Why is a square a rectangle?

Posted on

It’s possible that I am the mother of the world’s most literal thinker.  Or at least a boy who is still firmly grounded in the concrete thinking stage.

One of the questions in Josiah’s math book this week said this:square a rectangle

“Why is a square a rectangle?”

It took me a minute to figure it out myself, but I was greatly assisted by the printed definition of every quadrilateral listed on the top of the page.  So, the definition of a rectangle is “a parallelogram with 4 right angles.”  One can see that a square actually fits within this definition.  Now, a square does have an added feature, in that it has 4 sides of equal length, but nonetheless, it does in fact fit the rectangle criteria.  I can’t say I ever remember learning this little fact myself, but since I could easily see the explanation in the workbook, I accepted it within a few seconds.

For Josiah, however, this was completely unacceptable.  I think those six words completely blew his mind.  As if it revealed that the world was not round or that he was not actually human.

This is the gist of the conversation that ensued: Can you read the definition of a rectangle at the top of the page?  Can you see how a square would fit that broad definition?  No.  Well, it can be further classified, it’s true, but the reality is that a square is both a square and a rectangle, by definition.  No, it isn’t.  Okaaay, let’s use another illustration.  You were born in Saskatchewan, so that makes you a Saskatchewanite. (?? Does it ?? Is that what we’re called ??  I ran with that.)  If your whole life I only ever told you that you were a Saskatchewanite, and then all of a sudden, when you turned 10 I told you that you were also Canadian, that might seem confusing.  You’d say, no I’m a Saskatchewanite.  I’d say, yes you are, but you are also a Canadian.  You fit both definitions.  You were born in Saskatchewan, but you were also born in a broader country called Canada.  See what I mean?  Yeah, but a square is not a rectangle.  But it is, actually.  No, it isn’t.  It’s a square.  Mmhmm. …  I’ll just leave you to ponder this for a while.

Now the truth is, I LOVED this conversation!  I love to expand my child’s understanding.  I love blowing his mind now and then.  I love seeing him stretch his young thinking muscles beyond what was once expected of them- actually experiencing his brain develop and hit new stages.  It gives me great pleasure.  I think it’s exciting!  Josiah, however, may have wanted to burn me at the stake for false teaching.  It took him close to 20 minutes to bring himself to write the answer in his notebook, and I think that even as he did so, he believed it was heresy.

He begrudgingly finished the questions and packed up for an outside break, without any further comment.  I know him well enough to know that these ‘out of the box’ moments take some time for him to digest, but eventually he fully embraces them.  In the near future, I won’t be surprised if he pulls this question out in a social situation: “So, why is a square a rectangle?”  He will love that it sounds crazy, but it’s true.  It won’t take long for him to accept this new definition, but for now, please don’t mention this conversation if you see him.  I think he’s still a little raw from the stretching. 😉


4 thoughts on “Why is a square a rectangle?

    Dwayne said:
    April 4, 2014 at 4:17 pm

    Ah yes, but you must remember to turn it around, just to help him see this statement from another angle (and to confuse him even more!) I always tell my students, a square is a rectangle but a rectangle is not a square.

      jendhansen responded:
      April 4, 2014 at 5:38 pm

      Yes, I really should have looked for more ways to confuse him.

    David said:
    April 4, 2014 at 10:37 pm

    I love this post.
    I also struggle a bit with things like this, while my wife just accepts them with a shrug and says “It’s obvious what they meant”. My son also struggles with them for the same reasons that I do. It makes tests hell for both of us as many times questions are not phrased carefully and require you to assume what they meant, rather than just being able to read a precisely phrased question.
    If the sentence had been phrased as “Why is a square ALSO a rectangle?” I would have had absolutely no problem with it as it would allow for a square to fit within both definitions – as written, for me, it is not precise enough as it does not explicitly allow for both definitions – you have to assume that into the sentence. Probably why I enjoy programming and drafting contracts!

      jendhansen responded:
      April 7, 2014 at 4:43 pm

      It sounds like you and my son would really get each other. 🙂

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s