standard_description: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
problem_activity: Warm-up
The purpose of this warm-up is for students to choose the more likely event based on their intuition about the possible outcomes of two chance experiments. The activities in this lesson that follow define probability and give ways to compute numerical values for the probability of chance events such as these.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by time to share their response with a partner. Follow with a whole-class discussion.
Student Facing
Which game would you choose to play? Explain your reasoning.
Game 1: You flip a coin and win if it lands showing heads.
Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.
Student Response
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Anticipated Misconceptions
Some students may have trouble comparing
\(\frac{1}{2}\)
and
\(\frac{2}{6}\)
. Review how to compare fractions with these students.
Some students may struggle with the wording of the second game. Help them understand what it means for a number to be divisible by a certain number and consider providing them with a standard number cube to examine the possible values.
Activity Synthesis
Have partners share their answers and display the results for all to see. Select at least one student for each answer provided to give a reason for their choice.
If no student mentions it, explain that the number of possible outcomes that count as a win and the number of total possible outcomes are both important to determining the likelihood of an event. That is, although there are two ways to win with the standard number cube and only one way to win on the coin, the greater number of possible outcomes in the second game makes it less likely to provide a win.


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