options: 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.

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.

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.
problem_activity: Activity
The last activity in this lesson moves one more step closer to quantifying likelihood of scenarios by ordering them individually rather than into groups. Some of the scenarios have a numerical probability expressed as a percentage, some in decimal form, some as a fraction, and some do not have a numerical probability given (MP7). This gives students the opportunity to work with probabilities expressed as percentages, decimals, and fractions.
You will need the blackline master for this activity.
Launch
Arrange students in groups of 3. Distribute one copy of the blackline master for each group.
Tell students to take turns ordering the cards by beginning with one card, then adding in additional cards one at a time before, after, or between cards as needed.
Give students 5 minutes for group work followed by a whole-class discussion.
Student Facing
Your teacher will give you some cards that describe events. Order the events from least likely to most likely.
After ordering the first set of cards, pause here so your teacher can review your work. Then, your teacher will give you a second set of cards.
Add the new set of cards to the first set so that all of the cards are ordered from least likely to most likely.
Student Response
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Anticipated Misconceptions
Students may have trouble understanding the Rock, Paper, Scissors context. Tell these students that a player randomly chooses one of the three items to play in each round. If students still struggle, tell them that each of the three items are expected to be played with equal likelihood.
Activity Synthesis
The purpose of the discussion is for students to talk about the methods they used to sort the cards and compare likelihood of different situations.
Some questions for discussion:
"How were the numerical values of the likelihoods written?" (Some were written as percentages, some as fractions, and some as decimal values.)
"How did you compare them when there was a mix of percentages, fractions, and decimals?"
"Some of the cards did not have a percentage, fraction, or decimal. How did you determine where those cards would go in the order?"
Speaking, Listening: MLR7 Compare and Connect.
Ask students to prepare a visual display of their sorted cards. Students should consider how to display their cards so that another student can interpret the reasoning behind the order they selected. Some students may wish to add notes or details to their displays to help communicate their thinking. Invite students to investigate each other’s work, ask students to compare the order between displays. Listen for and amplify any comments about the use of percentages, fractions, and decimals to compare the likelihood of different situations. Then encourage students to make connections between the various ways to quantify the likelihood of a situation. Listen for and amplify language students use to explain that the percentage, fraction, and decimal used to quantify the likelihood of the same scenario are all equivalent. This will foster students’ meta-awareness and support constructive conversations as they compare and connect quantities that represent the likelihood of a situation.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


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