Math for Elementary Teachers Class Overview

Over the semester, my Math for Elementary Teachers class at MCC has taught me a lot of useful information. I am eager to apply some of the teaching techniques that I have learned. Math has always been my favorite subject, but this class put a fun and interactive twist on the subject.

One of the main focuses in the class was to bring the use of technology into the classroom. At first, I wasn't really sure how this could be accomplished with math, besides using calculators. Three out of our four learning projects required us to use technology to create our project. One of our learning projects was to make a digital map/web of a unit we were covering in class. We also had to create a digital presentation of a certain topic that we were going over in class. The third learning project, was to create a blog, which I have done here. These projects not only let us share our work with other people, but also made us experts on the topics we covered in our project.

The other main focus in the class was to create more hands-on activities to teach lessons. All of our books came with manipulative kits. The manipulatives made the lessons much more fun and is definitely a teaching technique that I hope to someday bring into my own classroom. Our fourth learning project was to create or find an activity in the book and then demonstrate and work it out with the class. The manipulatives were a very useful, and a lot of people incorporated them into their presentations. I found a website where you can go and print off your own manipulatives.

Overall, this class was very useful and helpful. It teaches you how to teach math in different and interactive ways. If you haven't taken this class and plan on going into Education, I would recommend taking it at MCC with Maria Andersen.

Volume

The number of units to fill its container is called its volume. For our Geometry Formulas Gateway, we had to know how to find the volume of a prism, cylinder, pyramid, cone, and sphere. The easiest way to find the volume of these figures, is to just memorize their formulas. Hopefully, this blog will help with learning how to find volume.

Finding the volume for rectangular prisms, such as the two examples below, can be found by simply multiplying the dimensions of their length, width, and height.

The volume of any prism can be found in a similar way compared to that of finding the volume of a rectangular prism. You have to find the area of the base first, and then multiply it by its height. I made up an example, which is shown below.

The formula for finding the volume of a cylinder is the same as that of finding the volume of a prism. This problem also takes a couple of steps. First, you have to use the area of a circle formula to find the area of the base. Then, you multiply that answer by its height. There is an example to explain this better, that I made below.

The formula for finding the volume of a pyramid is similar to finding that of a prism and cylinder. You multiply the area of the base by its height just like the formula for the volume of a prism and cylinder. Then, you have to multiply by 1/3. This type of problem also consists of multiple steps. I made another example, below.

The formula for calculating the volume of a cone is the same as that of a pyramid. You have to use the area formula of a circle to calculate the area of the base. Then you just simply multiply that by its height and 1/3.

All that is needed to calculate the volume of a sphere is the sphere's radius. Then, you just plug in the sphere's radius in the formula. I made up another example problem below.

Hopefully, this post helped with how to find volume. It's easiest if you just memorize the formulas for each figure, but they are all kind of similar. I found a website that also might be useful that covers the same information I just went over.

Area

Today, we took our Geometry Formulas Gateway. When I was studying for it before class, it seemed a little overwhelming to try and memorize all of the formulas. Most of the time, I found it easier to break up a figure into several parts to try and calculate its area or volume. Personally, I think it is easy to find the perimeter of a figure. All that you need to do is add up the lengths of each side. The perimeter of a circle, however, is just finding the circumference.

Finding the area of a rectangle and square are easy. All you have to do is multiply length and width to get the area. Calculating the area of a parallelogram is easy to understand when it is broken up. The picture below explains the process.

A trapezoid is a little different. An easier way to look at finding the area is duplicating the trapezoid and then rotating it to make a parallelogram as the picture shows below. Since you only need the area of one trapezoid, you multiply the area of the parallelogram that you formed by 1/2 to give you the area of just one.

Finding the area of a triangle can be easier understood if you duplicate it and then fit it together with the other to form a parallelogram. It is basically the same concept used to find the area of a trapezoid as discussed above. If you are trying to find the area of a right triangle, duplicating it and then fitting it together with the other will form a rectangle.

The easiest way to find the area of a circle is to just memorize the formula.

I found a website that goes over area formulas that may also be of some help.

Triangles and Quadrilaterals

There are certain triangles and quadrilaterals that occur often enough to be given special names. Sometimes I get some of the terminology confused, so I thought I could dedicate one of my posts to explaining what each of them mean.

Let's first start with triangles (three-sided polygons). An acute triangle is when all three angles within the triangle are acute (less than 90 degrees, but more than 0). A right triangle contains one right angle (90 degrees). An equilateral triangle is a triangle that has all three sides of equal length. A scalene triangle is a triangle that has three sides of different length. An isosceles triangle has at least two sides of equal length. Lastly, an obtuse triangle has one angle that is obtuse (greater than 90 degrees, but less than 180 degrees).

Now, I am going to go over quadrilaterals (four-sided polygons). A trapezoid has exactly one pair of opposite sides that are parallel. An isosceles trapezoid is a trapezoid in which its non-parallel sides are congruent. A rhombus has opposite sides that are parallel and all sides have equal length. A parallelogram has pairs of opposite sides that are parallel and of equal length. A rectangle has pairs of opposite sides that are parallel and of equal length, and contains all right angles. Lastly, a square has all sides of equal length and contains all right angles.

Hopefully, this helped a little bit with trying to figure out what makes each of them different from each other. I also found a game that relates to triangles and quadrilaterals.

Measurement

Yesterday, in my math class, we went over measurement. The overall consensus of the class is that the metric system is way easier to work with. The units with the English system are so much harder to remember if you don't use it on a regular basis. The metric system has common increments and prefixes that are universal for length, volume, and mass. Most people find it easier to work with decimals over fractions and the metric system uses decimals while the English system uses fractions.

We also worked on converting to different units in class. I remember learning how to do conversions a long time ago, but I felt like it was a good refresher and I caught on to it much quicker. There was a website that I found that was helpful with showing what to multiply by to convert between the metric and English systems of measurement.

Polyhedra

Yesterday, in my Math for Elementary Teachers class, there was a presentation on polyhedra. We were given five different Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) and were asked to find the vertices, faces, and edges of each. Then, our assignment was to make paper models for other polyhedral figures. It turned out to be much more time consuming than I anticipated. It reminded me of paper origami. I chose to construct a pentagonale hexacontahedron, which turned out to look like a disco ball. I also made a compound of cube and octahedron, which looked like a cube with pyramids coming out of the sides. It would definitely be a good hands-on activity to do with both elementary and middle school students. You would have to choose more difficult ones for middle school students, of course. There is a websitewhere you can go and print off paper models to make your own polyhedra. I also found a neat website where you can click on different kinds of polyhedra and see them 3D.