Data Analysis and Probability
Knowledge base & tools to develop mathematical literacy
Knowledge base
The mathematical knowledge base includes concepts necessary for learners to conceptualize to become mathemtically literate and misconceptions that must be over come to be literate in geometry and spatial reasoning.
 Data analysis
 Probability
 Concepts 912 from Science for All America s (SFAA) & National Assessment for Educational Progress (NAEP )
 Data analysis & probability vocabulary  lists of vocabulary for primary, middle, & upper levels.

Graphing sequence
 K  3 average, bar graph, concrete real object graph, data, grid, picture graph, table, tally, trial
 4  6 broken line graph, descriptive statistics, equally likely events, extrapolate, frequency, generalization, histogram, inference, interpret, interpolate, line graph, line plot, mean, media, midway, mode, ordered pair, outcome, probability, quadrant, random, range, ratio, sample, scale drawin,g simple event, statistics
 7  9 box plot, compound event, circle graph, error of measurement, extrapolate, mutually exclusive, outlier, quartile, scatter plot, skew, lines stem and leaf plot, whisker
 Statistics timeline and history
Information on the development of literacy in data analysis & probability & tools to achieve it
 Probability  Development with sample problems, explanation of experimental & theoretical probability (with examples) & Reader's Theater carnival problem to solve.
 Probability Rubric  applicable for all levels
 Probability Instructional map  Maps probability as theoretical & experimental concepts, to dice activities, & instruction with a learning cycle instructional method
 Coordinate Graphing Notes  Data sheet for data analysis, variables, relationships, and graphing
 Graph paper  11 high 9 wide 2 cm squares
 Normal curves  Visual graphs & charts with normal curve, standard deviation, z scores, stanines, percentiles, SAT, ACT, IQ, cummulative percentages, quartiles, percent in stanines
 Frequency distribution  visual examples with charts and graphs; central tendency; percentiles; and correlations
Activities to facilitate data analysis & probability literacy
Data analysis
 Find your class's hang time and vertical jump statistics  work sheet range, median, mean, mode, graph
 One variable analysis activities  pingpong ball race, how many stars in a minute, collect data, analyze mean, median. mode.
Probability
 One die & two die sum  Complete lesson plans & Work sheets
 Tiles in a sock  3 activities, Complete lesson plan in chart format
 Sampling number of chips in chocolate chip cookie  Complete lesson plan in linear format
 Spinners  3 activities with spinners of equal sections, some with the same numbers and others with different numbers. Work sheet with hints and spinner patterns.
 Create your own BINGO card for 09 addition  Work sheet with instructional suggestions
 Creat your own BINGO card for 09 subtraction  Work sheet with instructional suggestions
 Body proportions  Work sheet to compare the proportion of four body parts to arm length.
 Flippping 1, 2, 3, & 4 coins  Work sheet with hints.
 Pick two card game  Work sheet for card game to pick two of six to win includes charts, hints, & tree diagram.
 Sickle Cell investigation  Work sheet with Background information & hints. Use of a Punnett Square to determine different probabilities theoretically & experimentally probability
 M&M® Challenge  activity directions and work sheets for data analysis, mean, median, mode, & graphing of colors of M&M's. Can be used for probability.
 Simulation to count a species in a pond population with capture, tag, release, and recapture  Work sheet with hint
 Simulation to determine populations of five species with capture, release, and recapture using ratio and proportion  Work sheet with hint
 Frogs in a pond problem  Work sheet as assessment of ratio, proportion, and capture release. Also used as a Thinking Puzzles: Concrete and Formal Operational Thought Solutions
 The Case of the Carnival Probability Game  Instructional materials: Sample problem with explanation as experimental & theoretical probability & Reader's Theater script for the carnival problem to solve.
 Three coin problem  Work sheet with hints & discussion ideas
 Car keys sweepstakes fair or fixed?  Work sheet with hints & discussion ideas
 Envelopes of cash or not. What are the odds?  Work sheet with hints & discussion ideas.
 Aces for dinner: Which version gives you the better odds?  Work sheet with hints & discussion ideas.
 Sack lunches. Teacher randomly passes out lunches. What are the odds?  Work sheet with hints & discussion ideas.
 Rubber band stretch simulation  is it proportionally accurate?
 John Snow: Analysis for cholera in London, England.
 Snow's map, demonstrated the spatial clustering of cholera deaths around the Broad Street well, provided strong evidence in support of his theory that cholera was a waterborne disease. Snow used some protoGIS methods to buttress his argument: first he drew Thiessen polygons around the wells, defining straightline leastdistance service areas for each. A large majority of the cholera deaths fell within the Thiessen polygon surrounding the Broad Street pump, amd a large portion of the remaining deaths were on the Broad Street side of the polygon surrouding the badtasting Carnaby Street well. Next, using a pencil and string, Snow redrew the service area polygons to reflect shortest routes along streets to wells. An even larger proportion of the cholera deaths fell within the shortesttraveldistance area around the Broad Street pump.
 Finding Pi with probability. Use a toothpick, nail, or needle & sheet of construction paper. Draw parallel lines that are spaced apart the length of the nail across the width of the paper for the length of the paper. Drop the needle from about a half meter above the paper and record if the toothpick lands on a line or not 50 times. Calculate the ratio and see how close it is to π (pi = 3.141592653589793...)
Ratio and Proportion information
Page Overview:

Other development & activities pages:
Process dimensions:
Content dimensions:
 Number value and operations (addition & subtraction, multiplication & division)
 Algebra & patterns
 Geometry spatial reasoning
 Measurement

Excellent source of ideas and problems:
The Power of Logical Thinking:
Easy Lessons in the Art of Reasoning... and Hard Facts About Its Absence
in Our Lives.
Marilyn Vos Savant (1996) ISBN 0312139853 Saint
Martin's Press: New York.

One of the universal customs that man has successfully established on earth is the
Hindu  Arabic numerals
to record numbers.

Data is just numbers. They need an explanation or theory to make it data.



Read... Cell phone mathematics. The story of how Brad Parkinson used creativity and mathematics to enable the use of cell phones.