Mean, Median and Mode

[OntMathTeacher]

I am posting this problem to my grade 7 students and they are struggling to answer this problem.
5 positive whole numbers make the data set.
Median < mode < mean
Can anyone find a solution to this problem to help my students?
Thank you.

 

[Deleted member 4993]

I am posting this problem to my grade 7 students and they are struggling to answer this problem.
5 positive whole numbers make the data set.
Median < mode < mean
Can anyone find a solution to this problem to help my students?
Thank you.

Please share your thoughts about this problem with us!!

 

[Dr.Peterson]

I am posting this problem to my grade 7 students and they are struggling to answer this problem.
5 positive whole numbers make the data set.
Median < mode < mean
Can anyone find a solution to this problem to help my students?
Thank you.

It can be dangerous to assign a problem without even knowing whether there is a solution!

Unless I'm missing something, I think this has no solution; in that case, if this were an advanced class, I would expect them to prove that to you. As it is, however, I imagine they may rightly blame their struggle on you. You may want, at least, to extend the problem to 6 or 7 numbers.

 

[OntMathTeacher]

Normally I do not assign a problem without knowing the answer, but in this situation the school board provided the problem to teachers and did not provide us with the answer. There were similar questions before this one with the same style of restrictions and students had to solve those before getting to this problem. As a class we had lots of fun being challenged and working with numbers to create an answer that meets the restrictions.

Also, while I appreciate your answer I feel that your response was a little bit unnecessarily rude with the creation of the idea of students blaming struggle on me. You are taking my statement of struggle and replacing it with the negative idea of blame. Struggle isn't a bad thing as it means my students are being challenged and working with the problem to attempt to create a solution.

 

[Dr.Peterson]

Normally I do not assign a problem without knowing the answer, but in this situation the school board provided the problem to teachers and did not provide us with the answer. There were similar questions before this one with the same style of restrictions and students had to solve those before getting to this problem. As a class we had lots of fun being challenged and working with numbers to create an answer that meets the restrictions.

Also, while I appreciate your answer I feel that your response was a little bit unnecessarily rude with the creation of the idea of students blaming struggle on me. You are taking my statement of struggle and replacing it with the negative idea of blame. Struggle isn't a bad thing as it means my students are being challenged and working with the problem to attempt to create a solution.

I'm sorry for putting it that way; but whoever chose the problem appears to be causing unnecessary struggle, which could trouble some kids who aren't prepared for it. (I've seen students get upset when a teacher gave them an unsolvable problem that they "wasted hours on", even when the teacher did it intentionally.) That it's not you who initiated this is good, and that the students evidently don't have that negative attitude is even better.

I certainly like challenging students and being challenged, and I encourage them to appreciate challenge -- after working out a hard problem with a class or an individual, I will say, "that was fun", explaining that my definition of "fun" is "challenging". If you've turned this struggle into a positive, that's great.

I hope you're able to guide them to see why there is no solution, which would be a big win; the fact that "no solution" can be a solution is a great lesson.