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!

1st Day Activity

Got a great idea at camp today.  Have students sit back-to-back and create a drawing.  1st round, they describe their drawing to a partner.  The partner may not ask questions and needs to replicate the drawing.  2nd round, the partner may ask yes or no questions, but that is the only communication.  3rd round, full out conversation.  Then they discuss when it was easiest, which drawings looked the most alike.  This was a great introduction to teamwork and communication.  It works on SMP#6 attending to precision, as students must give precise directions to have any chance at having the drawings look the same.  This will also be a great intro in Geometry where precise definitions become so important.

Discussion led to when you might use this in your life, what portion was easiest, how we could improve our replications...overall really good.

This may be my first day activity for this year.  I also would love to use it when we start talking similar and congruent figures.  We can use tools to increase our precision, maybe even limit the number of clues in an effort to discover the triangle congruence and similarity theorems!

The Beginning

I'm officially joining the blogosphere!  After a great PD session on Twitter with @drpcarpenter, I joined, and it quickly progressed to blogs.  I've realized that my notions of what a blog was and what it is supposed to do were way off base.  A blog is a reflection tool that helps me reflect on my lessons and thoughts with the help of the internet community.  It is also a tool that can archive those thoughts, ideas, lessons and conversations to refer back to in the future.  I'm super excited to get up and running, I just need a new phone so that I can take pics of what's going on in classrooms and conferences to keep a photo back up of all the great info and learning.

On a content note: I actually had a math dream last night.  In true math nerd fashion, I was dreaming about fractions.  I dreamed about using common denominators for ALL fraction operations.  The pictures to go with the dream are really difficult to put into words, but if you represent your unit with a square, common denominators force your sub-units to be squares as well.  When I figure out how to make and post videos, I'll have to revisit this!