Tuesday, September 10, 2013

What's in the bag: Theoretical vs Experimental Probability

If I thought yesterday was boring--what did the kids think?!
Yesterday I reflected on how tragic it was that we talked all day about dice, coins and cards and never had them in student hands. I thought about what aspects of this new class I thought were important and what things could be discontinued (or as Google would put it 'deprecated').

What I want to continue:
1. Student self-reflection based on learning target rubrics on a semi-daily basis
2. Activities and labs centered on the learning targets (ideally incorporating multiple targets)
3. Short, meaningful yet challenging applications of the learning
4. Computerized practice and resources for kids that need it
What will be optional but not a focus in class:
1. Video lessons
2. Notes packets
3. 'I do, you repeat' cycle of examples

Here is an example of what we did in class today (using computers). I broke in periodically and asked the questions and invited student responses throughout the time.

Teacher questions to ask in class
Learning targets: 1.1 through 1.4

There are 4 tiles in the bag. The color options are red, blue, purple and green. It is possible that all tiles are the same color. Each draw a tile is shown and then replaced back in the bag. (Click here for game)

Play the game. Try to identify a strategy for scoring the most points in a round. (Hint: Analyze what makes the score in a round higher or lower)

What balance do you need to find in winning each round?

After the final color is revealed, identify the percent composition of each color in the bag (i.e. 25% Red; 50% Blue; 25% Purple).

Do the same for the percent composition for the colors that were actually drawn (i.e. 71% were blue, 14% were Red, 14% were Purple).

What do you think would cause the theoretical probability (what we expect to happen) to more closely match the experimental probability (what actually happened)?

How would this affect the score for the round?

What is a good situation to happen in the game to maximize points or a win? Explain.

What is a difficult situation that came up in the game? What makes it difficult?

Is there an accuracy score we seem to all be close to as we play more rounds?