Monthly Archives: April 2015

About that “5th Grade” Logic Problem…

by Jonathan Osters, The Blake School

Every once in a while, there will be math or logic problems that go viral on social media. When they do, these are fantastic opportunities to get students to think about their own learning. One such problem is the “Cheryl’s birthday” problem, supposedly from a fifth-grade textbook in Singapore.

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This problem is a great opportunity to engage students at any level, from high-school, down to – yes, even fifth grade, if the problem is framed in a way that students can approach it.

How could we make this problem “Experience First?” Here’s one way:

  1. Have students pick an answer off the top of their head. Do this by secret ballot, clickers, or some other way that forces students to “put some skin in the game,” but is not too intimidating. You will likely see the same set of dates chosen multiple times, and several dates not chosen at all. This brings us to the student experience.
  2. Allow students to act it out. Have a students work in groups of three. Have one student be “Cheryl” and the other two be the two other boys. Act out the scenario, having the “Cheryl” student select a birthdate from the list and telling each of the other students the information they get in the problem. Then ask the two students if either of them know the birthdate. The person receiving the month should always say “no,” but the person receiving the date will say “yes” for the birthdates of May 19 and June 18. This allows students to narrow down possibilities down to only the ones where neither of them knows the birthdate.
  3. Ask students why they didn’t know. Select specific dates, asking why neither of them knew the birthdate. Answers like “there was more than one 17th in the list” or “there are three choices in July and I didn’t know which one was it” allow students to explain their reasoning.
  4. Allow them to act it out again. This time, the student playing Albert has an extra job. For each date, he has to say whether he knows, and whether he’s sure Bernard knows or not. This allows students to see which dates result in the conversation we see in the problem.

This whole process is an exercise in both direct and indirect reasoning, a skill with which many students (and even adults) struggle, and the fact that this problem has been on social media highlights that struggle.

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But problems that go viral have pitfalls. First, many people fear getting the problem wrong – your response is out there for the whole world to see – so they don’t even attempt to solve it. Second, people online can get particularly stubborn – people have a tendency to pick an answer and are unwilling to listen to other opinions. That’s why it’s our job as teachers to take problems like these offline and place them in the classroom where they belong. Approaching this problem in an experience-first way removes the fear of failure from the problem, since in an experience-first classroom, making mistakes is all part of the learning process. It also allows students to not have to feel like they have to defend a wrong answer – they can acknowledge their incorrectness and understand the process by which the answer is truly obtained.

Viral math problems often underscore the lack of numeracy or critical thinking skills that many people have. By finding opportunities to address them in class, we can help our students become better thinkers so they can better interact with the world around them.