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

No class (Labor Day)

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

How do values influence probability situations?

Thursday

Quiz 1

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

try fair games? through "make fair"

What happens to probability when given new information?

3:

Monday

try fair games? challenge

What are some misconceptions about probability?

Wednesday

How can linear situations be identified?

Thursday

Quiz 2

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

Read Patterns of patterns

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

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

Quiz 3

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)

How can we measure variability of data? (IQR)

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)

Are variables related to each other?

Thursday

Quiz 5

Friday

No class

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

8:

Monday

finish scatterplot on comparisons

Student evaluations

Are variables related to each other? (continued)

Tuesday

Review

Thursday

Review

  • Questions only

Reminder: Final exam tonight!

Friday

Make-up final exams

Final exam

Make-up examination