PROBABILITY
Our first unit in our Math 2 class was on Probability. Probability is the likelihood or chance of an event happening. Even though probability is not and has never been my strong suit, I feel like I somewhat enjoyed learning about it. Our teacher introduced the project not by telling us we were going to be learning probability and to get out our books and learn a series of definitions but by asking us questions about ourselves and doing little activities which got us to excited about the topic.
Throughout this unit, we did many little activities and worksheets. These are listed below with a little explanation (they are not in the order we did them);
1. PRISN/PRISM (worksheet): In 2013, newspapers revealed a secret government program that monitored the phone calls and internet data of millions of Americans. This was called PRISM. The purpose was to catch terrorists before they struck. Our mission was to look at data collected on the effectiveness of versions of this program over the years and calculate a series of probabilities to determine whether the program is worth it or not.
2. Is Sarah's Math Class Fair?: Using data that our teacher, Sarah, collected, we were to solve and compare several probabilities to determine whether our teacher's math class was equal and fair for both boys and girls in her class. This was one of our two larger problems so we did a write-up where we described the problem and our steps to solve it and reflected on it. This is shown below.
Throughout this unit, we did many little activities and worksheets. These are listed below with a little explanation (they are not in the order we did them);
1. PRISN/PRISM (worksheet): In 2013, newspapers revealed a secret government program that monitored the phone calls and internet data of millions of Americans. This was called PRISM. The purpose was to catch terrorists before they struck. Our mission was to look at data collected on the effectiveness of versions of this program over the years and calculate a series of probabilities to determine whether the program is worth it or not.
2. Is Sarah's Math Class Fair?: Using data that our teacher, Sarah, collected, we were to solve and compare several probabilities to determine whether our teacher's math class was equal and fair for both boys and girls in her class. This was one of our two larger problems so we did a write-up where we described the problem and our steps to solve it and reflected on it. This is shown below.
3. Conditional Probability, Union and Intersections (worksheet): The purpose of this worksheet was to give us a more in-depth understanding of conditional probability. We were given a series of probability problems where we needed to use conditional probability to solve [P(A|B)]
4. Intro to Independence (worksheet): On this worksheet, we were to solve a few compound probability problems, compare them, and then determine and justify which problems were independent/dependent.
5. Titanic (worksheet): On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 712 of her 2,204 passengers and crew surviving. We were given data on the survivors and whether they were in first, second, or third class. Our mission was to calculate a series of probabilities (several of them being conditional probability) on the relationship between the survivors, non-survivors, and the different classes and then determine whether the chances of surviving were fair for all classes or if first class was favoured/saved more.
6. Skittles (problem) & Super Fruity Fruit Snax (worksheet): These two problems/worksheets we did more towards the beginning of our probability unit when we were still being introduced to, and mastering, the basics of probability. We practiced regular probability [P(event) = event/sample space] and drawing out our sample space and we were introduced to compound probability [P(event & event) = P(event) x P(event)].
7. Starburst Problem: This problem tested our sample space reading and using skills. We were to analyze a sample space and calculate several probabilities (compound, conditional, and 'OR') asking us about the probabilities of getting colours/flavours.
8. Dice Game and Problem: With our partners sitting next to us, we were to play a game that required rolling dice. The instructions were as follows:
With your partner. take turns rolling a dice twice. Player A scores a point if the sum of their two rolls is 5, 6, 7, 8 or 9. Player B scores if any other sum is rolled.
So after playing this game and recording the results, we had to figure out the chances of each player winning and determine whether the game was fair. This problem was one of our two larger problems that we did in the unit so we did a write-up. This is shown below:
4. Intro to Independence (worksheet): On this worksheet, we were to solve a few compound probability problems, compare them, and then determine and justify which problems were independent/dependent.
5. Titanic (worksheet): On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 712 of her 2,204 passengers and crew surviving. We were given data on the survivors and whether they were in first, second, or third class. Our mission was to calculate a series of probabilities (several of them being conditional probability) on the relationship between the survivors, non-survivors, and the different classes and then determine whether the chances of surviving were fair for all classes or if first class was favoured/saved more.
6. Skittles (problem) & Super Fruity Fruit Snax (worksheet): These two problems/worksheets we did more towards the beginning of our probability unit when we were still being introduced to, and mastering, the basics of probability. We practiced regular probability [P(event) = event/sample space] and drawing out our sample space and we were introduced to compound probability [P(event & event) = P(event) x P(event)].
7. Starburst Problem: This problem tested our sample space reading and using skills. We were to analyze a sample space and calculate several probabilities (compound, conditional, and 'OR') asking us about the probabilities of getting colours/flavours.
8. Dice Game and Problem: With our partners sitting next to us, we were to play a game that required rolling dice. The instructions were as follows:
With your partner. take turns rolling a dice twice. Player A scores a point if the sum of their two rolls is 5, 6, 7, 8 or 9. Player B scores if any other sum is rolled.
So after playing this game and recording the results, we had to figure out the chances of each player winning and determine whether the game was fair. This problem was one of our two larger problems that we did in the unit so we did a write-up. This is shown below:
As far as Habits of a Mathematician go, the two that I feel I used/grew in the most during this unit is number two (Considers different approaches to solve problems, with or without numbers) and number four (Asks questions to push their thinking). I found that I was trying multiple approaches to a lot of the problems we had, especially when I tried one and didn't fully understand it or when I wanted to confirm my answer on a problem. I also found that I was often asking questions so precise and well put together so I could really understand the problem. I realized (just now actually) that this is a really good skill to have because our teachers are always very busy with all the other students (because we all have questions) so they don't have time to continuously come back to you and answer your little questions. Its better to think it through before asking and then ask one that will answer multiple of those small questions. :)
Like I said in the beginning of the document, I feel like I, overall, really enjoyed this unit! It's not because I absolutely love probability (because I don't) but because of how it was taught. I would go to class every day being excited for what we were going to learn and leave class reflecting happily about it (I'm serious, I did!). When I look back at it, the part that I really feel like I enjoyed was starting each day by discussing a question given to us by our teacher with our group. It kept me enthusiastic and energetic! I really look forward to our next one!
Like I said in the beginning of the document, I feel like I, overall, really enjoyed this unit! It's not because I absolutely love probability (because I don't) but because of how it was taught. I would go to class every day being excited for what we were going to learn and leave class reflecting happily about it (I'm serious, I did!). When I look back at it, the part that I really feel like I enjoyed was starting each day by discussing a question given to us by our teacher with our group. It kept me enthusiastic and energetic! I really look forward to our next one!