 - Read Expected value - Supplemental Instructor's extra practice

### 4:

### Monday

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) #. finish fair games #. CA 16K (expected earnings: ~29 prizes, \$92-\$93) #. if time, challenge problems on fair games

Discuss 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 making
### Wednesday

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? #. groups: CA 16B (probability misconceptions), CA 16J (more probability misconceptions) #. 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:

### Monday

Class preparation

- read Chapter 9.5 - (optional) answer the "off topic" question in this week's discussion board

#### How can story problems be modeled different ways? #. 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 Classroom
### Wednesday

Class preparation

- try next problem on CA 9U #### How can story problems be modeled different ways? (continued) #. formative quiz (~10 mins) #. 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:

### Monday

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? #. create functions from tables (tutorial)

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Wednesday

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? #. finish functions from tables (tutorial) #. graded quiz (last 20 mins)

Extra practice

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

### 7:

### Monday

Class preparation

- start note sheet for exam (1-sided, handwritten) - (optional) answer the "off topic" question in this week's discussion board

Schedule reminders: SI review, drop-in, next week

#### Review #. review topics - creating practice problems

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Wednesday

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 #. approved calculators allowed #. one pages notes (1-sided, handwritten) #. manipulatives

Extra practice

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

### 8:

### Monday

Class preparation

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

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Wednesday

Class preparation

- n/a #### Return exam #. Exams will be return and discussed

Extra practice

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

### 9:

### Monday

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? #. revisit first class #. types of displays: pictographs, dot plot, bar graph, pie chart, histogram, steam-and-leaf, line graph, scatter plot #. 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 graphs
### Wednesday

Class preparation

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

### Monday

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) #. formative quiz (~10 mins) #. review preparation activities #. define quartiles (exclusive), five-number summary, IQR #. CA 15T

Extra 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)
### Wednesday

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) #. definitions: mode, bimodal, multimodal, outliers, and box plots #. CA 15U (box plots) #. graded quiz (last 20 mins)

Extra practice

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

### 11:

### Monday

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) #. discuss graded quiz #. CA 15W (compute MAD) #. stats variability practice (mean, IQR, MAD)

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice - Chapter 15.4 practice exercises: 4
### Wednesday

Class preparation

- n/a #### How can we measure variability of data? (var, SD) #. formative quiz (~10 mins) #. stats variability practice (var, SD) #. 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:

### Monday

Class preparation

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

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Wednesday #### Class cancelled for Math Retreat
### Thursday

Class preparation

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

Extra practice

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

### 13:

### Monday

Class preparation

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

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Tues/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? #. introduce quartile-quartile lines (with linear review) #. graded quiz (last 20 mins)

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice - Desmos: quartile-quartile line and interpretations
### Thursday

#### Class cancelled for "wellness" day

### 14:

### Monday

Class preparation

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

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Wednesday

Class preparation

- prepare for final exam #### Review #. formative quiz (~10 mins) #. Review topics #. Q&A

Extra practice

- try next problem on WeBWorK homework - Supplemental Instructor's extra practice
### Final exam - if needed, email instructor to request online version of final exam - Review topics - one page of notes, one sided, handwritten - approved calculator