Without offering the size of each pizza, this question is more like a riddle, which under the right circumstances, it can be fun seeing who can think out of the box better than the others… 

For an arithmetic test, this question has no place.  You’re testing for competency in a subject area; not who can solve a brain twizzler.

Yet, if we’re serious about developing depth and rigour, then this is a very interesting question. In a classroom context, and not necessarily on a test, the conversation around this question could go on for a long time. It leads into discussions about the amount of information necessary to solve a problem, the type of information that is most important, etc. It is a rich question.

My 9 year-old and I have been having a conversation for the past few days on whether ‘zero’ is an even or odd number. The answer really isn’t what is important, but the fabulous conversations (and arguments) that have emerged are powerful.

He even took the question in to his grade 3 math class yesterday and, this morning, I received an email from the teacher about the types of conversations that resulted.

Steve, nice to hear from you on this blog—it’s been a while.

While you and your son have interesting conversations, I’m sure, what matters is simply how much larger the pizza that had four slices eaten.  If the two pizza sizes were too close, then the area of the two pizzas would have to be calculated.  I honestly don’t understand what’s so complicated about all of this.

Too bad Malkin didn’t post this blog on International Pi Day, eh? 

Zero is neither even nor odd—zero = nothing!

Hi Bev,

You and I agree on the “zero” thing, but apparently there is some controversy over the answer in the mathematics community.

Here is the explanation that Luke’s class referenced:

http://mathforum.org/library/drmath/view/57132.html

I think that it’s a fascinating conversation and one that “zeros” in on the real meaning behind the concepts “even” and “odd”.

My six year-old chimed in last night with his own take on the question:

“It has to be even because the number after it is odd.” He’s figured out that there is an even-odd pattern when he counts.

I agree with you on the intricacies of the pizza problem. I guess my only point here is that when we jump too quickly to whether or not the answer is “right” or “wrong”, we miss some really great learning moments. In the article that Malkin referenced, I think that the teacher jumped too quickly, perhaps and shut down some opportunities for getting the student to explain his/her reasoning a little more.

It could be that the student did NOT, in fact, have a clear sense of the concept of fractional proportion but, perhaps, he understood more than we realize.

Fun stuff!

Hi Steve,

I agree, both fun and fascinating to see the depth of understanding that kids have for math.

Personally, I think all kids are geniuses!