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A1-D-2-1

Page history last edited by Brenda Butz 6 years, 2 months ago

A1.D.2.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

In a Nutshell

Students will calculate probabilities to solve real world problems in the form of experimental probabilities, probability as a fraction of sample space or area, and used random number generators to conduct simulations.

Student Actions	Teacher Actions
Students develop mathematical reasoning by using a counting procedure to determine the size of a sample space. Students will interpret real-world models to make conjectures, model, and generalize a sample space to calculate probabilities	Use and connect mathematical representations by having the students use multiple representations to determine size of the sample space. Implement tasks that promote reasoning and problem solving for students to calculate probabilities. Encourage productive struggle as the students explore and discuss how to determine the sample size and whether to use a multiplication or addition principle.
Key Understandings	Misconceptions
An addition principle is when two or more events have no common outcomes, the total number of outcomes can be calculated by adding up the possible outcomes for each event. Example: Suppose you want to buy a new cell phone. You have 2 makes to choose from, Apple or Samsung. Apple has 15 different models to chose while Samsung has 18. How many models altogether are there to choose from? Choose Apple: 15 Choose Samsung: 18 15+18= 33 different models A multiplication principle is when you can do one task in "a" number of ways and a second task in "b" number of ways, then both tasks can be done in a x b number of ways. Example: You are given a choice of 3 different sandwiches and 2 different drinks for lunch. How many different combinations can you choose from? Task 1, choose sandwiches: 3 Task 2 choose drinks: 2 3 * 2 = 6 possible combinations Sample space, in a probability model for a random process, is a list of the individual outcomes that are to be considered. A tree diagram is a visual to show all possible outcomes of an event.	Students confuse when to use the addition or multiplication principle to calculate the possible outcomes.