NCTM
Grades 9-12
Data Analysis and Probability
Develop and evaluate inferences and predictions that are based on data
Lessons (4)
Students discover algorithms as they sort shapes into Venn diagrams. Then students compare the efficiency of their algorithms using box plots.
Utilizes and reinforces concepts of probability, mean, line plots, experimental data, and chaos in analyzing a forest fire simulation.
Looks at statistics and data analysis concepts from the practical questions that arise in everyday life.
Introduces the normal distribution and looks at the bell curve controversy.
Activities (21)
Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Forest density, wind direction, size of forest.
Create a game spinner with variable sized sectors to look at experimental and theoretical probabilities. Parameters: Sizes of sectors, number of sectors, number of trials.
Choose one of N doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Number of doors, number of trials, staying or switching between the two remaining doors.
Experiment with a simulation to get an approximation of Pi by dropping a needle on a lined sheet of paper.
Simulation of a coin toss allowing the user to input the number of flips. Toss results can be viewed as a list of individual outcomes, ratios, or table.
Compare theoretical and experimental probabilities, using dice, cards, spinners, or coin tosses. Three different probabilities can be compared at once. Parameters: Type of probabilities, number of trials.
Experiment with the outcome distribution for a roll of two dice by simulating a dice throwing game. Parameters: Which player wins with which total rolled.
Run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will set fire to each of its eight neighbors.
Experiment with probability using a fixed size section spinner, a variable section spinner, two regular 6-sided dice or customized dice.
Run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree catches fire if its neighbor is on fire.
This applet allows the user to experiment with randomly generated data sets at various sample sizes and standard deviations. Then, users can compare the distribution of the experimental data to the expected distribution.
Run a simulation to generate results from running the Monty Hall for multiple trials. This is similar to the game show "Let's Make A Deal", where you choose one of N doors in hopes of finding a grand prize behind one of the doors. Parameters: Number of doors, number of trials, staying, or switching between the two remaining doors.
View histograms for built-in or user-specified data. Experiment with how the size of the class intervals influences the appearance of the histogram. Parameters: Data sets, class sizes.
Learn about sampling with and without replacement by randomly drawing marbles from a bag. Parameters: Number and color of marbles in the bag, replacement rule.
Change the standard deviation of an automatically generated normal distribution to create a new histogram. Observe how well the histogram fits the curve, and how areas under the curve correspond to the number of trials. Parameters: standard deviation, number of trials, class intervals.
In this applet you can adjust the parameters on two Gaussian curves to determine if there is a possibility of a difference between the two means.
Simulate a game where two players each roll a die, and the lucky player moves one step to the finish. Parameters: what rolls win and how many steps to the finish line.
Simulate a game where "N" players roll two dice, and the lucky player has an advantage for reaching the finish. Parameters: the number of players, number of trials and length of the race.
Choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Staying or switching between the two remaining doors.
Change the median and standard deviation of an automatically generated normal distribution to create a skewed distribution, allowing you to observe properties like what it means for the mean, median, and mode to be different. Parameters: median, standard deviation, number of trials, class intervals.
Play the Chaos Game by experimenting with probabilities. Learn about an apparently random process with a not-so-random, geometric fractal result.