Tasks | Early Adolescence | Birthday Problem

Tasks - Years 10, 11 & 12

Birthday Problem   by Stephen Spice, Shenton College

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Chance & Data	Collect and Organise Data Summarise and Represent Data Interpret Data
Working Mathematically	Mathematical Strategies Reason Mathematically Apply and Verify
Brief Description:	Students determine how many people need to be in a room for there to be a 50% chance that two or more have the same birthday date.
Expected Outcomes:	Students will learn how to generate list of random numbers using their graphics calculator to simulate an activity. Students will use their graphics calculator and pen and paper to record data and display data. Students will records and interpret data. Students will test and verify their results.
Context:	This activity could be used as a single lesson, or as a small project involving conducting a survey, simulation, statistics and analysis. As a series of lessons to any group of Year 9 - 11 students.
Learning Activities/ Experience:	Time Taken - One Period for high achievers, small project for Years 9 - 11. Introduce the problem - could visit and collect data from other classes. Guess the answer. Introduce the concept of 'simulation' and how to use the graphics calculator (see own instruction manual) to generate random numbers). Simulate sets of data (random numbers) and record data in an appropriate way. This is a difficult task to do efficiently. It may be useful to have a discussion of best practice to provide 2mm graph paper. Tabulate results - students should simulate at least 10 groups of people. Analyse results and determine the most appropriate statistic to use ie. mean, or median. Relate the solution to the required probability. Verify/check solution by visiting classrooms in the school, or checking list of birth dates from administration information.