Probability and Statistics

1. Probability and Statistics ECI 695 February 19, 2009 Day 6

2. Week 5 Homework • Read DMI Chapter 5 • Video: Woodpecker Habitat • Math Activity: Median as a Tool in Data Description • Reading: Stem and Leaf Plots in the Primary Grades • Reading: NCTM Yearbook Chapters 1 and 2 • Project 1: Feb 26

3. Steckroth Website • http://www.odu.edu/~jsteckro/ • Check this site for additional documents until Blackboard is operational

4. Week 6 Agenda • Read DMI Chapter 5 • Video: Woodpecker Habitat • Math Activity: Median as a Tool in Data Description • Reading: Stem and Leaf Plots in the Primary Grades • Reading: NCTM Yearbook Chapters 1 and 2

5. MATH ACTIVITY: MEDIAN AS A TOOL IN DATA DESCRIPTION

6. STEM AND LEAF PLOTS IN THE PRIMARY GRADES

7. Birthday Data

8. SWEDEN: BUS SCHEDULE

9. LOCAL BUS SCHEDULE

10. See Handout MATH ACTIVITY: TEETH

13. Kindergarten

15. TI Graphing CalculatorAnalysis of Grade 1 Data

16. Lost Teeth Data

17. Question 2 • Describe and compare the four sets of data. Are the four grades similar? Different?

18. Grade 2 n = 20

19. Grade 2 n = 20 Median = (8 + 8)/2 = 8

20. Grade 2 n = 20 Median = (8 + 8)/2 = 8 Q1 = (8 + 8)/2 = 8

21. Grade 2 n = 20 Median = (8 + 8)/2 = 8 Q1 = (8 + 8)/2 = 8 Q3 = (10 + 10)/2 = 10

22. Grade 2 n = 20 Median = (8 + 8)/2 = 8 Minimum = 2 Q1 = (8 + 8)/2 = 8 Maximum = 13 Q3 = (10 + 10)/2 = 10

23. Grade 2 n = 20 2, 8, 8, 10, 13 IQR = 10 - 8 = 2

24. Outliers? 5NS = 2, 8, 8, 10, 13 IQR = 2 1.5 ( 2 ) = 3

25. Outliers? 5NS = 2, 8, 8, 10, 13 IQR = 2 MWL = 1.5 ( 2 ) = 3 LF = LQ - MWL = 8 - 3 = 5 UF = UQ + MWL = 10 + 3 = 13

26. Grade 3 B&W

27. Question 3 • If just the mode for each grade were reported to you, what would that tell you about the data? • What wouldn’t you be able to tell?

28. Question 4 • Find the median number of teeth lost for each grade. If just the median for each grade were reported to you, how would that help you compare the grade levels?

29. Question 5 • Complete for Homework

30. Teeth Video

31. Woodpecker Habitat

32. Statistical Investigation Question Collect Data Analyze Interpret Communicate

33. Red-cockaded Woodpecker

34. Red-cockaded Woodpecker This endangered woodpecker is found in old, open pine forests. Creates nest cavities in living pine trees. Holes for pine resin to ooze are created in cavity trees to prevent snakes from climbing the tree. Males have a small red patch of feathers located near the ear (or cockade), which is rarely seen in the field. Also called RCW, this species is about the size of an eastern bluebird (8 1/2”).

37. RCW

38. Woodpecker Habitat Probability and Sampling

39. Mathematical Topics • Sampling • With replacement • Without replacement • Collecting data • Representing data • Making Predictions • Reliability of samples • Use of calculators

40. SIMULATION

42. GRAPHING WITH FOUR-YEAR-OLDS Yearbook Chapter 1

43. Emerging Mathematical Abilities • Comprehending one-to-one correspondence • Understanding set membership • Retrieving information • Creating order

44. Goal • Support children’s use of mathematical reasoning as they move from collecting to interpreting data.

45. Professional Development • What are children capable of doing? • How do you talk with young children?

46. Graphing through surveys Advantages: • Familiar activities • Interesting to children • Opportunities for mathematical reasoning • Cross-content areas

47. Harold’s Survey

48. Harold’s Accomplishments • Posed his own question • Demonstrated 1-to-1 correspondence • Displayed several levels of info • Invented symbols • Solved a problem (no answer) • Sought validity • Organized his recordings into groups

49. Intention vs. Convention • “Just because a child’s product may look unconventional on the surface, it does not mean that it lacks intention.”

50. Concerns • Graphs must conform to standard formats • Children must be shown “how” • Lack of confidence in their ability to collect and organize data • Fear of how to talk with children about their ideas