Probability Day 2

My district has some common material for certain CCSS units, especially those that are not covered in the text book. I don’t use our book much, but at least for the probability unit, I have been using some of the district provided material. I usually take a piece of it to use for warm up and to frame the topic of the lesson.

Example of Scope of Probability:

1. Review of Probability Ideas from Earlier Grades/ Single Events and Complement Events

2. Independence (or not) / Conditional Probability with Compound Events

3. Area/ Tree/ Venn Diagrams/ Two Way Tables and Union/Intersection of Events

Mixed into these are the analysis type questions and discovery of rules, etc. I have been taking the review section and the final Follow Up Activity which asks the students to put all the concepts together to solve a bigger issue. (It is sometimes a problem, an error analysis, or an explain x type of question)

Instead of the middle section, I usually use my own lesson here. After our first lesson discussed here, the students had an understanding of creating a sample space. So after of Day 2 warm up, I paired them off to play some games with dice. There for 3 different versions of 2 player, 2 dice games. 2 were unfair, 1 was fair. After they played the games, they answered some questions about theoretical vs experimental probability. Then, they had to create a new dice game that would be theoretically fair. I provided them with a blank area diagram model to create a sample space. They had to write the rules for a game. Afterwards, they played each others versions of games as time allowed.

I had two people observing this class. After the lesson, I saw that one of them had decided to try and create a game. She commented “I got one, but I broke a rule.” Her game basically had 17 outcomes for each player to win and 2 outcomes that meant no one won. I immediately said “That doesn’t break a rule, the only rule is that the game is fair, ie. theoretically the players should tie.”

That game/sample space became our next day’s warm up. I put it up, explained the rules and asked “Is this fair?” The class discussion on it was fun. Some students were convinced that only 18/36 and 18/36 would be fair. Others were really excited by this ‘new’ approach. I stayed out of the discussion, only asking follow ups or looking for dissenters. Some had a light bulb moment and asked to rewrite their own rules. By the end of the conversation, the majority of the class had decided the game was fair and were okay will the fact that I wouldn’t say if that was right or not, instead saying “The assignment said a fair game, just make sure you can defend why your game is fair.”

Then we moved back into the regularly scheduled programming. I am loving having a 5-10 class debate as a warm up or a check out. The confidence has increased over the year and they are getting better at not having a neat answer to every question. Now to get those great thoughts on paper!

***No photos 😦 Apparently being observed makes me forget to take pictures.

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Author:

I am a math teacher at a public, alternative high school school. I’m the only math teacher at my site, so I get to teach it all. This is good. The bad? I have 7 different preps! Twitter: @altmath

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