We can analyze outcomes of repeated experiments to determine that independent events do not change each other’s probability.
How can you tell that two events are independent by analyzing the outcomes of a repeated experiment?
I can tell that two events are independent by analyzing the outcomes of a repeated experiment by...
By studying this visual, students might:
- The probability of each event stays the same each time
- Different events are happening like flipping a coin or spinning
- The outcomes are recorded over many trials
- Event 1 does not change event 2
- Patterns repeat in the results
- Why does the probability stay the same each time
- How can you tell the events are independent
- What patterns do you notice in the outcomes
- Why does one event not change another event
- How can you use results to make predictions
Extending the Discussion
- After randomly calling on students, if there is anything from this list that was not mentioned, then ask the class, "Did anyone notice...?"
- After students have shared what they notice, ask the class, "Did anyone wonder...?" using the suggestions above or anything else you might think is interesting or relevant to the lesson.
Structured Conversation Prompts
What is an independent event?
An independent event is...
How is an independent event different from a dependent event?
An independent event is different from a dependent event because...
How can you tell that two events are independent by analyzing the outcomes of a repeated experiment?
I can tell that two events are independent by analyzing the outcomes of a repeated experiment by...
Example Student Responses to the Observational Question
An independent event is when one event does not affect another.
An independent event is when the outcome of one event does not change the probability of another event.
Responding to Responses
Emphasize and celebrate each student's use of the key vocabulary to support a culture of "no wrong answers."
Structuring Student Conversations
Have students list observations from the visual as a warm-up, then use the Q-SSS-A process to guide small-group conversations. In the slide decks, brackets can be moved to prepare the structured conversation. In the example to the right, students will be instructed: Q-SSS-A.
- To put a thumb up, then lower their hand when they are ready to answer the question
- To share with their elbow/shoulder partner, and that the student with the darkest shoe will share first
- That they will be randomly called on after the conversation
Here is an example of structuring a conversation with Q-SSS-A.
Note: the inferential question is the same as the language objective. It is recommended that students answer the inferential question in a small-group discussion before answering it individually as the closure or exit ticket of the lesson.
Structured Reading
The purpose for reading is to analyze how results from repeated experiments show that events are independent.
- Results from repeated experiments
- What happens in event 1 compared to event 2
- Whether the probability changes or stays the same
- Patterns in the outcomes
- Evidence that shows independent events
How does the spinner activity show that the events are independent?
The spinner activity shows that the events are independent because...
Structuring the Reading
Communicate the purpose of reading to the students and instruct them to make a note every time they see something on the PAT ("Pay Attention To") list. How you have students note items on the PAT list is up to you. This could include:
- Putting an asterisk in the margin
- Underlining text that supports the PAT list
- Putting a comment in the margin
Follow the reading with the post-reading discussion. Structure this discussion using the Q-SSS-A process just like the structured conversations in this lesson.
Note: you might find the relational question is better discussed before or after the reading. This depends on whether the relational question is directly related to the reading or might make connections across units.
Differentiating the Reading
You will notice that three different reading passages are provided with this lesson. Look at the shapes in the top-left of each passage to determine the grade level.
In a class with students at diverse reading level proficiencies, you can give the appropriate reading passage to different students, while having all students follow the same PAT list and post-reading discussion.