# Probability and statistical thinking

## Calendar of learning activities

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.

Special note: "CA" stands for "Class Activities" as found near the end of the course textbook or scanned into Canvas.

### 1:

WTh

Class preparation

- Complete Day 1 handout (syllabus game, statistical question, sampling, fraction operations) and bring to class.
- (optional) answer the "off topic" question in this week's discussion board

#### Class agenda: Introductions

- discuss class preparation activities (prep slides)
- assign groups
- Q&A

Extra practice

- Supplemental Instructor's notes
- read Grade 7: Chance and probability for background information
- experiment with NRICH: Which spinners?

### 2:

TMTh

Class preparation

- Play Roller derby on own or with friend. Bring record of dice rolls to class.
- Try Technology practice for online quizzes/exams before Friday
- Remember Monday students come to Wednesday's class. Wednesday students do not have class this week.
- (optional) answer the "off topic" question in this week's discussion board

#### Class agenda: How do experiments lead to probability? How can we determine probability without experiments?

- discuss class preparation activities
- teams need: 2d6 (different colors), d4, d8, Roller derby board
- notation for experimental 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)
- represent sample space for 2d6 using: list (e.g., dice), grid, tree diagram; then compute theoretical probabilities
- compute theoretical probabilities for 2d4 using a sample space (hint: P(5) = 1/4)

Extra practice

- Supplemental Instructor's notes and extra practice
- Chapter 16.2 practice exercises: 1, 2
- Monte Carlo simulation using Excel

### 3:

MTWTh

Class preparation

- Formative quiz (in this week's discussion board)
- watch counting principle
- Try CA 16F and bring to class (#1 hint, answer is NOT 6)
- Try CA 16G and bring to class

#### Class agenda: How can tree diagrams be used in different contexts?

- discuss class preparation activities
- tree diagram for CA 16G.2
- weighted tree diagrams for compound probabilities

Extra practice

- Supplemental Instructor's notes and extra practice
- 16.1 problems: 1 (3/8, 4/8, 6/8), 2 (various, 5/12, various)
- 16.2 practice exercises: 4
- 16.3 problems: 5 (9/16), 6 (1/64)
- NRICH: Odds and Evens

### 4:

MTWTh

Class preparation

- Complete compound probabilities except challenge
- Formative quiz (in this week's discussion board)

#### Class agenda: How can two-way tables be used to compute probabilities?

- discuss class preparation activities
- two-way frequency tables with experimental data
- two-way frequency tables with theoretical data

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- extra practice and challenges on conditional probability handout
- see WebWoRK problems for "conditional probability"

Assign Online Graded quiz (due day after in-person class)

### 5:

MTWTh

Class preparation

- Formative quiz (in this week's discussion board)
- Try challenge for compound probabilities
- On fair games, do you think the addition game is fair or not?
- (optional) answer the "off topic" question in this week's discussion board

#### Class agenda: How do values influence probability situations?

- discuss class preparation activities
- expected value = value1 * probability1 + value2 * probability2 + …
- use expected value to analyze fair games
- if time, CA 16K (expected earnings)

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- read Expected value
- To insure or not to insure? (NRICH)

( EV(insurance) = -75; EV(no insurance) = -50; no insurance is better) - Watch Dan Gilbert's discussion on decision making

### 6:

MTWTh

Class preparation

- Formative quiz (in this week's discussion board)
- Try CA 16B (probability misconceptions) and bring to class for discussion
- Try CA 16J (more probability misconceptions) and bring to class for discussion
- Try CA 16K (expected earnings) and bring to class for discussion
- Try spinners and bring to class for discussion
- (optional) answer the "off topic" question in this week's discussion board

#### Class agenda: How can equations be solved different ways?

- discuss class preparation activities
- discuss spinners

(angle more important than area) - CA 16B, CA 16J, CA 16K (~29 prizes, $92-$93)
- CA 9U, with strip diagrams and algebra

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- read Using a Model Approach to Enhance Algebraic Thinking in the Elementary School Mathematics Classroom
- 16.3 problems: 14 (1/10, 20, $30)
- CA 16A (both 2/3, both 1/4, various)
- CA 9W ($750, $1200, 8.5L)
- (optional) possible tool for future teaching, pickerwheel.com
- Challenge: Lost key puzzle

### 7:

MTWTh

Class preparation

- No formative quiz because of graded quiz
- Read Chapter 9.5
- Try next two problems on CA 9U (strip diagrams) and bring to class

#### Class agenda: How can (polynomial) formulas be developed from tables?

- discuss class preparation activities
- create functions from tables (tutorial, tutorial video)
- in-class group quiz (graded, last 20 mins)

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- 16.4 problems: 1 (1/16), 2 (1/12), 9 (3/8)
- Chapter 9.4 practice exercises: 3
- Chapter 9.5 practice exercises: 1, 2, 3

Note: Today there is a in-class graded quiz (absent students or students with accommodations may take the online version)

### 8:

MTWTh

Class preparation

- Formative quiz (10 minutes)
- Try next problem on CA 9U (strip diagrams) and bring to class
- Try next problem on functions from tables and bring to class

#### Class agenda: How can linear equations be identified?

- discuss class preparation activities
- finish functions from tables
- linear formats (also see Is it linear?)

Extra practice

- Supplemental Instructor's notes (with class recording) and practice midterm
- functions from tables challenge
- functions from tables random
- Read Patterns of patterns
- Finish CA 9U (check answers with instructor)

### 9:

MTWTh

Class preparation

- Review topics
- make note sheet (1-sided, handwritten)

#### Class agenda: Exam I

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

### 10:

MTWTh

Class preparation

- complete planning survey
- read Chapter 15.2

#### Class agenda: How can data be displayed different ways?

- discuss class preparation activities
- types of displays: pictographs, dot plot, bar graph, histogram, steam-and-leaf, line graph, scatterplot
- share types of displays
- CA 15E (data display errors)

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- CA 15C (see instructor to check answers)
- Chapter 15.1 practice: 1, 3
- Chapter 15.2 practice exercises: 1a, 2, 3

### 11:

MTWTh

Class preparation

- Formative quiz (10 minutes)
- Try CA 15K (mean as leveling out) and bring to class
- Try CA 15L (mean problems) and bring to class

#### Class agenda: How can we measure the "center" of data? How can we measure variability of data? (IQR)

- discuss class preparation activities
- arithmetic mean with leveling
- define: median, quartiles (exclusive), five-number summary, IQR
- start CA 15T (medians and IQR)
- plan for online learning starting Nov 23 (based on surveys)

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- Chapter 15.3 practice exercises: 1, 3
- Chapter 15.3 problems: 3 (32)
- Chapter 15.4 practice exercises: 3
- Try CA 15O (see instructor to check answers)

### 12:

MTWTh

Class preparation

- Formative quiz (10 minutes)
- Try CA 15T (quartiles and IQR) and bring to class
- Try CA 15P (misconceptions with median) and bring to class

#### Class agenda: How can we measure variability of data? (outliers and box plots)

- discuss class preparation activities
- definitions: mode, bimodal, multimodal, outliers, and box plots
- CA 15U (box plots)

Extra practice

- Supplemental Instructor's notes (with class recording) and extra practice
- review vocabulary on CA 15Q
- read Chapter 15.4 "Box plots"
- read Chapter 15.4 "Summarizing distributions with mean and MAD"

Assign Graded quiz (due day after in-person class)

### 13:

MTW

Video preparation

- Formative quiz (10 minutes)
- finish CA 15U (box plots)

#### Video: How can we measure variability of data? (MAD, variance, standard deviation)

- discuss class preparation activities
- CA 15W (MAD, IQR, variance, standard deviation)
- start stats variability practice

#### Zoom: Extra practice

- finish stats variability practice
- Supplemental Instructor's extra practice
- read Chapter 15.4 "Summarizing distributions with mean and MAD"
- Chapter 15.4 practice exercises: 4
- (optional) read Pool Puzzle (alternate variance formula)

### 14:

MTWTh

Video preparation

- Formative quiz (10 minutes)

#### Video: How can we compare different scores?

- discuss class preparation activities
- introduce student data and normal distributions
- standard scores (aka. z-scores)

#### Zoom: Extra practice

- Supplemental Instructor's extra practice
- Read: Chapter 15.4 "Normal curves and standardized test results"

Assign Graded quiz (due Friday 11:59PM)

### 15:

MTWTh

Video preparation

- Formative quiz (10 minutes)

#### Video: Are variables related to each other?

- discuss class preparation activities
- bivariate data and quartile-quartile lines

#### Zoom: Extra practice

- Supplemental Instructor's notes and extra practice
- compute measures of variability (Desmos)

Student evaluations?

### Final exam

- Tuesday, December 15 at 3pm (online)
- one page of notes, one sided, handwritten
- approved calculator