Five Educational Blogs

Five Blogs I am Following
http://coolcatteacher.blogspot.com/

http://www.speedofcreativity.org/ http://polkadottedteacher.blogspot.com/

http://www.thethinkingstick.com/

http://www.edpolicythoughts.com/

Attributes of Geometric Solids

In class we did an interactive group learning activity with geometric shapes. There were five different stations set up around the room and there were groups of 4-5 people at each station, the groups were randomly selected by our professor. The first station that my group went to had you cut out shapes and then fold the paper into a 3D geometric shape. There were only four different shapes at this station, a pyramid, cube, tetrahedron, and an octahedron. We used these 3D models to fill out notecards we were given before we began this activity. Each notecard asked you to draw a picture, state the number of vertices, faces, edges and then to name the shapes of the faces of each figure. Having the physical shape in your hand made it easier to see each vertice, edge, and face, thus making it easier to fill out our notecards. I liked this activity because I am a hands on learner so building the shapes brought a lot of excitement and interest for me in this one station. We also had a couple of stations that we used iPads for the given activities. I liked that there was technology incorporated into the learning as well as low-tech learning.

Another activity that really stood out to me in this group learning was a station that had nine shapes that we were supposed to match to the correct name. We were then given a packet to fill out the number of vertices, faces, edges, types of shapes in the faces and then we were to provide an example of where we would see it in real life. This was, again, something that appealed to my love for hands on learning, because we were able to grab the shapes, move them to make filling out the chart and seeing the shapes a lot easier for me. I also really liked that it had us think of where we would see these different shapes in real life. It really made me think and realize that some of the shapes that seemed unusual when I first saw them aren't really that unusual.
https://illuminations.nctm.org/activity.aspx?id=3521
I am a sophomore in college, and I feel that this is an awesome type of group learning activity for any grade or age group.

How Can We Make These Shapes Congruent? Symmetry!

I find symmetry to be an interesting subject to learn about, it may be simple, but I enjoy it. One type of symmetry is line symmetry, a figure has line symmetry if it divides a figure into two congruent halves. For those who may not know, congruent means the same thing as equal, but when doing geometry the word conguent is used instead. In class we practiced line symmetry with four regular polygons, a triangle, square, pentagon, and a hexagon. When I was first drawing the lines of symmetry in these shapes I thought that the triangle only had one line of symmetry and was a little surprised to find out there are three lines of symmetry. I realized that I failed to rotate my paper to see the other two lines of symmetry, but as soon as I did rotate the paper I understood why there were three lines sof symmetry in the regualr triangle.

Another symmetry that we learned about was rotational symmetry. A figure has rotational symmetry when it is rotated 0 degrees and 360 degrees the resulting figure coincides with the original. The number of times you get and identical figure when rotating the figure is called the order. For this we cut out a square, trappezoid, and a rhombus, then we were given a piece of paper and 3 brads (or paper fasteners if you don't know them as brads) to attach the shapes to the given paper so that you can still rotate them. This helped to show that a trapezoid does not have any rotational symmetry because when you rotate it there is no point in the rotation when it is symmetrical to the original position. The square had order 4 rotational symmetry, meaning that at 4 points of the rotation the figure is symmetrical to the original figure. The rhombus was order 2 in rotational symmetry, similarly to the square, this means that when rotating the rhombus there were two times in the rotation that the rhombus was symmetrical to the original figure.

https://www.mathsisfun.com/geometry/symmetry.html

The following two pictures are showing the activities that we did with the lesson.

Making Sense of Parallel Lines Transversal Lines and Angles

Geomettry hasn't ever been my strong suit when it comes to math. There are many times that the angles confuse me, but this week in our class things have begun to make more sense. There is still learning to come with the types of angles and what they are. I am still trying to memorize what angles will be correponding, alternate interior, alternate exterior, supplementary and so on. It is something that I need more practice with so that it will make more sense to me, but I am planning on putting in the work to do so.

It was nice in class on Thursday because we were able to practice naming the types of angles that were a part of the parallel lines with a transversal line through them. Corresponding angles are two angles that lay on the same side of the transversal but on is on the inside of the parallel lines and one is on the outside of them. Also with corresponding angles the angles will have the same measure. Alternate interior angles are angles that lie on opposite sides of the transversal, but both are inside the parallel lines, these angles will also have the same measure as each other. Alternate exterior angles lie on opposite sides of the transversal, but are outside of the parallel, these angles again will come out to have the same measure. Supplementary angles are two or more angles that will sum up to be 180 degrees.Vertical angles are two anlges whose sides form opposite rays. Same side interior angles lie on the same side of the transversal line between the two parallel lines, if you add these two angle measures together they will sum up to be 180 degrees.

https://www.shmoop.com/basic-geometry/parallel-lines-transversals.html

Polygons, Triangles, and Angles... Oh my!

Today in math class we were able to touch more on polygons and their different classifications. In our previous class (Thursday) we began our discussion of polygons with talking about Quadrilaterals and the different classifications that they fall under. One interesting thing that we talked about was how all squares are rectangles but not all rectangles are squares. This is a statement that people may not believe to be true. It is, in fact, a true statement and here is why: Squares and rectangles are both a part of the quadrilateral family. Each shape has different characteristics, however. Some of the characteristics of one shape are the same as another shape which causes some shapes to be both, for example, a square being a rectangle, but a rectangle cannot be a square. For a rectangle the characteristics for it are: 4 sides, 4 right angles, pairs of opposite sides are equal, and opposite sides are parallel. The characteristics for squares are: 4 equal sides, opposite sides are parallel, and 4 right angles. From looking at the lists of characteristics you can see the overlap that squares have in the rectangle category. To determine what a shape is it must fit every single one of the characteristics that I listed for you, so a square has all the same characteristics that a rectangle does, making it fit into the rectangle family. If you are to look at a rectangle and look at the list of characteristics for a square you will notice that it fits almost all the characteristics, except for having 4 equal sides, just this one thing does not allow rectangles to be squares. Poor rectangles…

Today's lesson focused on triangles which is another member of the polygon family. Triangles can be classified in two different categories, by their angles and by their sides. First, there are acute triangles, all of the angles in these triangles will be less than 90 degrees. Then there are right triangles which will have one right angle. The last classification according to the angle of the triangle is obtuse, which means there is one angle in the triangle that is greater than 90 degrees. There are also three different classifications for the sides of the triangle. The first is equilateral, which means all of the sides on the triangle are equal. The next is isosceles, this type of triangle has at least two sides that are equal in length. The final side classification is scalene which means that all the sides on the triangle are different lengths. To help with understanding of this we made a foldable that includes the different classifications for the triangles, their definitions, and also a picture to go along with each triangle. I'm exciteed to have this reference because this was such a good way to learn about triangles. 

https://www.mathsisfun.com/geometry/polygons.html

Protractor or Compass?

Yesterday in class we came in and were told that we were going to learn how to use a protractor. Initially I thought it was the tool that you put your pencil into in order to draw a circle, so I was of course confused as to why we were having a lesson on this because I thought there was no way drawing a circle could be that hard that it is necessary to have a lesson on how to use the tool to create it. I was a little shocked when our teacher pulled out the protractors and to my surprise, it was not the tool used to draw circles. It is the tool when turned to the side is looks like a capital D. It is used to measure or draw angles. Which is going to come in handy while learning geometry.

We then got a worksheet to practice using a protractor after being given a small instruction sheet on how to use a protractor. We learned that if you are two degrees above or two degress under the actual degree that the angle is, then your answer is still correct but anymore than that is going to be incorrect. Sometimes there are going to be angles that don't reach far enough for you to be able to measure the angle, so you can use a ruler to draw an extended line from the angle so that you can more accurately find the degree of the angle being measured. Below is the protractor and the instruction sheet on how to use the protractor.

https://www.mathsisfun.com/geometry/protractor-using.html

Theoretical vs. Experimental

In class we learned about theoretical probability vs. experimental probability. Theoretical probabilty is the probability of something happening under ideal conditions with no experiemnt occuring. For example, if you use coins, your outcomes are heads or tails, therefore making your theoretical probability of getting heads 1/2. Then with experimental probability it is calculated using observations from data. This means that if you took a coin and tossed it 20 times, you get 15 heads and 5 tails, what would the probability of getting heads be? I initially thought that nothing would change, but it does change because you use the data that you already have which is 15 heads out of 20 tosses and then you simplify that to get a probability of 3/4 of getting a heads on the next toss.

To help reinforce this idea we did an activity of playing rock-paper-scissors with a partner. The activity had us play 45 rounds of rock-paper-scissors in order to better see and understand how experimental probability. We were then instructed to write down our probability of winning ourselves, probability of our partner winning and the probability of us tying. The activity then asked us a series of questions about probability with rock-paper-scissors based off of the experiment that we performed. This was a good activity for me to do because it also compared the experimental probability to the theoretical probability so that I was able to actually see the differences between the two types of probability and how each one worked. I am going to attach some pictures of the activity that my partner and I filled out so that it is easier to see and understand what we were doing and understand why it was such a good learning tool for me. 

https://illuminations.nctm.org/adjustablespinner/