# Randomness and Chance Activities

Probability is a strand throughout the grades 6-12 Common Core State Standards for mathematics. With these activities, students can verify or challenge their intuition about randomness and probability, and develop their understanding of concepts like experimental versus theoretical probability. Every activity comes with a student worksheet and detailed teacher notes, including Common Core State Standards addressed.

Students investigate randomness by using a sampler that models lights that are turned on in an office building at night. Students compare their expectations of what randomly placed lights might look like to the results from a simulation model.

## Random Coin Flips  (Grades 5-8)

Students study random sequences of 21 coin flips and use what they learn to detect which of two sequences of 21 coin flips came from actually flipping a coin and which was made up by a student to look like random coin flips. ## The Ants and the Aardvark  (Grades 6-8)

Students identify the paths ants can take through an ant maze to help an aardvark catch as many ants as possible. Students begin by choosing the ant's path using a coin and evaluating how often ants come out of different holes. They then model the ants' paths, finally coming up with a list of all possible outcomes and using this list to explain what they observed from the simulation.

Students determine whether the game Wink, Blink, and Stare is fair. To do so, students first play the game themselves, and then use a sampler in TinkerPlots to model the game and collect more data. Students then work toward understanding why Wink is more likely. They are introduced to the terms simple outcome, combined outcome, and sample space. Finally, students use TinkerPlots to play the game repeatedly, observing that using a sample of 2,500 gives them the results they expect more often than using a sample of 100.

Students explore the distribution of the numbers of boys in families with four children by predicting what the distribution of the number of boys in a family will look like. Using TinkerPlots, they analyze data from 160 families with four children. Then, students systematically determine all possible simple outcomes and use them to construct the expected distribution for the number of boys in a family with four children, and calculate the probabilities of different outcomes.

## Sum of Two Dice  (Grades 6-8)

Students explore various outcomes associated with rolling two dice. They start by playing the Two-Dice Elimination game, and then simulate rolling two dice many times using TinkerPlots to determine whether a step model or a triangle model of the distribution of sums is correct. Finally, they use the triangle model to calculate the probability of rolling each sum.

## Modeling a Candy Factory  (Grades 6-8)

Students take on the roles of quality-control officers in a candy factory. They model the candy factory, using TinkerPlots, to investigate how likely it is that a bag of candy the company president received occurred by chance.

Students build models of real-life situations and use data from the models to estimate probabilities.