http://www.mathsisfun.com/definitions/net.htmlNets are things that seem easy once you have the shape and just have to cut out and tape together but have you tried making your own, things get a little trickier. In class we made our own nets for a cube that had three different size pieces. The picture that follows is just one of many ways to make this shape.
In my group we created three different nets that made the same end product. Which just illustrates that there are many different variations of how to draw net next for the same shape. I believe our professor wanted to see how many ways we could visualize the net because the one example was keep up at the front and we were to make the net with only looking at the shapes. This made the task harder and more of a challenge because we were using our imagination to make the shapes which didn't always work but in the end made what our nets all vary in ways.
As our professor illustrated its a good thing that in math there are many different ways to come to the final solution and nets are the same. So what are some strategies in finding nets?
- How I make them is starting with the the solid shape in front of you and trace that side that is on the paper. Following that you roll the shape across the paper and every time a face is flat on the paper trace it and only do ever face once. This will give you the shape as if you flattened it, then all that is needed is to add tab areas and you will have a working net.
- This can and will give many different net because you don't have to roll it the same way every time you start a net. An example of this is net number two below you can tell this because you can roll the shape up and makes the final cube.
- Some people just can just look at the 3D shape and see it flattened on a piece of paper.
- This will give the base as the center of your net and that makes it easier to build the shape.Most visualized nets will resemble net number one because you can see the sides are wings and the center makes up a four sided box.
These are the most common ways to make geometric nets without the use of technology. But since we are mathematician we like to think about how to optimize these nets and how can we find ways to make it easier, we are lazy and like using our technology. In my resent research I have found many web sites that will help and make shapes that you want nets for. Wolfram alpha has a nice set up for making 2D nets into 3D objects. But then there is always the math major's favorites of Geogbra, Sketch pad, and many other online resources.
I think that this is a very interesting topic that isn't covered very well in schools. I think that being able to take 3D shapes and turn them into 2D shapes and vise verse are very important ideas to help with students learning and understanding of geometry. It gives students hands on knowledge of how to make and build what they are have been learning about. I know that even in college I enjoyed the challenge of how to build what I saw in front of me. I think this activity is a good active that is needed more in schools because classrooms focus more on the abstract instead of hands on learning once students get into higher level math classes which is sad because there are many activities that can be done in high school math classes.