We have just begun our unit on probability:
We have just begun our unit on probability:
Today's problem (May 29):
Activation:
We looked at the question, "What are games of chance?"
First we discussed what "chance" means.
Then we looked for examples of games of chance.
[pic]
The Problem:
[pic]
Some groups decided that there were 14 slips of paper in the bag, so they did 14 trials:
[pic]
Some groups had a few more trials than 14, and then tried to guess what was in the bag:
[pic]
Some groups did many trials before trying to guess what was in the bag:
[pic]
Consolidation: We then decided to record ALL the trials in the class and add them up together. Together the class did 237 trials, and here are the results:
[pic]
From the results the students decided there must be 5 to 7 green, 3 blue, 3 red, and 1-2 orange. Indeed there were 7 green, 3 blue, 3 red, and 1 orange in every bag.
From this information the students were asked if they could conclude anything. Their conclusion was that the more trials you do, the more accurate the results are (which is indeed the Law of Experimental Probability):
[pic]
Well done!
Today's Problem (May 31):
Activation: We reviewed the law of experimental probability:
[pic]
Then we had a discussion about "luck":
[pic]
The problem:
[pic]
Some students solved the problem by simply making a tally of the times they flipped heads, and the times the flipped tails:
[pic]
[pic]
Some students only counted the coin flips that happened after a "heads" had been flipped (more accurate - to the problem):
[pic]
One groups looked at it as a theoretical problem:
[pic]
Consolidation: First we looked at all the coin tosses in the class and added them together. Doing this we found that heads and tails were almost flipped exactly the same amount of times (185 ti 181).
[pic]
Then we looked at how the one group looked at the problem from a theoretical point of view:
[pic]
Today's problem (June 4):
Activation: We reviewed information we have learned so far...
[pic]
We looked the connections between experimental and theoretical probability:
[pic]
The problem:
[pic]
We had a number of dice races, and here are what the results looked like:
[pic]
We will consolidate next math class.
The consolidation looked at the general shape of the games. The students noticed they were all similar, and in the shape of a triangle.
[pic]
They concluded that it could not have been that the lowest and highest number were unlucky. Here are all the winning numbers on a chart (for the 3 dice game):
[pic]
So from there we worked on the theoretical probability of rolling all the different numbers. The students made an interesting discovery. With 2 dice there were 36 different possible rolls... each die has 6 sides. And 6 x 6 = 36.
With 3 dice there were 216 possible rolls... and 6 x 6 x 6 = 216. The students discovered they have stumbled upon a formula to calculate how many possible outcomes there are for a certain event.
[pic]
All possible outcomes = all possible outcomes for event 1 x all possible outcomes for event 2
Today's problem (June 10):
Activation: We reviewed some things we learned about theoretical probability:
[pic]
...including how to use a list or a tree diagram to figure out all the possible outcomes...
[pic]
The problem:
[pic]
We will look at our work tomorrow.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.