# 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:

Monday

#### Introductions

- assign groups
- syllabus scavenger hunt
- what is a statistical question and sampling
- extra practice, read Grade 7: Chance and probability for background information
- extra practice, experiment with NRICH: Which spinners?

Tuesday

#### How do experiments lead to probability?

- discuss fraction operations
- teams need: 2d6 (different colors), d4, d8, Roller derby board
- Roller Derby with 2d6 (common misconception: uniform probability)
- Law of large numbers with Monte Carlo simulation using Excel
- Roller Derby with d4 + d8

Wednesday

Use Excel to create a Monte-Carlo simulation for d4 + d8

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

- 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

Friday

watch counting principle

finish CA 16g

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

- 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)

### 2:

Monday

Daily quiz (formative)

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

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

Tuesday

Daily quiz (formative)

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

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

Wednesday

try free throws challenge

Daily quiz (graded)

#### How do values influence probability situations?

- 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)

Friday

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

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

### 3:

Monday

try spinners

Daily quiz (formative)

#### What are some misconceptions about probability?

- discuss spinners

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

Tuesday

CA 16K

Daily quiz (formative)

#### How can linear situations be identified?

- 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)

Wednesday

Daily quiz (graded)

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

- start finite differences
- extra practice, read: Patterns of patterns

Friday

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

- finish finite differences
- extra practice, read: Patterns of patterns

### 4:

Monday

try CA 9U #1

Daily quiz (formative)

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

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

Tuesday

finish through #4 on CA 9U

Daily quiz (formative)

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

- 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

Friday

#### Exam I

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

### 5:

Monday

New groups & review exam

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

- 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)

Tuesday

Daily quiz (formative)

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

- 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

Wednesday

Daily quiz (graded)

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

- 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)

Friday

find medians for each list in 15K.2

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

- 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

### 6:

Monday

finish CA 15P

Daily quiz (formative)

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

Tuesday

finish CA 15U

Daily quiz (formative)

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

- 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

Wednesday

Daily quiz (graded)

Planning for final exam

#### How can we compare scores between different groups?

- example student data
- analyze standard scores using 68-95-99.7 rule
- extra practice, practice: measures of variability
- extra practice, read Chapter 15.4 "Normal curves and standardized test results"

Friday

finish standard scores

#### Are variables related to each other?

- discuss z-scores and normal distribution
- comparisons
- quartile-quartile line and interpretations (Desmos)
- extra practice, compute measures of variability (Desmos)

### 7:

#### No classes

### 8:

#### Spring break

### 9:

#### No classes

### 10:

#### Final exam Friday, April 10 (see Canvas for more details)

### End of course information

- Use the arrow buttons to see the previous weeks