Thursday, December 13, 2012

Lesson 8- Perspective, Illusions, and Distance

*A student asked a question about why the moon seems to follow you while driving, and that inspired this lesson

Materials: toy, Incredible Visual Illusions- You Won’t Believe Your Eyes! ,or just the optical illusion pictures used in this lesson, craft sticks

Summary: This was an unusual lesson, because a lot of kids were sick, and the ones that came weren't paying much attention. Next time, I would split this lesson into two separate lessons, one with optical illusions, and the other one about perspective.

1.      Why does the moon always stay in place as if it is not moving, while the trees are always moving when we drive?
Answer offered by the kids:
“The moon is big!” – Possible response from teacher: “What if it was something that was small and we could barely see it, but it was very far away? Would it still seem to stay in place all the time?”
Kids thought after the comment, and then decided that as long as we can see the object, if it is far enough away, it would seem to stay in place, and not go away from us.

A great activity on this topic suggested by Maria Droujkova:

1. Draw 2 parallel lines on a paper; add perpendicular lines (so it looks like a railroad)
2. Put the paper behind the window laying down on the windowsill.
3. Take a transparency; lay it against the window; use markers to trace the railroad you see through the window.
4. The resulting railroad tracks will not be parallel anymore.
5. Now, take two lego men and start moving them along the railroad, at the same speed.
6. It will look like at the same time interval, the lego men cover different distances, since the distance between two railroad ties in the front seems to be bigger than the distance between the railroad tracks in the back.
7. For the moon, which can be considered to be at  in infinite distance, the speed of movement is almost negligible.

2.      Ask the kids to sit right next to a toy on the floor, and see how far they can move without turning their head. Then put a toy on the opposite side of the table, and ask them to move until the toy comes out of their view. Can you see the toy longer if it’s on the opposite side of the table, or if it’s right next to you?
This activity was interesting for the kids, but it was a mistake that I put a hands-on activity at the beginning of class. DO NOT put hands-on activities at the beginning of class. First of all, the kids get very involved in it, and then they want to keep doing it, and also, they start to think that since they've already done the hands-on activity, they don’t have to pay attention anymore, because they already did the fun stuff!

3.      How do we measure distances? Can distances only be measured with a ruler? Measure distances in steps, sitting people (let them sit on the floor), and toys.
At first, when I asked the kids if distances can only be measured with a ruler, they said, no, they can also be measured with a meter stick! Again, it would be better if this would be closer to the end of class, because the kids actually do something. Also, hands-on activities should be spread through the entire class, not bunched up one after another, as in this lesson.

4.      How does an airplane look like in the sky? Is it big or small? Why do you think it looks that way? Take a toy, and show close up in front of the kids’ faces, and then slowly move it away. What happens? Why?
Kids had a pretty good answer: “Airplanes look small in the sky because they are so far away, and there are many things around us that are closer to us, and look much larger compared to the far away airplane.” At this age, kids have an intuition that things closer to us seem larger, and things farther away seem smaller, but they don't yet know why.

5.      Show the kids the illusions in the Incredible Visual Illusions- You Won’t Believe Your Eyes- discuss what is going on and why.

As soon as I showed them those two illusions, they wanted to start seeing more, and wouldn’t let me move on to the next activity. It was hard for the kids to understand why the pictures were optical illusions, and how they worked, but they still liked them.

6.      Optical Illusions can use color, light and patterns to create images that mislead our brains. Optical illusions occur because our brain is trying to interpret what we see and make sense of the world around us. Optical illusions simply trick our brains into seeing things which may or may not be real.
This is actually a good explanation of optical illusions, and kids understood it well.

7.      Do the Extra Floating Finger Illusion, and the Hole in Your Hand Illusion.
The kids thought it was extremely cool that they themselves could make an optical illusion. When kids just see an optical illusion on a picture, it feels fake, but when they themselves can make an optical illusion, they prove to themselves that optical illusions are real.

8.      Is this possible:
Try making it with craft sticks to double-check the kids’ answers.
The kids were all certain that it was possible, but after we tried making it with craft sticks, they realized that pencils can’t interconnect like in the picture.

Is it possible that the blue trees are the same size?
There were two different answers from the kids. Some kids said that the blue trees were the same size, and found it easy to explain this way. Other kids were certain that the trees were different sizes, because when they put their finger on top of the far away blue tree, it was higher than the top of the closer blue tree. This shows that some kids at this age still don't understand that the linear measurement depends on the difference between two points - final and initial, not just the final one. This was noted by A.K.Zvonkin in his book " Math from three to seven" as well.

Is this possible? 
If kids don’t understand how this is possible, this is a possible hint: “Are the people actually standing on the man’s hand?” After this hint, the kids figured out right away that the people are just standing behind the man, and the man is just sticking his hand in front of them, making it look like they are standing on his hand.

The two yellow lines are the same size!
The kids didn’t seem amazed at this one, and seemed to know that the lines were the same size from the really beginning. The kids checked themselves by placing their fingers on the sides of both of the yellow lines, and they were parallel. 

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