NCTM
Grades 9-12
Data Analysis and Probability
Understand and apply basic concepts of probability
Lessons (5)
Introduces conditional probability and the probability of simultaneous events.
Introduces students to concepts that lead to probability.
Introduces students to simple probability concepts.
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Introduces the concept of tree diagrams as a way to compute probability of a multi-step event.
Activities (13)
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.
Run a simulation of how a fire spreads through a stand of trees, learning about probability and chaos. Track the results of multiple burns and use the data to draw conclusions.
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.
Experiment with probability using a fixed size section spinner, a variable section spinner, two regular 6-sided dice or customized dice.
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.
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.
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.