On the weekend, I posted a couple of scanned images of the homework, but they were cut off. Here they are, in the correct form:
I am going to post the first slideshow I made for the Math investigation. The slides went too fast, but take a look at it.
I attempted to create a second show, but the images looked very poor, so I am going to upload and provide some context for it. I will not do this now but before the end of the evening. I will explain it tomorrow.
Sometimes, keeping things simple makes it easier. So, let me explain this example. I am going to assume you viewed the short video and heard how I introduced the lesson, you should have a sense of the investigation.
When you draw on the grid paper, be sure to use a ruler and keep your points on the vertex. What is that? In the following diagram, the black dots are on the vertex of the grid paper. This is where the lines meet. When there is more than one vertex, they are known as vertices.
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| https://www.quora.com/What-are-some-of-the-most-interesting-applications-of-Picks-theorem |
1. The first shape to be drawn is a rectangle. It is on the right side of the page. As you can see, I have cut it out. Before I did this, I calculated the area. Since the squares are not in cm, I use units squared as the unit of measurement for the area of the rectangle. The formula I used was base x height.
2. On the rectangle, a diagonal line was drawn from the top to the corner. Both shapes were cut out from the grid paper. At this point, I was suggesting you "play" in order to discover the new shape.
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| She played, she discovered! |
3. The next shape was a Triangle. You had to draw two of the same shape. In the above diagram, I have two. The area for the top one was calculated, in order to contrast it with the second part of the exercise.
4. In the topmost triangle, I decorated it with red dots. In the picture, I have cut it out and moved it. Don't do this yet. In the second triangle, I drew a "roof" around it and created a rectangle. With this Rectangle, I calculated the area using the dimensions of base and height so I can compare it.
5. I now cut and moved the triangle on top of the second one, under the roof. If you compare the areas of the two shapes, you will notice something.
6. In this picture, I cut the red-dotted triangle in half and discovered something interesting. What was it?
I anticipate people doing their best to discover the relationships themselves. Perhaps my attempt at guiding them caused too much confusion. I will hold off on sharing this post, until the work is handed in. Here are two images of the students at work:
I anticipate people doing their best to discover the relationships themselves. Perhaps my attempt at guiding them caused too much confusion. I will hold off on sharing this post, until the work is handed in. Here are two images of the students at work:
