What are Your Chances? By Alexander 3/14/2006

Homework Madness In this part of the unit we pulled out cubes from two bags and recorded our results on a calendar thingingy. The bags were labeled “H” and “T”. In this part of the unit we pulled out cubes from two bags and recorded our results on a calendar thingingy. The bags were labeled “H” and “T”.  This was our probability for the first part; P(Homework)=12/20 and P(No Homework)= 8/20.  The second part of Homework Madness’ probability was; P(NH)=15/20 and P(H)=5/20.

Place Your Chips  In this unit we used small game boards, which we placed little chips on and rolled a number cube 36 times.  We removed a chip on each row when we rolled that number.When there were no more chips in the column, we couldn’t remove any chips from that column.

Sums and Products  We didn’t do very much in this unit, but we did learn why 7 is most peoples lucky number.  7 is most peoples lucky number because it has the most possible outcomes on two number cubes: 1 and 6, 2 and 5, 3 and 4, 3 and 4, 5 and 2, and 1 and 6.

Odd or Even  In this unit we spun two spinners, Spinner A and Spinner B, 16 times and we recorded our results.  I was paired with Stephanie, and we accidentally did this too many times.  We found out that even though it seemed the even numbers had a larger chance than odd numbers, they both had the same probability of happening.

The Carnival of Chance  In this unit we got to create a slightly unfair carnival game.  I was paired with Saman, and we chose a bag with dice, so we had to make a dice rolling game.  The slightly unfair game turned out to be really unfair, one-hundred something to thirty or forty something.

2 in 28  The game Saman and I created was 2 in 28. In this game you roll 27 number cubes and you have 28 chips. All the chips must be on a game board that has the numbers 1-6. Once all the chips are down, you roll all 27 number cubes at the same time (we had a cup). What ever the amount of number cubes that were on a certain number, that is how many chips you remove from a column. If there are more cubes than chips, you can only take off all the chips in that column. If you are left with 0,1,or2 chips, you win. If there are more, better luck next time.

What I Learned  I learned that probability is the chance of something happening, like a coin landing on heads (50%). These units really helped me learn probability. I think this unit was my favorite all year.

Glossary Certain Event-an event that will definitely happen Composite Number-a number that has more than two unique factors Compound Number-combination of two or more simple independent events such as rolling two number cubes or tossing a coin and spinning a spinner Equally Likely-two or more possible outcomes of a given situation that have the same chance of occurring or the same probability. An equally likely event, such as tossing a heads using a fair coin, has a probability of ½.

More Glossary Even Number-a multiple of 2, i.e. 0, 2, 4, … Experimental Probability-a statement of probability based on the results of a series of trials Fair Game-a game in which the theoretical probability of each player winning is equally likely Favorable Outcome-outcome of interest in a probabilistic situation Law of Large Numbers-states that experimental probabilities collected over many trials will predict the theoretical probabilities only when a very large number of trials are conducted Odd Number-a number that has a remainder of 1 when dividing by 2

Even More Glossary Possible Outcomes-all of the possible numbers or results of an action. For instance, the possible outcomes from rolling a number cube are 1, 2, 3, 4, 5, and 6. Probability-the chances of an event happening. Probability is often represented as a number. This can be expressed as 0(impossible), 1(certain), or a fraction in between 0 and1. Product-the answer to a multiplication problem Systematic (Organized) List-a list of data of any sort that is arranged in such way as to minimize omitting any member of the list Theoretical Probability-a statement of probability based on analysis of a situation P(event)=number of favorable outcomes number of possible outcomes number of possible outcomes Tree Diagram (counting tree)-visual method of listing combinations or outcomes

Extra Glossary Trial-one round of an experiment Unequally Likely-two or more outcomes that do not have the same chance of occurring or that do not have the same probability. For example, in a bag that holds three cubes, two that are green and one that is yellow, the probability of randomly select a green cube is 2/3 and a yellow cube is 1/3.

M3-Good Points, Bad Points I really liked the probability unit the best yet, especially since we got to create a slightly unfair carnival game. What is really good about M3 is it challenges people who are really good at math. I really think it should keep going. The only thing I would suggest is a smaller amount of Think Deeplys. They are good, but I think there should be a slightly smaller amount, like no beginning activity not in the book and having Think Deeplys as the first few pages.

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