options: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

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.
problem_activity: Warm-up
The purpose of this warm-up is for students to use their intuition to think about the upcoming unit on probability. In particular, students guess what type of fish might be caught after knowing the results of the previous 10 fish caught. Although no answer can be given with absolute certainty, the results being heavily skewed towards one type of fish should lead students to the idea that it is more likely to be the most commonly caught fish will be caught again.
Launch
It may be helpful to explain that there are many types of fish that are caught while fishing for fun or sport. The two types listed in this warm-up, bluegill and yellow perch, are typically found in lakes and caught with the same type of bait. Both of these types of fish are suitable for eating after being caught or release back into the water.
Student Facing
Andre and his dad have been fishing for 2 hours. In that time, they have caught 9 bluegills and 1 yellow perch.
The next time Andre gets a bite, what kind of fish do you think it will be? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of the discussion is to show students that no single answer can be certain for this problem, but previous results can help inform the likelihood of future outcomes.
Poll the class regarding the type of fish they think will be caught next. Begin by asking for students who think the next fish caught will be a bluegill followed by students who think the next fish caught will be a yellow perch followed by students who think that another type of fish will be caught (or that they will not catch another fish). Display the results from the poll for all to see. Following the poll, ask at least one student representing each group with more than 1 vote for their reasoning. Tell students that we cannot know for certain what the next type of fish will be, but based on the results we have available, it is most likely that a bluegill will be caught next.


correct_option_index: 1