Estimating Probabilities Using Simulation
10 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images of spinners. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the image for all to see. Ask students to indicate when they have noticed which image does not belong and can explain why. Give students 2 minutes of quiet think time and then time to share their thinking with their group. After everyone has conferred in groups, ask the group to offer at least one reason each image doesn’t belong. Follow with a whole-class discussion.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
- A, B, and C go together because the green region is one fourth of the circle.
- A, B, and D go together because each region is less than half of the circle
- A, C, and D go together because they have 4 regions.
- B, C, and D go together because the regions are not all the same size.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “outcome,” “region,” or “sample space,” and to clarify their reasoning as needed. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
Standards
- 7.SP.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- 7.SP.7.b·Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. <em>For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?</em>
- 7.SP.C.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- 7.SP.C.7.b·Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. <span>For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?</span>
15 min
10 min
Knowledge Components
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Estimating Probabilities Using Simulation
10 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images of spinners. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the image for all to see. Ask students to indicate when they have noticed which image does not belong and can explain why. Give students 2 minutes of quiet think time and then time to share their thinking with their group. After everyone has conferred in groups, ask the group to offer at least one reason each image doesn’t belong. Follow with a whole-class discussion.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
- A, B, and C go together because the green region is one fourth of the circle.
- A, B, and D go together because each region is less than half of the circle
- A, C, and D go together because they have 4 regions.
- B, C, and D go together because the regions are not all the same size.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “outcome,” “region,” or “sample space,” and to clarify their reasoning as needed. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
Standards
- 7.SP.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- 7.SP.7.b·Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. <em>For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?</em>
- 7.SP.C.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- 7.SP.C.7.b·Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. <span>For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?</span>