Pictures can be deceiving

So after reading a bunch of blogs and tweets, I understand that the MTBoS (myself included) loves mistakes.  They are a great learning experience for the person making them and the people involved with the person making them, whether they are teacher mistakes or student mistakes.  There is a lot of power and value in owning up to and moving forward from them.  But to make my blog meaningful for me, I will be archiving the ideas that worked just the way I wanted them to.  These moments don't happen nearly enough for me, but one happened today and it inspired my first post in a while.

I was trying to think of ways to demonstrate that pictures can be deceiving and took the following picture of my classroom.

I asked students just to look at the picture with the following terms in mind:  parallel, perpendicular, right angle, distance and length.  We then discussed their observations.  Some students claimed that the lines going across the room were parallel while the ones running to the front of the room were not.  I highlighted them in different colors on the whiteboard then asked them to look up.  Students agreed that they were parallel in real life but not necessarily on the picture.  We did the same thing with the lengths of the sides of the rectangular tiles using a meter stick on the picture.  We repeated with a protractor.  Students had a great discussion about how the picture can be misleading and even though lines did not appear parallel they were.  Same for right angles and distance.  We then went into the hallway and looked at our sprinkler heads (which are all in a row).  They determined they were collinear both in reality and the picture.  A similar discussion was held about betweeness.  Students began forming the ideas about what a picture tells you for certain and what you must prove or derive by other means.

When we returned to the classroom, I had the following statement and picture posted on the board.

At first students did not believe the statement, arguing vehemently that this was a rectangle.  I simply sat in the back repeating "The red figure is a square!".  Slowly, one by one, students caught what was happening.  It led to a great discussion about the need for good definitions and for needing new tools to determine how long a segment is.  For 8 minutes in class I only uttered those six words and the students took over the discussion.  They were initially so infuriated with the idea that they weren't satisfied until they understood what was meant by the statement.  The discussion and passion were immense and this is definitely an atmosphere I'd like to create.  I'd love to hear other people that have experienced similar situations and what they did to promote this lively debate!