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Magic box with 50-50

Lesson Overview

This course builds on the concept and mechanism of “random number”, provide students with the opportunity to experience real-life phenomena related to probability. Especially, how the experimental probability could be different from our expectation, what is meant by independent events, and how to use probability to build a fair game system.

Learning Objectives

  • Use “pick random number [XX - XX]” to simulate probability conditions.

  • Use random number and conditional codes to simulate the real-life event.

  • Draw conclusions and inference from the results of large number trials.

  • Extend to more conditions.

Task Description and Resources

Task 1: 50% + 100, 50% - 100

Purpose: Get students familiar with the drawing paradigm of “scan the whole stage”.

Objective: To observe how the money going to change following this rule for several trials and large number of trials.

Suggested Steps:

  • Use “pick random number [XX - XX]” to simulate the random event. Set variables to store a single event. Determine the conditions that can fulfil the situation. For example, we can set take random number [1 - 2], or [1 - 100], the condition could be [= 1] and [= 2], or [< 51] and [> 50], respectively. Use list to store the results after a trial. Run multiple number of trials to observe the results.

  • Ask students to reflect on the results. The sample guiding questions are: (1) What results do you expect? Does the computer simulation close to your expectation? And why? (2) Image that after 1000 trials, we got the results of -5000. Now I run another 1000 trials, what would you expect?

Reference Code:

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Task 2: 50% * 2, 50% / 2

Objective: To observe how the money going to change following this rule for several trials and large number of trials. Think about the differences between the rules in Task 1.

Suggested Steps:

  • After simulation, reflect on the results: What are the differences between Task 1 and Task 2, and why? What can we infer from the results?

Reference Code:

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Task 3: 30% * 2, 40% / 2, 30% unchanged. Or other conditions

Purpose: To observe how the money going to change following this rule for several trials and large number of trials. Change the condition to design a playable game.

Suggested Steps:

  • The key is to choose the value of [pick random number] to simulate different probability situations.

Reference Code:

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Link to Scratch:  https://scratch.mit.edu/projects/1000375798/

Summary

This course guides students to experience experimental probability by using random numbers to simulate real-life probability phenomena. Through this experience, students will feel the differences between concepts like “theoretical probability”, “expected value”, “experimental probability” and “instance trial”. The real-life and unpredictable situation could be engaging for students and create conflict to help the knowledge construction.

Acknowledgement 

The author would like to thank Zhi Hao CUI for co-designing this lesson and appreciate all the anonymous teachers and students who participated in this research.

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