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Day 36: Intro to Squares

Ok, time to actually start implementing the modeling part of the class. My main idea for this unit was to take everything we've already covered in measuring distances and understanding angles and start out with the simplest possible shape, a square, to help students get comfortable with the idea of discovering the content on their own.

We started making sure that everyone knew the definition of a square. I know it seems simple, but I learned a long time ago to never assume students know anything they "should" know. Students had a lot of good (and scattered ideas), so to ensure consensus, I simply googled "definition of a square." Google is becoming so powerful that it didn't simply give me a link to the answer, it actually just answered the question.

Then I took suggestions for the different ways we could measure the lengths of sides. I wanted students to understand that there are multiple representations of the same idea. Students suggested the typical meters, cm, feet, inches, etc. Some suggested simply counting boxes on the graph which was nice to see. Nobody suggested using some form of coordinate subtraction , so I led the class to that idea. At this point, I kept things horizontal/vertical, so we're not getting into the actual distance formula just yet, just the ideas behind the Ruler Postulate (I do NOT use that phrase in class).

From here we transitioned into other things we could quantify from our pictures. I asked all students to count the total distance "walked" around the outside edge of their square. Some knew this was perimeter, but I explicitly avoided the word. Then we counted the number of boxes inside the square. Again, did not use the word area.

Looking back, I will need to make sure that all students are measuring side length and perimeter with the same units here. I'll probably go with boxes just to avoid the mess and confusion that comes with the rulers.
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