By Caitlin and LauraBy Caitlin and Laura

March 2006March 2006

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

Homework madnessHomework madness

• Homework madness was one of our activities in our probability 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 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 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 on Tails we picked a cube from the other bag that was marked “T”. There were two color cubs: Red or Blue. Blue symbolized “T”. There were two color cubs: Red or Blue. Blue symbolized no homework and red symbolized Homework.There were 3 red no homework and red symbolized Homework.There were 3 red cubes and 4 blue cubes in bag “H” and there was 1 red cube 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 only in bag “T” We conducted the experiment 20 times to see which color cube came up mostwhich color cube came up most. .

A+A+

• What we learned doing this experiment is that this game is What we learned doing this experiment is that this game is part chance and part sure to happen. The chance part is when 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 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 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 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 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 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 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 and a 3/7 chance of picking a red cube. This means that homework/red has the advantage of being picked more often 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 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 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 likely to be picked. But No homework/Blue has a disadvantage because the probability of picking this color is less than red. 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 totalIn 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 in this bag that’s where we got our denominator. The number of cubs total regardless of bags is 8.of cubs total regardless of bags is 8.

• In bag”T” P[Red]=1/1In bag”T” P[Red]=1/1

Carnival games Carnival games

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

ReflectionReflection

• I learned a lot about what I learned a lot about what really makes a game fair really makes a game fair or unfair. In fair games, or unfair. In fair games, the chances of winning or the chances of winning or losing are equally likely. losing are equally likely. In unfair games, the In unfair games, the chances of winning or chances of winning or losing are unequally losing are unequally likely. It took a lot of likely. It took a lot of concentration and hard concentration and hard work to come up with the work to come up with the theoretical probability of theoretical probability of wining for some of the wining for some of the more complicated games, more complicated games, though. -Caitlinthough. -Caitlin

• What I learned in making my What I learned in making my game Pick a froggy any froggy game Pick a froggy any froggy was that since the game had to was that since the game had to be ¾ chance and ¼ setup It be ¾ chance and ¼ setup It took a long time to figure out took a long time to figure out what our probability of our what our probability of our game was but to have a full game was but to have a full explanation on the theoretical explanation on the theoretical and experimental probability and experimental probability you needed to have the you needed to have the theoretical probability of theoretical probability of wining and the theoretical wining and the theoretical probability of losing and the probability of losing and the same data for experimental same data for experimental probability .I learned how to probability .I learned how to find out that data and write it find out that data and write it correctly.-Lauracorrectly.-Laura

WritingWriting ProbabilityProbability

• How to write theoretical probability How to write theoretical probability • You start by writing “P”. “P” stands for You start by writing “P”. “P” stands for

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

Writing Probability Writing Probability (continued)(continued)

• How to write experimental probabilityHow to write experimental probability• To write experimental probability you start by To write experimental probability you start by

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

CComposite omposite CCapersapers

• Another one of our activities was called composite capers. In this Another one of our activities was called composite capers. In this project we first recognized composite and prime numbers. 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 A prime number can onlyonly be divided by 1 and itself. be divided by 1 and itself.

• This activity was actually a game. There were two columns on a This activity was actually a game. There were two columns on a sheet of paper. One was for when you rolled composite numbers sheet of paper. One was for when you rolled composite numbers and the other was for when you rolled prime numbers. Under the and the other was for when you rolled prime numbers. Under the prime column you wrote all the prime numbers that were an the prime column you wrote all the prime numbers that were an the number cube and beneath the other composite column you wrote number cube and beneath the other composite column you wrote all the composite numbersall 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 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 the two columns. Then what we did was roll the dice 45 times and saw what type of number came up the most frequently.saw what type of number came up the most frequently.

ReflectionReflection

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

Diagrams Diagrams

• We also got introduced to lots of new kinds of diagrams. We also got introduced to lots of new kinds of diagrams. There were tree diagrams, Carroll diagrams, and Pole There were tree diagrams, Carroll diagrams, and Pole diagrams. Here are some examples of these diagrams.diagrams. Here are some examples of these diagrams.

• This is a small example of a tree diagram:This is a small example of a tree diagram: This is an example of a Carroll This is an example of a Carroll diagram: diagram:

W/ chocolate sauce

sprinklesCherry ice-cream

Unit ReflectionUnit Reflection

• I liked the games we I liked the games we played and the activities played and the activities we did in this unit. we did in this unit. Learning about probability Learning about probability was kind of fun. I didn’t was kind of fun. I didn’t love the Think Deeplys, but love the Think Deeplys, but I’m getting used to them! I’m getting used to them! The carnival was fun, and I The carnival was fun, and I also liked Place Your Chips also liked Place Your Chips and Composite Capers. It and Composite Capers. It was fun learning all the was fun learning all the mathematical words we mathematical words we learned. - Caitlinlearned. - Caitlin

• I enjoyed the activities that I enjoyed the activities that we did. I thought that they we did. I thought that they were very exiting for math were very exiting for math games usually and one games usually and one thing that I liked especially thing that I liked especially was the carnival games. was the carnival games. The one thing I would do to The one thing I would do to make this program better make this program better is make the Think Deeplys is make the Think Deeplys a little more inviting a little more inviting because personally I think because personally I think they are very dull. - Laurathey are very dull. - Laura

THE ENDTHE ENDWe love math!!!!!!!!!!We love math!!!!!!!!!!