Rarely will folk draw a parallelogram like B and even more rare will they draw a rectangle or square. This might seem innocent enough but can be a big clue to a huge misconception that often goes unnoticed. This was evident in a Grade 6 class I saw this week. We had given them this question from the 2012 Ontario Junior EQAO test:

It's a nice question as there are a variety of ways to think about solving this. One student solution was shared with the class and provoked some great discussion:

Some students argued that the shape on the left wasn't a parallelogram. One student argued that it was as parallelograms are shapes that have "...two pairs of parallel sides." Years ago I would have left this statement unchallenged. Now, I jumped at the opportunity it gave and asked if the shape below was a parallelogram:

Probably half the students said yes it was; they understood that a parallelogram is *any*shape with two pairs of parallel sides. The remainder of the class seemed unsure. We then got in a debate as to whether or not a regular hexagon is a parallelogram(!); some said no as it had three pairs of parallel sides, others said yes as it had

*at least*two pairs of parallel sides.

As we mused how to deal with this, a student asked if she could look up the definition of parallelogram. This she did, and there it was: "A parallelogram is a

*quadrilateral*with two pairs of parallel sides." This was news to a lot of students. However with this new knowledge they were now OK with saying that the rectangle in the solution is also a parallelogram.

On reflection, I now realise that giving insufficient examples and using imprecise language restricts students' understanding of what a parallelogram is. It would be better for students to construct their own understanding of what a parallelogram is by showing them something like this (from Ontario's MOE's

*Guide to Effective Instruction Grades 4 to 6: Geometry*) and asking them to define 'parallelogram'.

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