How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”* Take a guess as to what percentage of them would give a numerical answer and then watch the video below:

Of the 32 students I interviewed, 75% of them gave me numerical responses. Going into this, I predicted it would be closer to 50%. Here are some of my observations from the 32 students:

2 students calculated the answer to be 130 (125 + 5)

2 students calculated the answer to be 120 (125 – 5)

12 students calculated the answer to be 25 (125 ÷ 5)

0 students calculated the answer to be 625 (125 x 5)

4 students stated that they guessed their answer (90, 5, 42, and 50)

4 students tried to divide 125 by 5 but could not correctly implement the procedure

Three particularly interesting students included:

The student who found the shepherd’s age by using the old “add the sheep and dogs and divide by two” trick and got 65. You didn’t know about that trick?

The student who got 120, then said that you don’t have enough information to figure out the shepherd’s age, then seemed to feel so uncomfortable with that conclusion that the student decided to guess 90 years old.

The last student who explained that the reason for dividing was because it didn’t say “sum,” “difference,” or “product” in the problem.

Something I had not thought of until Cari Noble mentioned it in the comments was the idea of intellectual autonomy. Many of the students knew I was crazy for asking them this question, yet they felt like they couldn’t question the questioner and were obligated to answer me. So, they repressed that feeling and gave me an answer anyway. That’s certainly not where we want students to be. I do understand that it is important to be respectful of authority figures, but you can be respectful and still express your thinking.

As for Math Practice 1 from the Common Core’s Standards for Mathematical Practice, here are expanded versions of the quotes from the video:

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.

They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.

Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”

There’s no better way to see if your students are making sense of problems than to ask your students this same question. You have to make sure you keep a straight face and have them write their answers on a piece of paper. When everyone is done, have them crumple the paper into a ball and throw it at someone else in the classroom. After a few rounds of this, the papers will be sufficiently mixed that you can then ask each person to open up the paper and read what was written to have a conversation about their classmates’ answers. When you’re done with the conversation, show them this video so that they realize they’re not alone. You can download it by clicking the “Download Video” button below. After you try it out with your students, please post a comment about how it went along with the students’ grade level.



Download Video





*The “How Old Is the Shepherd?” question was popularized by an essay written by Professor Katherine K. Merseth in 1993 and was based on research by Professor Kurt Reusser in a paper presented at the 1986 American Educational Research Association annual meeting. It is noteworthy that Professor Merseth wrote that “researchers report that three out of four schoolchildren will produce a numerical answer to this problem.” Twenty years later that statement still held true.