The Birthday Problem: Standing in a line in a random order, you and your peers must rearrange yourselves based on your birthdays (date and month). The student whose birthday is closest to the start of the year (1st of January) should be standing on the extreme right/front of the line and the student whose birthday is closest to the end of the year (31st of December) should be standing on the extreme left/end of the line. You can only speak to the person on your left. How will you and your peers solve this problem?
Lesson idea and curriculum links: Introduce ‘The Birthday Problem’ to the students and allow students to work independently or in pairs to come up with a logical sequence of steps/instructions to solve the problem (Year 3: WATPPS16; Year 4: WATPPS21; Year 5: WATPPS27; Year 6: WATPPS33). As mentioned in the video from this week’s CSER MOOC lesson, there can be multiple pathways that students can take that will bring them to the same end point. This birthday problem has more than one solution and it allows students to explore different ways that can still provide a solution to the problem. In this way, students are provided with an open-ended task that is differentiated to cater to the different ability levels of the students. As there are multiple solutions to this problem, all students will be able to access the problem and be provided with the option of taking different routes to get to the same end point. If necessary, teachers can scaffold the process by providing some guiding prompts for students.
Students can also be asked to develop and communicate ideas and alternative solutions using annotated drawings to present to the rest of the class (Year 3: WATPPS17; Year 4: WATPPS23; Year 5: WATPPS29; Year 6: WATPPS35). To extend the lesson even further, with all the ideas from the class, students can role-play, use blocks/objects or illustrate to test out each solution, following the visually represented sequenced steps (algorithms) to identify the most efficient and effective solution (ACTDIP011). To recognise the efforts of students, the class can also vote for the most creative solution rather than only acknowledging the ‘best’ (i.e. most efficient and effective) solution. Students are provided with choice of how they would like to process and analyse the information based on what thinking strategy works best for them. This activity fits nicely into the critical and creative thinking learning continuum of the Australian Curriculum that highlights the need for students to have the skills and strategies to explore situations to propose a range of alternative solutions and to assess and test options to identify the most effective solution. Students should be guided to identify and justify the thinking behind choices they have made.
Integration: This lesson can be integrated in Mathematics as students learn the months of a year and the use of a calendar (ACMMG040). Alternatively, teachers can also assign each student to a specific time (e.g. 3p.m., 3.30p.m., 4p.m….) and get students to order themselves in proper order as they learn to tell time (ACMMG062). If students were learning about the past, current and future needs/technologies in relation to food and fibre production in Design and Technology, students can be given cards that represent a particular need/technology and be asked to order themselves along a timeline.
Criticisms/concerns: Students might be very confused with the expectations of this task if teachers simply pose the question and get students to tackle the problem on their own. Teachers should preferably model a similar process of using a sequence of steps/instructions to solve a problem before getting the students to work on ‘The Birthday Problem’. Teachers can explore this website: https://www.transum.org/software/River_Crossing/ that provides 3 levels of difficulty that students can attempt to solve as a class or in small groups. This website allows students to drag and drop (similar to an virtual manipulative) to help visualise the process as they work towards a solution. Teachers can use the River Crossing problem to model the process before posing the Birthday Problem to the class to solve.
How would you solve this birthday problem? (: