I have been teaching fifth grade math for four years, and I would appreciate any ideas or advice you could offer regarding a new approach that you would suggest when introducing geometry. Every year I find myself repeating the way I recall my own fifth grade teacher introduced the topic. I start the class off by asking students about various shapes that are important to them in their lives, and then I ask them to share with the class what properties the shape has that they believe other shapes do not. Now, though, when I ask the question, I get either blank stares or responses that almost never lead the class into deeper though about the importance of geometry nor how real it actually is in day-to-day experiences. So after several people in the last year or two suggested I ask you, I now discover that you finally answer questions from students and teachers through the internet! Thank you for doing that, and, well... any ideas?
(Geometrically Lost in Space)
I do have some suggestions. First, though, take a deep breath. There is nothing wrong with what you've been doing, because I could tell just from the way you were instantly excited by geometry as a child, that after the 'blank stares' or whatever it is that you notice, you then move along and somehow manage to share your enthusiasm. Whether you realize it or not, when you teach something that you feel so passionate about, it somehow works. One way or another, it just works. Still, here are some ways that I would do it.
(oh, but before I forget, you can let your breath out if you haven't already fainted. Hello? Hello? Anyways, when you get a chance go ahead and email me that you're okay.)
Okay. Before you ask the class a question, try telling them a story.
There once was a man who, more than anything else in the whole world, wanted a fishing rod. He had spent his boyhood years fishing with his father and his grandfather, and now that they were both gone, he thought a lot about fishing, and particularly a fishing rod he had seen for months in a store window. Finally, he gathered up the money he had accumulated by setting aside a few dollars each week, and took the local bus to the store.
He bought the rod.
It was exactly five feet long.
The woman at the register wrapped the rod in clear plastic and tape, and the man returned to the bus stop in time to catch the next bus. . . BUT, as the busdriver opened the doors and saw the man with his fishing rod, she said, "I'm sorry sir, but we have a rule on this bus, and it's law of the city: No one is allowed onto a bus with any object that has a length of more than four feet. Sorry."
The door snapped closed and she drove away.
The man shrugged and returned to the store where he purchased the fishing rod. He was determined to keep the rod and take a bus home with that rod. So this time he did something in the store.
And, although I won't tell you what he did, I will tell you what he did not do: He did not fold the rod, collapse it bend it break it, exchange it for another or have it shortened. He did not have it shipped.
He then took the rod back to the same bus stop and – miraculously -- got the exact same bus driver (although they may have been twins).
This time, she opened the door and welcomed the man as he stepped into the bus and went home.
And still did not believe in breaking the law.
QUESTION: When the man was in the store the second time, what did he do to the rod?
At this point, instead of just seeing blank stares, you will also probably see some hands shoot up excitedly. One person will proudly volunteer that the man somehow bent the rod.
No, and didn't we already say that he didn't bend it?
Next hand: The man returned it and got a smaller one.
Uh, no. I think we might've said he didn't bend it.
Next hand leaping out of the back: The man stuck it in his pocket and, um hid it, right?
Next hand: He ummmmmmmmmmm, I mean, was he kind of...was the driver paying attention the second time? I mean, was she maybe tired from going all through town and back in just a few minutes or... um...
Next hand: Did he catch a lot of fish?
Take another deep breath and this time let it out whenever you wish.
ANSWER: The man took the fishing rod, which was still five feet long, and had it packed in a rectangular box that measured four feet long and three feet high. (It was only a few inches deep, and had a handle on one side, like a large brief case.)
Now you'll see blank stares, but they will be different.
Give them a chance to think and chat.
In the meantime, draw a rectangle on the board and label it with a 3 on each vertical side and a 4 on each horizontal side. Then draw the rectangle's diagonal. And label it with a 5.
Explain to the class that there really can be a rectangle with these dimensions and that a five –foot-long fishing rod really would fit inside, because there really is something called a 3-4-5 triangle, and they really would fit together to make a rectangle like this because the 3-4-5 triangle is what's called a right triangle...
That means, of course, that it has one corner the same as a square's corner. Or a rectangle's corner. Provide lots of rulers and let the students try it out on the floor.
Now you have angles, triangles, rectangles, diagonals, measurements, and fish.
Have fun teaching!