In this lesson, students will learn how to calculate probability. Students will explore theoretical probability using various contexts, including single events and basic compound events. While working, students will also collect data to help support their learning of experimental probability in the next lesson. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to calculate probability.
Because you will need to teach experimental probability after theoretical probability, it is recommended that you have students collect data during this lesson. Give each student a rolling die and a data sheet. Then, throughout the class when they have time in between questions, they can roll the die and record what number they rolled. Each student should roll the die `10` to `15` times. Make sure you collect students’ data before the end of class.
To help introduce the idea of probability to students, have them answer some basic questions regarding the spinner shown. Students should be able to answer these questions relatively easily.
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Ask students what the word “probability” means to them. Spend a few minutes capturing the words and scenarios they’re using. Students are likely to talk about weather, dice, “chance”, etc.
Ask them questions like:
You can tell the students they can replace the word “chance” with “probability”.
You could end with a question relating to the spinner they started with. “If you spin the spinner, what is the probability that it will land on the letter `C`?” They may try to be more general and say it’s a low probability, or they will say “`1`” because there is `1` section. This is a good time to discuss how you write probability as a fraction, and a probability of `1` means something has to happen.
Encourage students to write the probability of landing on `C` as a fraction. At this point, it’s quite likely that students will say that there is a `1/8` chance of landing on `C` since there are a total of `8` sections, and `C` is only on one of them.
To help connect students’ informal understanding of probability from the previous discussion, provide the vocabulary that is relevant to probability.
It is important that students understand the language and notation that probability uses. Let students know this probability is theoretical, meaning it does not take actual data into account beyond the number of favorable outcomes and total number of outcomes. Consider asking questions to help students explore the vocabulary:
Now that students have been exposed to the basics of probability, it is important they understand what the value represents. Give students a few minutes to answer the questions and check their thinking with a partner.
With the last question, students will ideally recognize that the probability would be `2/2 = 1`. Ask them why it makes sense that the probability is `1` for the last question. You can extend this by asking students what the probability would be of flipping a coin and it not landing on heads or tails. This can help students see that impossible events always have a probability of `0`.
For the next examples involving a die, allow students time to work with a partner to determine the probabilities for each event.
As students are working, circulate to listen to their conversations. Encourage students to use the vocabulary to help them. When students get to the last two questions, they may need help to recognize what the favorable outcomes actually are. Consider having students list the favorable outcomes for these questions if they get stuck.
With this example, the total number of possible outcomes must be calculated. Give students a few minutes to work with a partner to determine the probability of each event. Two of the questions will also require students to simplify their answers.
When reviewing what students found, make sure students are able to explain how they determined the number of favorable outcomes and the total number of outcomes.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for probability. Check out the online practice and assign to your students for classwork and/or homework!
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