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PA-D-2-1

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.D.2.1 Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown

In a Nutshell

Students enter Pre-Algebra with a knowledge of comparing fractions and decimals. This knowledge can be extended to also compare probabilities when represented as percents, fractions, and decimals. Students also have a working knowledge of theoretical probability from previous grades, which can now be extended and built upon. Students at this level need to conduct experiments and record outcomes and calculate experimental probability as fractions and decimals, and be able to represent a probable chance as a percent. They must develop the understanding that an experimental probability will allow you to make predictions when theoretical or actual probabilities are unknown. This provides students the opportunity to gather data on a small number of events when a larger population is not feasible. It is important for students to understand every probability will have a value between zero and one, including an impossible probability is equal to zero, while a probability that includes all possibilities, a certain event, is equal to one.

Student Actions	Teacher Actions
Develop Mathematical Reasoning when given an activity, such as rolling a number cube, to calculate experimental probability, while making meaning of the term sample space by describing the possible outcomes. Develop Accurate and Appropriate Procedural Fluency by being able to describe what is meant by and the importance of “randomly selected” or “at random” as part of the criteria for calculating probabilities. Develop Accurate and Appropriate Procedural Fluency when conducting experimental probabilities and writing the probability as a fraction from 0-1, a percent 0-100, and as a decimal between 0-1. This requires recalling how to calculate simple theoretical probability. Develop Ability to Make Conjectures, Model or Generalize when given a group of objects or numbers, create simple theoretical probability questions that have a rate of occurrence of 0 or 0%; as well as, a rate of occurrence of 1 or 100%. Develop Mathematical Reasoning by combining several small simple experimental probability trials and analyzing computer simulations, draw conclusions that support the fundamental idea that the more times experimental probability is calculated, the closer it is to the theoretical probability value. Develop Problem Solving Strategies when exploring real life contexts and activities that use simple experimental probability to make predictions when theoretical probabilities can't be calculated or are not efficient. Ex) animal populations or cell mutations	Promote procedural fluency by providing students with multiple activities to calculate experimental probabilities. Facilitate meaningful mathematical discourse when allowing students to discuss various data collection techniques. Emphasize the important idea of random selection for fairness when calculating probability. When this is absent, bias skews the probability making the calculation not valid. Implement tasks that promote reasoning and problem solving by usingreal world contexts for students to explore probability (lottery, student selection,weather, etc…) Promote procedural fluency by reinforcing that probability can always be written in fractional form from 0-1, decimal form from 0-1 and percent form from 0-100. Encourage students to make probability predictions before calculations. Implement tasks that promote reasoning and problem solving when using technology for experimental probability simulations to produce several outcomes to allow students to make the connection that the more trials completed, the closer the experimental probability matches the theoretical probability.
Key Understandings	Misconceptions
Calculate experimental probability. Represent probability at fractions, decimals, and percents. Make predictions of unknown probabilities Perform experiments and collect data Use words such as impossible, unlikely, equally likely, likely, or certain to describe the likelihood of an event occurring Understand that relative frequencies (experimental probability) doesn’t always fit with theoretical probability Understand that relative frequency (experimental probability) comes closer to theoretical probability as the number of trials increases.	Students think the odds of an event occurring is the same as probability. Students mistakenly believe probability can be a number larger than 1. Students may confuse experimental and theoretical probability. Students predict the likelihood based on absolute rather than relative size.