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Friday, November 14, 2008

Draw Squad Lesson 3 / Geometry Session 4

How did he get from this ...

To this?...

Can you spot the difference?

This was one of D's Draw Squad drawing this week. In the book, each lesson explains the concept to be grasped and the concept is demonstrated as one copies the drawings in the lesson.

Copying is a skill that requires a great deal of one's power of observation. And power of observation has to be honed. Notice the first attempt at drawing the house has lines tilting in the wrong directions. Of course the lines were right in the book but were copied incorrectly.

I noticed that my boys do not employ reasoning and logical thinking when they draw. I decided to help them by introducing 2 concepts: parallel and perpendicular lines, and vanishing point in perspective drawing.

The time was ripe for me to introduce parallel and perpendicular lines in the context of our Mathematics / Geometry sessions (See my post on our Geometry Sessions 1, 2 and 3). After a short review of how to construct an equilateral triangle, I taught my boys how to construct perpendicular lines using the compass and ruler.

We then constructed parallel lines with a ruler and square.

I gave my boys time to construct as many perpendicular and parallel lines as they wanted.

I proceeded to teach them alternate and corresponding angles as described in this site.

This site has a helpful mnemonic system.

The letter X can help us find opposite angles.
The letter F can help us find corresponding angles.
The letter Z can help us find alternate angles.

This is when I brought out the book The Librarian Who Measured the Earth by Kathryn Lasky again. We have read it some time ago (See my post on Erathosthenes). I started this series of Geometry session just so I can explain what we have read in this book. Now I could finally wrap everything up. My boys FINALLY understood how Erathosthenes measured the circumference of the Earth. (See my post on Geometry Session 1) Their reaction was a jaw-dropping, "Wow! Erathostenes was SO clever!"

Now back to D's Draw Squad drawing... Perpendicular and parallel lines are just all around us. We cannot escape these when we draw. We talked about these lines in real life (corners of walls, windows, boxes, tables etc.). We talked about what things really are and what we perceieve them to be. That is to say lines that are in fact parallel may not appear to be so because of perspective.

This is where I showed them the "magic" of the vanishing point in 3 dimensional drawing with a simple rough sketch of a street scene on our white board. B was excited when he saw this. He was inspired and drew his own street scene. Here it is...

With all this information, I then asked D to correct his first sketch of a house.

What a BIG detour we took?! Nonetheless a necessary one.

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