Geometry week 4

This week we learned about tiling. We learned that there is regular tiling which is using only one regular polygon to make 360 degrees at the vertex. There are also semi regular tiling- which is when it takes more than one regular polygon to create  360 degrees at the vertex.
There are only three regular polygons that fit into the category of regular tiling, those three shapes are triangles, squares and hexagons.
Here is an example of what Regular tiling looks like:

Here is what the difference looks like when the tiling is semi regular:


A good way to tell if it is it semi regular or regular, is semi regular requires more than one type of shape to make it fill up a blank page when repeating the shapes.

Geometry week 3

 We moved on from pyramids and prisms to cylinders and cones. Cones have a circular base and all the line segments meet at the apex. Cylinders on the other hand have two parallel curved bases and all line segments attach to the base. however, cones and cylinders can also be right or oblique just like pyramids and prisms depending on the angle in which the line segments meet the base.
Here is a picture of  standard cones, cylinders, pyramids and prisms just to refresh your memory and put some pictures to the descriptions:

This week was a frustrating one for me. I have a really hard time understanding translations, rotations, reflections and glide reflections. The definitions are as follows
Translation(aka slide) is the rigid motion in which all points of the plane are moved the same distance in the same direction.
Rotation(aka turn) is another basic rigid motion, one point of the plane called the turn center or center of rotation is held fixed, and the remaining points are turned about the center of rotation through the same number of degrees- the turn angle or angle of rotation.
Reflection(aka flip)is another basic rigid motion. The motion is determined by a line in the plane called the line of reflections or the mirror line.
Glide Reflection is the last basic rigid motion, this is a combination of a slide and a reflection. The line of reflection is called the glide mirror and it must be parallel to the direction of the slide. The slide is usually called a glide and its vector is called the glide vector or glide arrow.
The definitions sound like a bunch of mumbo jumbo but arent important to know so you have a geometry vocabulary and can refer to remember the differences in the movements. This aspect of geometry has always been the hardest for me but this youtube video helped a lot  because it applied it to real life when this information would be useful and gave me a picture in my head to think of when trying to remember what each term meant and I hope it does the same for you!
http://www.youtube.com/watch?v=dVtz55mIuz4

Geometry week 2

     Getting a little deeper this week into geometry terminology and concepts was a challenge for me. It is hard to remember which shapes fit into which categories, can a square be a rhombus? Can a rhombus be a rectangle? I found this family tree online which helps me remember the relationship between all the different types of quadrilaterals,and I figured I would share:

    This week we transitioned from quadrilaterals to polygons. We learned about regular polygons- which are polygons that have all sides equal and all interior angles equal, but an equilateral polygon- has all sides the same length, but it is not a regular polygon because its interior angles are not all the same. We also and learned how to measure the  sum of the interior angles  with the formula , (N-2)180, where N stands for the number of sides of the polygon when the polygon and then to find one single interior angle you use the formula then divide by N. The formula for finding one interior angle then looks like this, (N-2)180/N. We transitioned  from regular and irregular to learning about prisms and pyramids which also fall under the polygon category. It was nice to refresh my memory and although the book definitions were not fantastic having three dimensional shapes in class to give me a visual representation were really helpful. I believe this is something I would carry over into teaching in my own classroom, if I ever had to teach this subject.

   

Geometry Week 1

     When I was younger, I would always think, why am I learning this, even if I did not say it aloud. Geometry was one of the worst grades I received in high school, and it frustrated me more than anything. This first week in Math 252 I have gained some insight as to why it was so frustrating and have learned so much more of the material already. I believe I was so frustrated and confused because I could not see the images off the page, I did not know any real world applications for the new vocabulary I was being given. Geometry in itself has its own language and without understanding that vocabulary it makes learning concepts or having full understanding really difficult.

     This week we learned a new way to learn definitions which helps us try and apply them to every day life. I have learned how to make flash cards before, but not ones like this. This way of defining words is called Marzano's organizational Diagram. The card is split up into four sections with the word you are defining in the center. Each section has its own purpose, one for  a formal definition, one for your own definition, one for a visual representation, and one for a real world example.
    
     Some of the most useful real life applications where for things such as complementary angles- which are two angles that add up to 90 degrees and a good real life example or visual is a sandwich cut diagonally. I also liked the example for congruent- which is sides or segments having the exact same length, such as a piece of pizza or pie. This week taught me that geometry is all around us and by trying to find real life examples the material is much easier to comprehend and remember.