Math and Science: Measuring Angles

Up until now, our studies in Math and Science haven't really overlapped much.  There has been some reading of thermometers and volume measures; we haven't even graphed results.  Use of the protractor is yet another form of measurement, though one that isn't used in our daily lives, so I consider this experiment to have led to as much math learning as science.


BatBoy has been interested in learning more about how light works.  One of the first experiments we put together involved looking at shadows of an object while changing first the distance at which a flashlight is held and then the angle at which the flashlight is shone. SpiderGirl joined in as soon as she saw we were experimenting.

First they learned how to use a protractor to measure and draw angles.  Then they used a ruler to measure the shadow of a domino placed at the centre of the angles when shining the flashlight from 30, 40, 50, 60, 70, 80, and 90 degrees.  They were delighted when they saw that the shadow disappears at 90 degrees. 

I then asked them, what if we continue past 90 degrees?  The answer:  Let's try it!  They found that the shadow was on the other side.  More, they noticed that at 110 degrees, the shadow was the same length as it was when the flashlight was at 70 degrees, only on the other side of the domino. 



I asked, "Why?" 
SpiderGirl looked at the angles and said, "Because it's the same angle."
"Same angle?  One is 70 degrees and one is 110 degrees."
"But it's the same angle, the same size."
"Same angle from where?"
"It's the same angle."
"But an angle is measured from somewhere.  Where are you measuring from?"
"It's the same angle!" 

She was frustrated, but not too frustrated to keep trying to communicate what she was seeing.  Finally, she was able to articulate that 110 degrees is 70 degrees from the horizontal if you extend the zero line.  Yes!

After they had had more time to play with the light and experiment with shadows, BatBoy came back to me to ask for more angle practice.  I showed him how he could measure angles in a triangle.  He had fun measuring the angles in some other shapes.  After some time, we needed to leave the house to go to an activity.  He didn't want to stop though, so I challenged him to use his eye to estimate some angles.  BatBoy and SpiderGirl both amused themselves by looking for 30-, 60-, and 90-degree angles as we made our 20 minute trip.