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# Expected Outcomes

Lesson 4 of 5

## Objective: SWBAT calculate the expected number of outcomes by multiplying the probability times the number of trials

## Big Idea: If I roll a die 30 times, how many times can I expect to roll a 1? If I flip a coin 50 times, how many should I expect HEADS?

*50 minutes*

#### Introduction

*10 min*

I will begin with the essential question: how can we predict the number of times an event can be expected to happen?

I will give the example: football players often says "tails never fails" when it comes to selcting the result of a coin toss to determine possession. Is tails expected to occur more often then heads? If a coin is flipped 16 times, how many times can we expect heads?

The lesson also has some notes notes with fill in the blanks. The first blank should be "event". The second blank should be "trial".

The notes show multiplication as the method for finding the number of outcomes. I sometimes show this as a set of equivalent ratios too.

So for example 1 there are two choices:

1/5 * 35 = 7

or

1/5 = ?/35

In either case, a four can be expected to occur seven out of thirty-five times.

#### Resources

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#### Guided Problem Solving

*15 min*

The guided problem section only has two problems. Students may work in pairs or groups on these problems.

There is another method I may present to students for finding outcomes. This works especially well with a spinner. Problem GP1, has 6 equally divided parts. That means out of 24 spins each part should be expect to occur 24 divided 6 = 4 times. Labeling 4 in each section is often helpful for students.

Watch out for errors on the second problem. Especially when asked how many times the outcome of 5 or 6 can be expected. This could be solved by multiplying 2/6 * 42 = 14.

#### Resources

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#### Independent Problem Solving

*20 min*

This set of problems should be done independently. The first two problems are more similar to the guided problems. Problems 3 and 4 are trickier in that each section of a spinner is not necessarily occupied by a different value. On problem 3, the spinner has 6 equal parts; the letter A has 4 of those parts and the letter B has the remaining two parts. Sometimes students think that means the sample space is A, B. In this case it might help to say "list all the places where the spinner might stop".

Problem 4 has the spinner divided into one one-half section and two one-fourth sections. The number 2 sits in a one-half space and the number 3 sits in a one-fourth section. Look out for students who think the probability of either a two or three (or four) is one-third. I may ask "What fraction of the spinner is occupied by the 3?"

#### Resources

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#### Exit Ticket

*5 min*

The exit ticket has 3 items. The first two are multiple choice and the last one is open ended. If students can answer the two multiple choice questions then I know they have the basic fundamental of determining expected outcomes.

The third question asks students to explain how to find the expected outcomes. It almost forces them to answer using the two steps presented in the lesson. I will take any valid answer that I can follow and apply to correctly determine the expected outcomes.

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