If we were to spin this spinner, what is the probability that the arrow will land on blue?

In this lesson you will learn how to calculate the probability of an event by creating a ratio.

Lets review, ratios can be used to represent fractions of an area like in this example in which the shaded area takes up 3/8 of the whole circle. Or a fraction of a set like this in which one out of the four stars is shaded orange. And in this lesson we are going to use ratios to represent the likelihood of a certain event occurring.

One common mistake that people often make when talking about probability is that we need to remember that every event must have an equal probability of occurring. For example, with this spinner, we cannot say that there is a 1/3 chance of the spinner landing on blue because the blue section of the spinner takes up much more space then the other two colors. Meaning not every event is equal. This second spinner is an example of three equal parts and therefore we can conclude that there is a 1 in 3 chance of the spinner landing on blue.

Now…probability is the likelihood that a certain event will take place. We use probability constantly in our daily lives in order to make crucial decisions. For example, when the weather man tells us that there is an 80% chance of rain on the news we know that we should probably bring our umbrella if we are going to go outside. Because there is a high probability that it will rain. We can write a ratio that represents the likelihood of an event. Think of some event that I will call A. The P(A) then is going to equal the number of outcomes that result in event A OVER the total possible outcomes. Let’s take a look back at our spinner problem and make a ratio.

So…back to our question So…back to our question. What is the probability that the spinner will land on blue? Well I’m going to write the p or probability of my event blue in parenthesis equals a ratio. The denominator is going to be the total possible outcomes which I cannot say yet, BECAUSE if I remember the common mistake every event must have an equal opportunity. So I’m going to break up this circle into even parts and I see that the smallest increment is the size of this orange triangle. So lets break up the circle into equal parts. The yellow dotted lines are how we could break up the circle into eight equal parts. Blue takes a lot of the spots but now we can compare it to the orange. We now have our denominator representing the total possible outcomes which is eight. The numerator represents the number of times we could possibly get blue. And there is 1. 2. 3. 4. 5…5 chances of getting blue. So there is 5 out of eight equal chances that the spinner will land on blue.

Let’s try an even harder problem now. Read problem.

So I’m trying to find the probability as P then parenthesis and the two events I am looking for is a pear or an apple which I will write as P or A and we are trying to get some ratio. The things we know is that there are 3 apples….2 oranges…and 5 pears. For my denominator I want the total of possible outcomes which would be the total number of fruits here. If I add them all up I get 10 fruits total. I have my denominator. Now the desired outcome is an apple or a pear. There is 3 apples and 5 pears meaning 8 possibilities of getting the desired outcome. So an 8 out of 10 possible of getting a pear or an apple. This reduces to 4/5 fifths.

In this lesson you have learned how to calculate the probability of an event by creating a ratio.

LearnZillion Notes: --The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

LearnZillion Notes: --On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly 20-40 minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient. --If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

LearnZillion Notes: --On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly 20-40 minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient. --If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

LearnZillion Notes: --On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly 20-40 minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient. --If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.