# 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/Tues

Class preparation

- n/a

#### Agenda: Introductions

- make seating chart
- introductions and discuss Day 1 handout
- assign groups
- Q&A

Extra practice

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

Wed/Thurs

Class preparation

- finish Day 1 handout
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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:

Mon/Tues

Class preparation

- Monte Carlo simulation using Excel
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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

Wed/Thurs

Class preparation

- finish CA 16G
- watch clever combinations, e.g., the counting principle (CC version)
- Try Technology practice for online quizzes/exams before Friday

#### Agenda: 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:

Mon/Tues

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

#### Agenda: 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

Wed/Thurs

Class preparation

- try problems from "conditional probability" in WeBWorK homework
- try Free Throws Challenge on compound probabilities

#### Agenda: 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:

Mon/Tues

Class preparation

- next problem fair games
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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

Wed/Thurs

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

#### Agenda: 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:

Mon/Tues

Class preparation

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

Discuss graded quiz

#### Agenda: How can story problems be modeled different ways?

- CA 9U (strip diagrams and algebra)

Note: Last Zoom class

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

Wed/Thurs

Class preparation

- try next problem on CA 9U

#### Agenda: 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:

Mon/Tues

Class preparation

- try next problem on CA 9U
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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

Wed/Thurs

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

#### Agenda: 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:

Mon/Tues

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

#### Agenda: Review

- review topics
- creating practice problems

Extra practice

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

Wed/Thurs

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 ;-)

#### Agenda: 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:

Mon/Tues

Class preparation

- n/a

#### Agenda: 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

Wed/Thurs

Class preparation

- n/a

#### Agenda: Return exam

- Exams will be return and discussed

Extra practice

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

### 9:

Mon/Tues

Class preparation

- Read Chapter 15.2: Displaying Data and Interpreting Data Displays
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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, scatterplot
- 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

Wed/Thurs

Class preparation

- Read Chapter 15.3: The Center of Data: Mean, Median, and Mode

#### Agenda: 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:

Mon/Tues

Class preparation

- finish CA 15L
- try CA 15P
- (optional) answer the "off topic" question in this week's discussion board

#### Agenda: 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)

Wed/Thurs

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

#### Agenda: 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:

Mon/Tues

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

#### Agenda: 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

Wed/Thurs

Class preparation

- n/a

#### Agenda: 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:

Mon/Tues

Class preparation

- Read Chapter 15.4 "Normal curves and standardized test results"

#### Agenda: 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

Wed

#### Class cancelled for Math Retreat

Thurs

Class preparation

#### Agenda: How can we compare different scores? (z-scores)

- formative quiz (~10 mins)
- introduce standard scores (aka. z-scores)
- start scatterplots

Extra practice

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

### 13:

Mon

Class preparation

#### Agenda: How can we compare different scores? (z-scores)

- formative quiz (~10 mins)
- introduce standard scores (aka. z-scores)
- start scatterplots

Extra practice

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

Tues/Wed

Class preparation

#### Agenda: 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:

Mon/Tues

Class preparation

- prepare for final exam

#### Agenda: 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

Wed/Thurs

Class preparation

- prepare for final exam

#### Agenda: 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