![IMG_1631.JPG](https://steemitimages.com/DQmcUTVYgVi6g9afnTV11B4vhVNCwnL1AMRiLpNTmsngNwi/IMG_1631.JPG)

I have been teaching math for a couple of months and I've learned that teaching is hard work!  I have had the benefit of loving math and enjoying new intellectual challenges. 

What happens when a child has no interest in math?  You end up having to make things really fun. The lesson becomes an excercise in finding what the student enjoys and building a bridge between that passion and some mathematical concept.  

I had the added challenge of being in classrooms that were next door to students who were testing all day and needed a silent environment.  

The best I could do was create math lessons on folding paper.  Folding paper is pretty silent, and you end up with a tactile result and the pride of procuding something in the class hour. 

![IMG_1630.PNG](https://steemitimages.com/DQmUE1cq9W5hvMCPnHzAA57ptQEFEeN9JGBYRhhCYrUV6iC/IMG_1630.PNG)

<a href="https://www.amazon.com/Origami-Design-Secrets-Mathematical-Methods/dp/1568814364">Origami Design Secrets by Robert Lang</a>

Everything starts with a book I have called ORIGAMI DESIGN SECRETS by Robert Lang.  Lang is a retired physicist that has used his passion for origami to design foldable satellites and extended his expertise to design perfect folds vehicle airbags. He has gone full time with origami and his Origami Secrets is jam packed with lots of difficult designs. But their complexity is only achievable with the mathematical toolset he's developed.  Mapping vectors, vertexes and edges to mountain and valley folds allows him to design origami moose, detailed scorpions and cuckoo clocks. 

I took his method and applyed it to analyze paper airplane folds.  

https://youtu.be/WK5CPJhx9tU

Any paper airplane when it is unfolded presents a barely visible fingerprint that hints at the heart of the design that allows it to fly.  

https://youtu.be/IDxSoOxJTuo

First unfold a paper airplane.  

https://youtu.be/8VlA4yStMjk

Everytime a fold crosses another fold or touches the edge of the paper make a dot.  

https://youtu.be/DRsPOtrzjYM

Outline each fold and connect the dots between vertices. 

https://youtu.be/q2WfFnR-hgA

Label each dot with a letter. 

https://youtu.be/Q-wQQpBGIRg

![IMG_1624.JPG](https://steemitimages.com/DQmfXkurxUnsiz7fxmkHpizJHEdNGAnqUmRRfc5GWSUkGpz/IMG_1624.JPG)

These dots are your vertices and the lines between dots are your edges. The number of vertices one edge (one hop) away from a vertex is called the degree. 

![IMG_1625.JPG](https://steemitimages.com/DQmVYnvNhPFHothpf1j4mZztNubCkEapTdzFcY2DfHuJi9q/IMG_1625.JPG)

I could make a table mapping every connection, or I could use a matrix to store this imformation.  

The rows will store the names of vertices and the columns will have the names of edges.  If an edge touches a vertex, I enter a 1. If there is no connection between the edge and vertex in question I write a 0. 

From here you get into more detail on graphs, tree graphs, or even how to use matrices to solve linear systems.  

![IMG_1629.JPG](https://steemitimages.com/DQmd2FpHNDeSeg48WyVjhpqRQuQzHcg8jzMbt8xz1TzANdz/IMG_1629.JPG)

![IMG_1628.JPG](https://steemitimages.com/DQma2UTKp7K8hXgWjYNJSKDtKNLSFBXiXBAZ4VKX71hndgb/IMG_1628.JPG)