Week 10 Reflection

We're nearing the end of the course. You can tell, because stress levels are high, as is the work load. However, I still manage to find time to write reflections of my math adventures. We focused on chapters 19, 20, and 21 from our textbook this week, which is a lot of reading. We mainly focused on data management and probability in our class. This is actually one of my favourite topics in math, which is really saying something, since (as I'm sure I've mentioned before) I do not really like math. 

Probability is almost always a hands on unit, using many fun manipulatives to model chance and probability. I think that this would be my favourite unit to teach, even if it is one of the hardest concepts to understand. Students need to understand the concept of odds, certain to, likely to, equal chance, not likely, and never. The least possible value of a probability is 0, which indicates that the event could never occur; the greatest is 1, which indicates that the event must always occur. If students do not understand value or fractions, they may not grasp this concept, so i must be sure that they understand this first.  

Theoretical probability can be confusing, because as the title suggests, it is based on theory. It is probability based on reasoning, written as a ratio of the number of favourable outcomes to the number of possible outcomes. To make it easier to see the possible outcomes, it is a good idea to model out all outcomes. You can use tree diagrams, which gives more details and maps out the probability of outcomes, or area models, which I find to be more confusing and harder to read. You can also graph out the possible outcomes, to find the chances or the outcomes like we did with our prof. He challenged us to pick a die to roll against his and see how many times we could roll a higher number. He had already calculated which particular die would have the highest outcome, so naturally we lost, because we just chose a die randomly. I think this was a good lesson because it proved that the theoretical probability matched the actual outcomes. 

We had a lot of fun activities this week, lots that I would use in my own classroom. Some were simple, and others were a bit more complex, but still lots of fun. For one, we had a spinner with numbers 1-4. We spun 10 times and calculated the outcomes based on our spins: 

Woolley, E. © 2015 

Another activity involved cards, as many probability activities do. Out of a standard deck of 52 cards, we had to write out the odds of various cards. For example, what are the odds of pulling a red card (26/52). We also did the same for a spinner and for rolling a die.

Woolley, E. © 2015

 We got to create our own survey and collect data. I think this is a great activity for students to use their own ideas to collect data. My group chose "how do you get to school" and used a pictograph to collect information. We asked our peers to select their answer and use a picture to response. An awesome, hands on activity for students! 

Woolley, E. © 2015

 Finally, we played a horse racing game, which was a lot of fun. We rolled two die and recorded the number rolled on the graph below. We rolled 52 times before we found the winner, which was #5. It was fun to see how chances worked. We had predicted that 7 would win because there are more variants of 7, but as chance and probability prove, the theoretical outcomes are not always what happens in practise. This was a fun way to play with students and show them theory vs. practise, and also a good way to teach students not to gamble! 

Woolley, E. © 2015