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

Labor Day - no classes

Wednesday

Introductions

Thursday

experiment with NRICH: Which spinners?

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

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

Daily quiz (formative)

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 Kobe Bryant free throws

Daily quiz (graded)

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

Thursday

try free throws challenge (will discuss next class)

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

Friday

free throws challenge

Daily quiz (formative)

How do values influence probability situations?

3:

Monday

Daily quiz (formative)

How do values influence probability situations? (continued)

Wednesday

try spinners

Daily quiz (graded)

What are some misconceptions about probability?

  • discuss spinners
    (angle more important than area)
  • CA 16K
  • extra practice, Lost key puzzle

Thursday

CA 16B and 16J

How can linear situations be identified?

  • start Is it linear?
  • extra practice, 16.4 problems: 1 (1/16), 2 (1/12), 9 (3/8)

Friday

Daily quiz (formative)

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

4:

Monday

Daily quiz (formative)

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

  • finish finite differences
  • start CA 9U, strip diagrams
  • extra practice, 16.3 problems: 14 (2/20, 20, $30)
  • extra practice, read "Using a Model Approach to Enhance Algebraic Thinking in the Elementary School Mathematics Classroom" (in Canvas)

Wednesday

finish through #4 on CA 9U

Daily quiz (graded)

How can linear equations be solved different ways?

  • 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

Thursday

Review

Friday

Exam I

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

5:

Monday

New groups & review exam

What is statistics?

  • What is a statistical question (CA 15A.1)
  • 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)

Wednesday

Daily quiz (graded)

How can data be displayed different ways?

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

Thursday

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

No class

6:

Monday

find medians for each list in 15K.2

Daily quiz (formative)

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

Wednesday

finish CA 15P

Daily quiz (graded)

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

  • discuss CA 15P
  • definitions: mode, bimodal, multimodal, outliers, and box plots
  • CA 15U: also create data with outlier
  • extra practice, review vocabulary on CA 15q
  • extra practice, reading: Chapter 15.4 "Box plots"

Thursday

finish CA 15U

How can we measure variability of data?

  • CA 15W: compute MAD, IRQ (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, reading: variance alternative computation

Friday

Daily quiz (formative)

Planning for final exam

How can we compare scores between different groups?

7:

Monday

finish standard scores

Daily quiz (formative)

Are variables related to each other?

Wednesday

Daily quiz (graded)

Are variables related to each other? (continued)

Student evaluations

Thursday

Review

Final exam at 7 pm (Hibbard 100)

  • one page of notes (1 sided, handwritten)
  • approved calculators

Friday

Make-up exams 11am - 2pm (HHH 312)

End of course information