Games+and+Activities


 * This is an incomplete listing of games and activities for this unit.********


 * Introduce the idea of probability by discussing the likelihood of events occurring.
 * Encourage students to focus on the language of probability as they use their life experiences to recall events that are certain, impossible, likely, and unlikely to happen.
 * Record these events on a probability scale, ranging from zero to one.
 * Introduce the idea of sample space and how it relates to outcomes of certain events.
 * Encourage students to find probabilities through their games and activities.=

Basketball Trash //Content Questions:// //What is probability?// //How do you measure the likelihood of an event?//


 * 1) Stand ten feet away from the trash can and hold the ball of paper in your hand. Ask the students, “//What are the chances I will make it in the trash can on my first try//?” Focus the discussion on vocabulary terms: //certain, likely, unlikely, and impossible.//
 * 2) Ask students what the word “probability” means. Ask them to name situations that use probability.
 * 3) Tell the class that probability can be expressed on a probability scale. Draw a number line on the chalkboard representing the scale. Ask the students to name a number that would best represent an event that is impossible (0 or 0%). Write “0 IMPOSSIBLE” at one end of the scale. Ask students to name events that are impossible such as: there will be 12 hours in the day tomorrow or, when your roll two dice you get a sum of 0. List student responses on chart paper to refer to throughout the unit.
 * 4) Ask students to name a number that would best represent an event that is certain (1 or 100%). Encourage students to name events that are certain and record their responses in their math journals. For example: there will be 24 hours in the day tomorrow or, there will be seven days in the week next week.
 * 5) Mark 1/2 or 50% on the scale and ask students what they think this means on a probability scale. Ask them to name events that would fall under “equally likely” events. Ask the students to make a prediction about the weather for tomorrow. Predict where on the probability scale best represents the likelihood of their weather prediction coming true. Students need to explain their reasons for predicting a particular place on the scale. If time allows, have students create their own graphic organizers in their math journals, making a probability scale and putting events at designated places along the scale.

Mystery Pasta Activity //Content Question:// //How do you determine and represent probable outcomes?//

In preparation for this lesson, fill three bags (for each group) with the following proportions of shell and elbow pasta shapes. Write on the board: Bag 1: 8 shells, 16 elbow Bag 2: 16 shells, 8 elbow Bag 3: 4 shells, 20 elbow
 * Students take turns reaching into the bag without looking, drawing out one pasta, and noting its shape.
 * Explain to the class that the amounts of shell and elbow pasta in each bag is written on the board but the bags are not labeled so they don’t know which bag has which population of pasta.
 * Select a student to choose one of the bags and tell the class that the student’s task will be to try and figure out which population of pasta is in the bag without looking inside, but instead by using some mathematical ideas of probability. Then the student will replace the pasta and someone else will have a turn.
 * //How do you determine and represent probable outcomes?//
 * Lead a discussion to generate answers to this question.
 * Write the numbers one through six in a column on the chalkboard and explain to the class that they will need to keep track of the results. Begin the experiment, recording the results and shaking the bag each time a student has a turn.
 * After six tries, ask the class, “//What does the information from our sample tell you about what’s in the bag?”// After a few guesses, do six more tries (numbering 7-12), and recording the results.
 * Ask students: “//What fraction of our sample came up shells?”//
 * Have students work in groups to figure out what fraction each of the populations A, B, and C is made up of shells. Have them compare this to the sample and predict which of the populations they think it is and why. After discussing their ideas and rationale, tell students that mathematicians have experimented and found that when you make many random draws as they are with the pasta, a pattern emerges. Probability is a way to predict that pattern. Return to the activity and continue drawing until most students can see a pattern emerging and are able to confidently predict what is in the bag. Then empty the bag to check if their prediction is true.
 * Individual assessment in math journals or on team blog:
 * //There is some pasta in a bag. Students took turns drawing out pasta noting its shape and replacing it. After 12 draws, they had drawn 6 shells, 4 elbows and 2 bow-ties. Write what you know for sure about what is in the bag and what you know is probably true.//

Rock, Paper, Scissors

//Content Question// //Is this game fair? Why or why not?// //What determines fairness?// //What is the difference between experimental and theoretical probability?// Game 1 Rock Paper B Game 2 Game 15
 * Divide the class into pairs (player A and player B) and have them play the game 15 times. Have the pairs record the results:
 * __Player A Player B Winner__

A wins if all three hands are the same B wins if all three hands are different C wins if two hands are the same
 * Use chart paper to record the results of player A in red and player B in a different color (How many A players won game 1, 2, 3, etc? How many B players won? How many ties?) Compare the results.
 * Ask the class "//Is this game fair?//" Ask students to explain why they think it is fair. Try to elicit from students that it is fair because each student has an equally likely or equal chance of winning (50% or 1/2).
 * Introduce students to a tree diagram as a visual tool for keeping track of the possible outcomes of this game: This is known as a probability tree. Compare this mathematical model with what happened when students played the game (theoretical vs. experimental probability).
 * Ask the students to play the game now with three players using the following rules:


 * Ask students to consider the following questions,
 * //Is this game fair? Why or why not?//
 * //What determines fairness?//
 * Ask students to construct a probability tree in their math journals to determine the possible outcomes (There will be 27 outcomes—three more branches off of each of the above nine possibilities. It is not fair because player C has more chances of winning than players A and B)
 * Remind students of the Essential Question they discussed at the beginning of the unit, //Is life really fair, Take A Chance?//

A Roll of the Dice //Content Questions:// //How do you measure the likelihood of an event?// //How do you determine and represent probable outcomes?// //What is the difference between experimental and theoretical probability?//


 * Introduce the activity by discussing the possible outcomes that can be obtained when a die is rolled. Students should be able to identify that the possible outcomes are the numbers from 1 to 6.
 * Then ask; “//What are the possible sums if the two dice are rolled?//” Have students work in groups to investigate the chances for rolling a particular sum. Have each person in the group create a line graph for the possible sums (2,3,4,5,6,7,8,9,10,11,12) and place “x’s” each time the sum is rolled. Have students roll the dice 15 times. Create a classroom frequency distribution graph (a number line with the “x’s” to represent how many times each sum occurred).
 * Ask students to compare their own group data to the whole class data. Ask students; “//Are all sums equally likely to occur? If not, which ones are more likely to occur and which ones are least likely to occur?”//
 * Introduce students to the idea that a table can be a useful tool in showing the possible outcomes of the sums of two dice. Ask students for other times this type of table can be used.


 * Ask students the following questions:


 * //Which sum is most likely to occur on the next roll of dice? Least likely? Why?//
 * //How many total possible outcomes?// (36)
 * //How many times does each sum appear in the table?//
 * //What does this tell us//?