abingdon

Trains anyone?

A lesson on probability for upper Primary

Read the problem through aloud. Clarify word meanings and restate the conditions of the problem.

Review its conditions:

Tom's arrival is "random" i.e., that Tom does not make any decisions: such as which platform to face, to hurry to get a train, etc.
Discount unstated possibilities: he might take the bus, he dislikes busy shopping centres, a strike, etc.

The advice to 'read the problem' means to understand the conditions therein. Solving the problem will come from addressing what is in it. Taking about it, interpreting it, is part of the process of problem solving.

On the blackboard, visualise the problem:

a timetable for the Abingdon train (with arrow)
and another parallel line for the Centreville line (other arrow)
insert checks for stops at Tom's station. Experiment with random spaces 10 mins apart.

Discuss whether the two trains ever stop at the same time. Show this as a no possibility on the diagram.

Draw a third and parallel line below the two and place all stops on this line. Show that some spaces are larger than others, that some are 2 mins and others 8 for instance. Flies fly through larger holes than smaller and Tom is more likely to arrive in the larger spaces than he smaller.

Conclude with the fraction for the probabilities to solve the puzzle.

Review the process, to show HOW we solved it: the talk, the visualisation, the conditions, the reconciliation of all information, the possibilities, the answer.