Data Analysis and Probability
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
- Concepts 9-12 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.
- 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
- Stem-and-Leaf Plotter
- Box and whisker plotter
- 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
- Find your class's hang time and vertical jump statistics - work sheet range, median, mean, mode, graph
- One variable analysis activities - ping-pong ball race, how many stars in a minute, collect data, analyze mean, median. mode.
- 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 0-9 addition - Work sheet with instructional suggestions
- Creat your own BINGO card for 0-9 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 water-borne disease. Snow used some proto-GIS methods to buttress his argument: first he drew Thiessen polygons around the wells, defining straight-line least-distance 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 bad-tasting 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 shortest-travel-distance 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
Other development & activities pages:
- Number value and operations (addition & subtraction, multiplication & division)
- Algebra & patterns
- Geometry spatial reasoning
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 0-312-13985-3 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.