# Determine Probabilities

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## Objective

SWBAT determine probabilities represented in word problems, tables, and graphs as a ratio

#### Big Idea

Students represent probabilities using the probability ratio

## Introduction

10 minutes

I will begin with the essential question:  How can you describe the probability of an event using a ratio?

I will then present the probability ratio: the number of ways an outcome may occur to the total number of possible outcomes.

The examples use only simple probability.  Later in the lesson students will apply what they have learned in previous lessons about list outcomes to determine compound probabilities.

Each example it paired with a check for understanding question.  I'll use these to determine how best to support students during the guided practice.

## Guided Problem Solving

15 minutes

Students will work on these problems.  They may get help from their neighbors.  Students should list the sample space for each problem.  This will make sure they are not overlooking anything.  It will also help me diagnose their work.

The first 3 problems are simple probability problems.  The last two problems are compound probability problems.

## Independent Problem Solving

20 minutes

Students have 5 problems to solve on their own.  These are very similar to the previous 5 problems.  Again I will expect students to list the sample spaces for each problem.  Also I will encourage students to write in values on the bar graph for problem 3.  I always encourage students to do this so that they don't have to keep re-interpreting the graph; it is much easier to read the number.

The extension problems add an element of complexity.

Problem 6 simply provides a ratio of red to green apples - twice as many red apples.  Look out for students who think the sample space is a multiple of 2 - it should be a multiple of 3.  Also, some students will say that the problem doesn't tell how many of each apple there are.  I may say "if there are 20 red apples, how many green apples are there? How about if there are 10 red apples/30 red apples/100 red apples?  Does the probability change?"

Problem 7B asks students to change the probability of a white token to 25%.  Students find two different ways to make this happen.  When students struggle with this, I may offer that they follow a guess and check strategy by saying "What have you tried?  What did you notice?".

## Exit Ticket

5 minutes

Students will take a 4 question multiple choice exit ticket.  This could just as well be an open response exit ticket, but I like including multiple choice from time to time.  For one thing, it is easier to grade.  Also, it helps me see what "gotchas" students are falling for in the wrong answer choices, since all wrong choices are based on common errors and misconceptions.

A students should be able to answer at least 3 problems correctly to show mastery of the lesson content.