Geometry Geometry Middle School

Always, sometimes or never true: “A parallelogram is a rhombus.”

ASN 6 2


What’s the next step for this student? How would you help?

Thanks to Tina C for the submission.

4 replies on “Always, sometimes or never true: “A parallelogram is a rhombus.””

I think that the confusion is about how subsets work.

If parallelograms are always those slanty things that look like drunk rectangles, then a rhombus clearly isn’t a parallelogram!

I’d start with asking the student about themselves. What makes them unique? Are they part of a team? Do they participate in a club? Or are they just a loner with no other human contact? (Hopefully even your angry goth middle schooler has one friend they tolerate!)

The same is true of shapes. Unfortunately, some sets (like squares, those jerks) are really exclusive and hard to join. Others, like parallelograms, are pretty wide open. Not as psycho as quadrilaterals, but not as picky as the rhombus club.

Once a middle schooler sees subsets as social cliques, they have an easier time completing tasks like this one. Not easy, though! Subsets are always a pain in the butt for 12-year-olds.

I would ask the kid “Why is it not a parallelogram?” and then probably “How can you tell if a quadrilateral is a parallelogram?” with the hope of getting the idea of “two pairs of parallel sides: yes. Not two pairs of parallel sides: no”.

I’d probably also have them make something like a Venn diagram of quadrilaterals to help them see that things can be in multiple naming groups at the same time.

And herein lies my frustration: we made a diagram with all the quadrilaterals after students sorted shapes based on various characteristics. There was a half page for parallelograms with circles for rectangle and rhombus overlapping in a square. I think this is a case of needing to unteach years of preconceptions. More examples and discussions required.

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