# Probability and statistics in grades 1-8

## Calendar

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:

Wed/Thurs

Class preparation

#### Class: Introductions

- discuss class preparation activities
- assign groups
- discuss class preparation activities
- extra practice, read Grade 7: Chance and probability for background information
- extra practice, experiment with NRICH: Which spinners?

### 2:

Mon/Tues

Class canceled due to Labor Day

Wed/Thurs

Class preparation

- fraction operations
- play Roller derby on own or with friend, bring record of dice rolls to class

#### Class: How do experiments lead to probability?

- discuss class preparation activities
- teams need: 2d6 (different colors), d4, d8, Roller derby board
- introduce notation for experimental probability
- Law of large numbers with Monte Carlo simulation using Excel

### 3:

Mon/Tues

Class preparation

#### Class: How can we determine probability without experiments?

- discuss class preparation activities
- Sample space for d4 + d8 using: list (dice examples), grid, tree diagram
- Create list, grid or tree diagram for 2d4 (hint: P(5) = 1/4)
- CA 16F, CA 16G
- extra practice, Chapter 16.2 practice exercises: 1, 2

Wed/Thurs

Class preparation

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

- discuss class preparation activities
- tree diagram for CA 16G.2
- weighted tree diagrams for probability: compound probabilities
- extra practice, 16.2 practice exercises: 4
- extra practice, 16.1 problems: 1 (3/8, 4/8, 6/8), 2 (various, 5/12, various)

### 4:

Mon/Tues

Class preparation

#### Class: How can tree diagrams be used in different contexts? (continued)

- discuss class preparation activities
- discuss and finish compound probabilities
- extra practice, 16.3 problems: 5 (9/16), 6 (1/64)
- extra practice, NRICH: Odds and Evens

Wed/Thurs

Class preparation

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

- discuss class preparation activities
- two-way frequency tables
- extra practice, see WebWoRK problems for "conditional probability" in Canvas

### 5:

Mon/Tues

Class preparation

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

- discuss class preparation activities
- expected value and fair games
- extra practice, read: Expected value
- extra practice, To insure or not to insure? (NRICH)

( EV(insurance) = -25; EV(no insurance) = -50; insurance is better)

Wed/Thurs

Class preparation

#### Class: How do values influence probability situations? (continued)

- discuss class preparation activities
- fair games challenge problems
- extra practice, Watch Dan Gilbert's discussion on decision making

### 6:

Mon/Tues

Class preparation

#### Class: What are some misconceptions about probability?

- discuss class preparation activities
- discuss spinners

(angle more important than area) - CA 16B, CA 16J, CA 16K (~29 prizes, $92-$93)
- extra practice, Lost key puzzle

Wed/Thurs

Class preparation

#### Class: How can linear situations be identified?

- discuss class preparation activities
- start Is it linear?
- extra practice, 16.3 problems: 14 (1/10, 20, $30)
- extra practice, 16.4 problems: 1 (1/16), 2 (1/12), 9 (3/8)

### 7:

Mon/Tues

Class preparation

#### Class: How can (polynomial) formulas be developed for non-linear situations?

- discuss class preparation activities
- start finite differences
- extra practice, read: Patterns of patterns

Wed/Thurs

Class preparation

#### Class: How can (polynomial) formulas be developed for non-linear situations? (continued)

- discuss class preparation activities
- finish finite differences
- extra practice, read: Patterns of patterns

### 8:

Mon/Tues

Class preparation

#### Review

- discuss class preparation activities
- clean out folders
- review topics

Wed/Thurs

Class preparation

#### Exam I

- discuss class preparation activities
- approved calculators allowed
- one pages notes (1-sided, handwritten)
- manipulatives

### 9:

Mon/Tues

Class preparation

Review exam

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

- discuss class preparation activities
- start CA 9U, strip diagrams
- extra practice, read "Using a Model Approach to Enhance Algebraic Thinking in the Elementary School Mathematics Classroom" (in Canvas)

Wed/Thurs

Class preparation

#### Class: How can linear equations be solved different ways? (continued)

- discuss class preparation activities
- continue CA 9U, strip diagrams
- (if time) CA 9W
- extra practice, read Chapter 9.5
- extra practice, Chapter 9.4 practice exercises: 3
- extra practice, Chapter 9.5 practice exercises: 1, 2, 3

### 10:

Mon/Tues

Class preparation

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

- discuss class preparation activities
- sampling 1b
- types of displays: pictographs, bar, pie, dot, histogram, steam-and-leaf, line graph, scatterplot
- extra practice, Chapter 15.1 practice: 1, 3
- extra practice, CA 15C (see instructor with questions)

Wed/Thurs

Class preparation

#### Class: How can data be displayed different ways? (continued)

- discuss class preparation activities
- share types of displays: pictographs, bar, pie, dot, histogram, steam-and-leaf, line graph, scatterplot
- data display errors (CA 15E)
- extra practice, read Chapter 15.2
- extra practice, Chapter 15.2 practice exercises: 1a, 2, 3

### 11:

Mon/Tues

Class preparation

#### Class: How can we measure the "center" of data?

- discuss class preparation activities
- arithmetic mean (leveling): CA 15K, CA 15L
- median: CA 15K.2
- extra practice, Chapter 15.3 practice exercises: 1
- extra practice, Chapter 15.3 problems: 3 (32)

Wed/Thurs

Class preparation

#### Class: How can we measure variability of data? (IQR)

- discuss class preparation activities
- discuss CA 15K.2 medians
- define quartiles (exclusive), five-number summary, IQR
- CA 15T, 15P
- extra practice, Chapter 15.3 practice exercises: 3
- extra practice, Chapter 15.4 practice exercises: 3

### 12:

Mon/Tues

Class preparation

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

Wed/Thurs

Class preparation

#### Class: How can we measure variability of data?

- discuss class preparation activities
- CA 15W: compute MAD, IQR (if time)
- CA 15W: compute variance, standard deviation
- extra practice, reading: Chapter 15.4 "Summarizing distributions with mean and MAD"
- extra practice, Chapter 15.4 practice exercises: 4
- extra practice, read variance alternative computation

### 12:

Mon/Tues

Class preparation

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

Wed/Thurs

Class preparation

#### Class: How can we measure variability of data?

- discuss class preparation activities
- CA 15W: compute MAD, IQR (if time)
- CA 15W: compute variance, standard deviation
- extra practice, reading: Chapter 15.4 "Summarizing distributions with mean and MAD"
- extra practice, Chapter 15.4 practice exercises: 4
- extra practice, read variance alternative computation

### 13:

Mon/Tues

Class preparation

#### Enrichment activities

- discuss class preparation activities

Wed/Thurs

#### No class for Thanksgiving break

- discuss class preparation activities

### 15:

Mon/Tues

Class preparation

#### Are variables related to each other? (continued)

- discuss class preparation activities
- comparisons "sequels" practice
- extra practice, compute measures of variability (Desmos)

Student evaluations

Wed/Thurs

Class preparation

#### Review

- discuss class preparation activities
- clean out folders
- review topics

### 16:

Mon/Tues

Class preparation

Review

#### topic

- discuss class preparation activities
- questions only
- review topics

### Final exam

- Date, time (location)