The purpose of this Warm-up is to engage students' intuition about likelihood of events. The following activities in this lesson continue to develop more formal ways of thinking about likelihood leading to the definition of probability in the next lesson.
Arrange students in groups of 2. Give students 2 minutes of quiet work time and time to share their response with a partner. Follow with a whole-class discussion.
Which is more likely to happen? Explain your reasoning.
When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, a left shoe is pulled out.
When listening to a 5-song playlist in shuffle mode, the first song on the playlist plays first.
It is more likely that a left shoe is pulled out than the first song on the playlist being played first in shuffle mode. Since the shoes come in pairs, it is equally likely that a left or right shoe would be pulled out, so half of the time we would expect to get a right shoe. For the playlist, there are 5 different songs that could play first, and only 1 of them is the first song on the list.
The purpose of the discussion is to help students recognize their own intuition about the likelihood of an event even when prior outcomes are not available.
Ask partnerships to share responses with the class, and ask at least one student that chose each option for their reasoning.
It may be helpful to reiterate that the likelihood of these actions only give a sense of what might be expected to happen. Even though the first situation is more likely to happen, it is possible someone might pull out a right shoe and have the first song on the list play first, but it might be a little more surprising than if someone pulled out a left shoe and a different song played first.
Students may think that it is required to pull out a specific shoe rather than any left shoe. Ask students to visualize the problem and determine how many left shoes are in the closet.
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The purpose of this Warm-up is to engage students' intuition about likelihood of events. The following activities in this lesson continue to develop more formal ways of thinking about likelihood leading to the definition of probability in the next lesson.
Arrange students in groups of 2. Give students 2 minutes of quiet work time and time to share their response with a partner. Follow with a whole-class discussion.
Which is more likely to happen? Explain your reasoning.
When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, a left shoe is pulled out.
When listening to a 5-song playlist in shuffle mode, the first song on the playlist plays first.
It is more likely that a left shoe is pulled out than the first song on the playlist being played first in shuffle mode. Since the shoes come in pairs, it is equally likely that a left or right shoe would be pulled out, so half of the time we would expect to get a right shoe. For the playlist, there are 5 different songs that could play first, and only 1 of them is the first song on the list.
The purpose of the discussion is to help students recognize their own intuition about the likelihood of an event even when prior outcomes are not available.
Ask partnerships to share responses with the class, and ask at least one student that chose each option for their reasoning.
It may be helpful to reiterate that the likelihood of these actions only give a sense of what might be expected to happen. Even though the first situation is more likely to happen, it is possible someone might pull out a right shoe and have the first song on the list play first, but it might be a little more surprising than if someone pulled out a left shoe and a different song played first.
Students may think that it is required to pull out a specific shoe rather than any left shoe. Ask students to visualize the problem and determine how many left shoes are in the closet.