-Read question -”Would we say that it is very likely? Unlikely? Impossible?”
Read objective.
Lets Review -We know that probability is the likelihood that a certain event will take place. -One way to describe the probability of an event is using a ratio. So the probability of event A equals the number of outcomes that result in event A and total possible outcomes.
A common mistake that students often make is understanding that… If an event is independent then its’ probability remains the same no matter the number of trials.
Heads Tails 2 8 Say for example I tossed a coin 10 times and got the following results. 2 heads and 8 tails. Based off the results what is the likelihood of getting a heads in the next toss? Now, since I have rolled 8 tails already I might be thinking I’m due for a heads and the probability might be something higher like 3/4ths. But this is not the case because the toss of the coin is an INDEPENDENT event. The last ten tosses do not effect my likelihood of tossing a heads the 11th time which is why the probability remains 1 out of 2.
l l Being able to describe probability in numbers is important but it is also important to understand what those numbers mean in words. We can do this using a probability continuum,. Probability tells the likelihood of an event and the two different extremes are an event that is completely impossible or an event that is certain to occur. -For example, fish will never fall from the sky and that is an impossible event. On the opposite end, the sun will always rise which makes it certain to occur.
The probability continuum: l l impossible certain If we were to describe an impossible event in numbers it would be 0, it has a zero chance of occurring because it is impossible. And a certain event has a 1 out of 1 chance of occurring or just one because it is certain. The majority of probability is concerned with things in between, events that are not certain.
l l l l l So we know that the probability of an event occurring is between 0 and 1. Then directly in between zero and 1 is ½, this would be an event that is equally likely. For example, getting either a heads or a tails on a coin has a probability of 1/2 because both scenarios (heads or tails) have an equally likely chance of occurring. -In between 0 and ½ is ¼ which is an unlikely event. Then in between ½ and 1 is ¾ which is a likely event. The probability of an event occurring can fall anywhere on this line and we use these words to describe their likelihood in words.
So how could we describe in words what the probability is of the spinner landing on green? First we need to divide the spinner into equal parts. If we draw a line here then we would have the circle in to equal parts. This breaks each spot into equal spots and there are eight total, with four of them being green. So 4/8th is the probability of this spinner landing on green which reduces to ½.
l l l l l Looking back at the probability continuum we see that ½ has an equally likely chance of occurring. So the probability of that spinner landing on green was equally likely meaning there is an equally likely chance the the spinner will land on green as there is that it won’t land on green.
What if the problem had asked to describe the probability of the spinner landing on yellow? We again draw our line to divide the circle in to equal parts. Even though green is not our desired outcome in this situation we still need to divide in to equal parts so that the total number of possibilities is correct. There are 8 equal sections, so our denominator is 8. There is one section of the 8 that is yellow so 1 is our numerator. The fraction cannot be reduced and therefore the probability of the spinner landing on yellow is 1/8.
l l l l l Again we look back at our probability continuum so that we can describe the likelihood of yellow occurring in words. The interesting thing is that 1/8 is not one of the values we have here on our number line. 1/8/s would be halfway inbetween 0 and ¼…here. When describing values that are not ¼ or ¾ we must use our best sense according to what we know about probability. We know that ½ is equally likely and therefore as we get above ½ the closer and closer we get to one, the more certain an event becomes. As the probability gets below ½ it becomes more unlikely that it will occur…the closer the probability gets to impossible or 0 the less and less likely it is to occur. So again our spot of 1/8 is very close to 0 so we can say that the likelihood of the spinner landing on yellow is very unlikely.
Read objective.
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: --”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.