Teacher resources and professional development across the curriculum

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RepresentationSession 05 OverviewTab atab btab ctab dtab eReference
Part A

Observing Representation
  Review Matrix Multiplication | Taxicabs | Student Work | Student Work Reflection #1 | Matrix Approach | Interpreting Matrices | Student Work Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal


Think about the student work and reflect on the following questions. Once you've formulated an answer to each question, select "Show Sample Answer" to see a sample response.

Question: How does this problem prompt students to work with a representation to model situations that require the multiplying of probabilities?

Show Answer
Sample Answer:
The student's tree diagram shows the various possible outcomes at each stage and labels them with a weight, or probability of happening. If the diagram is drawn neatly, it is clear that the sum of the different probabilities at any given stage is 1. The diagram also helps make clear which probabilities need to be added or multiplied in the problem-solving tasks. And the situation shows why it is reasonable to multiply. For example, the probability of starting in Northside, going to Downtown, and then going to Southside can be thought of as "20% of the time a cab will go from Northside to Downtown, and then 50% of the cabs in Downtown will go on to Southside, so the probability is 0.5 times 0.2, or 10%.

Question: Why are representations a critical part of solving this problem and finding the probability?

Show Answer
Sample Answer:
The answer to the probability question comes from the sum of a number of probabilities and can't be calculated using a basic formula. A representation helps ensure that all of the appropriate probabilities are multiplied and then added.

Next  Extending the problem

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