By Caitlin and Laura March 2006

I this unit we learned about Probability and the chances of certain events happening.We conducted several experiments, did fun activities like Homework madness and composite capers, and we all created a carnival game that had to do with chance / Probability. We also leaned how to find and write theoretical and experimental probability.

Homework madness Homework madness was one of our activities in our probability unit. This is how it works.First we flipped a coin. If it landed on Heads, we picked a cube from a bag marked “H”. If it landed on Tails we picked a cube from the other bag that was marked “T”. There were two color cubs: Red or Blue. Blue symbolized no homework and red symbolized Homework.There were 3 red cubes and 4 blue cubes in bag “H” and there was 1 red cube only in bag “T” We conducted the experiment 20 times to see which color cube came up most. Homework madness was one of our activities in our probability unit. This is how it works.First we flipped a coin. If it landed on Heads, we picked a cube from a bag marked “H”. If it landed on Tails we picked a cube from the other bag that was marked “T”. There were two color cubs: Red or Blue. Blue symbolized no homework and red symbolized Homework.There were 3 red cubes and 4 blue cubes in bag “H” and there was 1 red cube only in bag “T” We conducted the experiment 20 times to see which color cube came up most. A+ A+

What we learned doing this experiment is that this game is part chance and part sure to happen. The chance part is when you flip the coin. This is because when you flip the coin there is an equally likely chance that the coin would land on heads over tails. The sure to happen part of this game is the fact that in bag “T” there is only a red cube meaning that if your coin lands on Tails it is certain that you will have a homework day. If your coin lands on Heads you have a 4/7 chance on picking blue and a 3/7 chance of picking a red cube. This means that homework/red has the advantage of being picked more often because red has his own bag and in bag “H” there is a little less chance of picking red but it still has its own bag making it more likely to be picked. But No homework/Blue has a disadvantage because the probability of picking this color is less than red. What we learned doing this experiment is that this game is part chance and part sure to happen. The chance part is when you flip the coin. This is because when you flip the coin there is an equally likely chance that the coin would land on heads over tails. The sure to happen part of this game is the fact that in bag “T” there is only a red cube meaning that if your coin lands on Tails it is certain that you will have a homework day. If your coin lands on Heads you have a 4/7 chance on picking blue and a 3/7 chance of picking a red cube. This means that homework/red has the advantage of being picked more often because red has his own bag and in bag “H” there is a little less chance of picking red but it still has its own bag making it more likely to be picked. But No homework/Blue has a disadvantage because the probability of picking this color is less than red. In bag “H” P [Blue]=4/7 P[red]=3/7 *There are 7 cubes total in this bag that’s where we got our denominator. The number of cubs total regardless of bags is 8. In bag “H” P [Blue]=4/7 P[red]=3/7 *There are 7 cubes total in this bag that’s where we got our denominator. The number of cubs total regardless of bags is 8. In bag”T” P[Red]=1/1 In bag”T” P[Red]=1/1

Carnival games At the end of our unit the whole class made carnival games and we held a carnival called the “Carnival of Chance”. We worked in partners to create different games that were slightly unfair. Doing this helped us learn about what makes something “fair” or “not fair”. We also had a lot of fun! Laura’s game was called “Pick a froggy, any froggy” and Caitlin’s game was called “Confusing Cards”. “Confusing Cards “ was about picking two cards and adding them to try to get a prime number. If you got a prime number, you won. We used certain cards and put them in certain spots to make it unfair. “Pick a froggy, any froggy”used a spinner. The spinner ws split into fourths. One each fourth there was a number 1-4. On the side there were 8 cups that had the numbers 1-8 on them. You spun the spinner twice and added up the two numbers, then you matched your numbers to a number on a cup. If you got a certain cup there might be a symbol on the bottom then you got certain candy. We used the numbers on the spinner and cup to make it slightly unfair. At the end of our unit the whole class made carnival games and we held a carnival called the “Carnival of Chance”. We worked in partners to create different games that were slightly unfair. Doing this helped us learn about what makes something “fair” or “not fair”. We also had a lot of fun! Laura’s game was called “Pick a froggy, any froggy” and Caitlin’s game was called “Confusing Cards”. “Confusing Cards “ was about picking two cards and adding them to try to get a prime number. If you got a prime number, you won. We used certain cards and put them in certain spots to make it unfair. “Pick a froggy, any froggy”used a spinner. The spinner ws split into fourths. One each fourth there was a number 1-4. On the side there were 8 cups that had the numbers 1-8 on them. You spun the spinner twice and added up the two numbers, then you matched your numbers to a number on a cup. If you got a certain cup there might be a symbol on the bottom then you got certain candy. We used the numbers on the spinner and cup to make it slightly unfair.

Reflection I learned a lot about what really makes a game fair or unfair. In fair games, the chances of winning or losing are equally likely. In unfair games, the chances of winning or losing are unequally likely. It took a lot of concentration and hard work to come up with the theoretical probability of wining for some of the more complicated games, though. -Caitlin I learned a lot about what really makes a game fair or unfair. In fair games, the chances of winning or losing are equally likely. In unfair games, the chances of winning or losing are unequally likely. It took a lot of concentration and hard work to come up with the theoretical probability of wining for some of the more complicated games, though. -Caitlin What I learned in making my game Pick a froggy any froggy was that since the game had to be ¾ chance and ¼ setup It took a long time to figure out what our probability of our game was but to have a full explanation on the theoretical and experimental probability you needed to have the theoretical probability of wining and the theoretical probability of losing and the same data for experimental probability.I learned how to find out that data and write it correctly.- Laura What I learned in making my game Pick a froggy any froggy was that since the game had to be ¾ chance and ¼ setup It took a long time to figure out what our probability of our game was but to have a full explanation on the theoretical and experimental probability you needed to have the theoretical probability of wining and the theoretical probability of losing and the same data for experimental probability.I learned how to find out that data and write it correctly.- Laura

Writing Probability Writing Probability How to write theoretical probability How to write theoretical probability You start by writing “P”. “P” stands for probability. Then you write the topic in parentheses. Lastly, you write the probability as a fraction. Example: P (h) ½ (“h” stands for homework so this expression is saying that there is a one half chance of getting homework.) You start by writing “P”. “P” stands for probability. Then you write the topic in parentheses. Lastly, you write the probability as a fraction. Example: P (h) ½ (“h” stands for homework so this expression is saying that there is a one half chance of getting homework.)

Writing Probability (continued) How to write experimental probability How to write experimental probability To write experimental probability you start by writing “P” like when writing theoretical probability. Then you write the name or an abbreviation for the name in parentheses. Finally, you write a fraction for it with the number of times the event occurs over the number of trials taken place. Example: P (h) 5/10 (“h” is for homework again). This expression states that kids got homework 5 out of every 10 times that there was a chance of getting it. To write experimental probability you start by writing “P” like when writing theoretical probability. Then you write the name or an abbreviation for the name in parentheses. Finally, you write a fraction for it with the number of times the event occurs over the number of trials taken place. Example: P (h) 5/10 (“h” is for homework again). This expression states that kids got homework 5 out of every 10 times that there was a chance of getting it.

C omposite C apers Another one of our activities was called composite capers. In this project we first recognized composite and prime numbers. Another one of our activities was called composite capers. In this project we first recognized composite and prime numbers. Composite numbers can be divided by more than two numbers. Composite numbers can be divided by more than two numbers. A prime number can only be divided by 1 and itself. A prime number can only be divided by 1 and itself. This activity was actually a game. There were two columns on a sheet of paper. One was for when you rolled composite numbers and the other was for when you rolled prime numbers. Under the prime column you wrote all the prime numbers that were an the number cube and beneath the other composite column you wrote all the composite numbers This activity was actually a game. There were two columns on a sheet of paper. One was for when you rolled composite numbers and the other was for when you rolled prime numbers. Under the prime column you wrote all the prime numbers that were an the number cube and beneath the other composite column you wrote all the composite numbers Prime=1,2,3,and 5 Prime=1,2,3,and 5 Composite= 4 and 6 Composite= 4 and 6 You had 45 chips and you had to theoretically put them in each of the two columns. Then what we did was roll the dice 45 times and saw what type of number came up the most frequently. You had 45 chips and you had to theoretically put them in each of the two columns. Then what we did was roll the dice 45 times and saw what type of number came up the most frequently.

Reflection Before we did this activity we wrote a theoretical probability that would help us decide how many chips to put in each column. Since we had 45 chips we had to divide them logically between the two categories, composite and prime numbers. The number of chips we decided to put into each column were 15 chips into the composite side and 30 chips into the prime. Our Experimental probability was very close to our theoretical probability. Before we did this activity we wrote a theoretical probability that would help us decide how many chips to put in each column. Since we had 45 chips we had to divide them logically between the two categories, composite and prime numbers. The number of chips we decided to put into each column were 15 chips into the composite side and 30 chips into the prime. Our Experimental probability was very close to our theoretical probability.

Diagrams We also got introduced to lots of new kinds of diagrams. There were tree diagrams, Carroll diagrams, and Pole diagrams. Here are some examples of these diagrams. We also got introduced to lots of new kinds of diagrams. There were tree diagrams, Carroll diagrams, and Pole diagrams. Here are some examples of these diagrams. This is a small example of a tree diagram: This is an example of a Carroll diagram: This is a small example of a tree diagram: This is an example of a Carroll diagram: W/ chocolate sauce sprinkles Cherry ice-cream

Unit Reflection I liked the games we played and the activities we did in this unit. Learning about probability was kind of fun. I didn’t love the Think Deeplys, but I’m getting used to them! The carnival was fun, and I also liked Place Your Chips and Composite Capers. It was fun learning all the mathematical words we learned. - Caitlin I liked the games we played and the activities we did in this unit. Learning about probability was kind of fun. I didn’t love the Think Deeplys, but I’m getting used to them! The carnival was fun, and I also liked Place Your Chips and Composite Capers. It was fun learning all the mathematical words we learned. - Caitlin Ienjoyed the activities that we did. I thought that they were very exiting for math games usually and one thing that I liked especially was the carnival games. The one thing I would do to make this program better is make the Think Deeplys a little more inviting because personally I think they are very dull. - Laura

THE END We love math!!!!!!!!!!