Tuesday, April 10, 2018

Parallel Lines Cut by a Transversal

I have always had a problem with remembering the proper terminology in math. Especially when it comes to the angles made by parallel lines and a transversal line. In class, we were given a few handouts that we put in our notebooks and they help you to define all the angles. I don't remember receiving any type of handouts in elementary school regarding transversal lines. A color-coded, easy-to-read, diagram that we could keep in our notebooks would have been extremely helpful when I initially learned this. Below I have attached a photo of the diagram from my notebook. I coordinated the colors with my definitions so they would be easy to identify.
If a transversal line cuts through a set of parallel lines, then the pairs of corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent as well. Of course, none of this makes sense without knowing the proper definitions.
A transversal line is a line that intersects two or more lines at different points.
Corresponding Angles are two angles that lie on the same side of the transversal in corresponding positions on different lines.
Alternate Interior Angles are angles that lie on opposite sides of the transversal inside the parallel lines.
Alternate Exterior Angles lie on opposite sides of the transversal outside the parallel lines.
Vertical Angles are two angles whose sides form opposite rays.
Consecutive Interior Angles or Same Side Interior Angles are angles that lie on the same side of the transversal between two lines. ** These two angles add up to 180° **
Same Side Exterior Angles are angles that are on the same side and they add up to 180°.
Supplementary Angles are two or more angles that add up to 180°. 
The sum of two Complementary Angles is 90°.

Monday, April 9, 2018

Gumdrop Polyhedrons

The last station I visited during my last math class was station 2. This station was by far the most fun and it was the quickest. We had to make the polyhedrons we had identified at previous stations out of gumdrops and toothpicks. The shape I decided on was a triangular prism. A triangular prism is a five faced shape composed of two triangle bases and three rectangular sides. It also has six vertices, nine edges and is the basic shape of a roof. If and when I do this activity in class, I would give them a sheet for each polyhedron they needed to create and they would need to list three real life objects similar to a sheet we did in a previous station.
I used nine gumdrops and twelve toothpicks to make my triangular prism. If I used six gumdrops and nine toothpicks, I would have a pyramid so it is important to remember that a rectangle means the shape is longer. This is another hands-on activity that would allow the student to physically manipulate the shape and see the vertices and edges. I really enjoyed this station because you got to eat the gumdrops after you were done. Below is a photo of my rectangular Prism

Saturday, April 7, 2018

Polyhedron Foldables

During our last class period, we got to do several activities. The first station I went to was station 3 and it had four different unfolded shapes that we had to cut out, fold and identify on fact sheets. Now, this activity can be very challenging if you have difficulty thinking spatially. I am fortunately pretty good at thinking that way, so the cube I had was easy to make. The octahedron was by far the hardest one because we didn't really understand what three-dimensional shape it was supposed to become. I really enjoyed this activity because it's hands-on and you get to build something.
Being able to hold the shape in your hands really helps with keeping track of the vertices and edges especially when it is a shape bigger than an octahedron. I know that I had a hard time working at station 1 with ipads because it had two shapes bigger than an octahedron and it was really hard to try and figure out how many vertices and edges they had since it wasn't tangible. Below are the classifications for each three-dimensional shape.

A cube is composed of six square faces, eight vertices, and twelve edges.
A Pyramid has one square face as the base and four triangle faces, five vertices, and five edges.
A Tetrahedron consists of four triangle faces, four vertices, and six edges.
An octahedron is made up of eight triangular faces, twelve edges, and six vertices.