# 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.

### 1:

Monday

Wednesday

#### Introductions

Thursday

Read Grade 7: Chance and probability (CCSSM Progressions) for background information

#### How do experiments lead to probability?

• 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
• Extra practice, Nrich: Which spinners?
Friday

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;

### 2:

Monday

watch counting principle

finish CA 16G (in Beckmann book or D2L "Content")

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

• tree diagram for CA 16G.2
• weighted tree diagrams for probability: free throws
• Extra practice, 16.2 practice exercises: 4
• Extra practice, 16.1 problems: 1 (3/8, 4/8, 6/8), 2 (various, 5/12, various)
Wednesday

try free throws challenge

Thursday

#### Quiz 1

• experimental probability
• theoretical probability
• sample space
• expected value (on group part)
Friday

try fair games? through "make fair"

### 3:

Monday

try fair games? challenge

Wednesday

Thursday

#### Quiz 2

• expected value
• conditional probability
• linear situations and equations
Friday

### 4:

Monday

finish finite differences

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

• CA 9S, pan balance
• CA 9U, 1 together, rest on own
• Extra practice, Chapter 9.4 practice exercises: 3
Wednesday

finish 1-6 on CA 9U (in book or D2L)

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

• CA 9U, equations and word problems (in book or D2L)
• Extra practice, Chapter 9.5 practice exercises: 1, 2, 3
Thursday

#### Review

• clean out folders
• review topics
• team challenge (as time permits)
Friday

#### Exam 1

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

### 5:

Monday

New groups & review exam

#### What is statistics?

• What is a statistical question (Class Activity 15A #1)
• types of displays: pictographs, bar, pie, dot, histogram, steam-and-leaf, line graph, scatterplot
• Extra practice, Chapter 15.1 practice: 1
Wednesday

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

• types of displays: pictographs, bar, pie, dot, histogram, steam-and-leaf, line, scatterplot
• CA 15E (data display errors), CA 15C (random sampling)
• Extra practice, read Chapter 15.2
• Extra practice, Chapter 15.1 practice: 3
Thursday

Friday

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

• arithmetic mean (leveling): CA 15K, CA 15L
• arithmetic mean (balancing): CA 15M
• median: CA 15M
• Extra practice, Chapter 15.3 practice: 1
• Extra practice, Chapter 15.3 problems: 3 (32)

### 6:

Monday

Class activity 15P (in book or D2L Content)

Wednesday

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

• definitions: mode, bimodal, multimodal, outliers, and box plots
• CA 15U: also create data with outlier
• Extra practice, review vocabulary on 15Q (in book or D2L)
• Extra practice, read 15.4 "Box plots"
Thursday

#### Quiz 4

• content up through box plots and outliers
Friday

Class activity 15W (in book or D2L Content)

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

• CA 15W: compute MAD, IRQ
• define variance and standard deviation
• CA 15W: compute variance and standard deviation
• compute variance different way
• double-check CA 15W
• Extra pracitce, read 15.4 "Summarizing distributions with mean and MAD"
• Extra practice, 15.4 practice: 4

### 7:

Monday

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

Logistics for final exam

Wednesday

Read "Normal Curves and Standardized Test Results" (p. 692-693)

Thursday

Friday

#### No class

• Includes z-scores, percentiles
• Does not include scatterplots

### 8:

Monday

finish scatterplot on comparisons

Student evaluations

Tuesday

Thursday

#### Review

• Questions only

Reminder: Final exam tonight!

Friday

### Final exam

• Thursday, October 25, 7pm (location HHH 100)
• approved calculators
• one page notes (1-sided, handwritten)

#### Make-up examination

• Friday, October 26 during "class" times (HHH 312)