Stay in Shape! Convex and Concave Polygons!

            We are coming to the end of our math trek and I feel that I have learned a lot through both of the math classes I have taken over this summer. The only thing that I would change would be that we could meet together face to face. I know their faces from the pictures I see, and I know that we will all finish the trek together and that makes me very happy. We are on our way to becoming Elementary educators. We have to make sure that we stay in shape ourselves learning new methods of teaching and also knowing what we struggle with most. Most of all we need to work together so that all of our students finish the trek strong.

On the math Trek we need to stay in good shape by knowing what content will be coming so that we can keep moving forward and making progress on our trek! We have to make sure that all of our students are doing their exercises or they will get out of shape on the math trek and then fall behind.  

Today we are going to be covering more terminology and we need to know the names and facts about differing shapes in math. We are going to be learning about concave and convex polygons. I will start off my giving the definitions of both.

Convex: polygon that has all interior angles less than 180°
(Result: All the vertices point 'outwards', away from the center.)

Concave: A polygon that has one or more interior angles greater than 180°
(Result: some vertices point 'inwards', towards the the center.)

When you feel that you have a firm grasp on convex and concave polygons please try this fun game!

I hope that you have enjoyed my posts and that I have helped you on your math trek! Math is challenging, but it can also be very fun! We just have to help each other along the way, and help our students succeed and finish strong so that they can successfully make the trek of life!

Let's Talk Polygons!

One of the hardest things that I struggle with along the trek is the basics of running the trek. What pace to set for myself, and what to focus more on than other things so that I can run the race efficiently without slowing down or even stopping along the way. I find myself tripping over roots in my path and I wonder where these roots come from. Some of the biggest roots that trip me up are terminology. I struggle with knowing which terminology goes with which shape. Do I have it backwards or am I correct? There is a lot of terminology used on our math trek and I want to make sure that we all have

That being said the lesson on polygons got my mind racing again, because really the last time I had any education on polygons (except for this class) was many, many years ago. This is why I want to focus on some polygons, and convex and concave polygons for my next two posts.

             Now let’s start off by giving the definition of a polygon and some examples to show you what I am talking about.

 A polygon is- A plane shape (two-dimensional) with straight sides.

 Here is a picture of some regular polygons:

         Here is some pictures of shapes that are not polygons and some that are. We call these Non valid, and valid polygons. 

         There are many different polygon! Take a look at Math is Fun for more information on polygons. Also take some time to watch the video below if you are still struggling.

        After you have watched the video take a peek at this song. Songs always help me remember information better and it is always nice to have a song in your head to help you along the trek!

     When you feel that you have a good grasp of what a polygon is as well as what they are called please try out this fun game! I hope this helps you along the trek and I will be back again soon to review convex and concave polygons! Have fun on the trek and if you are struggling never be afraid to ask for help!

Place Values with Decimals!

As we continue the trek we all know that we need certain pieces of equipment to finish the trek. We could try and run the race with just socks on, but we would not be able to go on some of the paths even if we wanted to and the trek would get more and more painful and frustrating. We need another piece of equipment to make it further into the trek. Just as we need pieces of equipment to make it along the trek we need many pieces of knowledge in math to learn how to solve problems. As the problems get harder we need to add more knowledge (or equipment) along the way and build on previous knowledge so that students can finish the trek with minimal strain and frustration. How will you equip your students? Who knows we just might have a photo finish at the end of the trek where we need to use tenths, hundredths, or even hundredths of a second!

Last time we talked about place values. Today we are going to talk about place values with decimals. I am going to include some of the place values that we learned about before and then add a decimal into the number.

When you have a decimal in the number you know that you have a value on the right side of the decimal that is less than one but larger than zero.  Also note that we do not have a ones place on the right side of the decimal. The first place value on the right hand side of the decimal is called the Tenths place. The second place value right of the decimal is the Hundredths place. Then we have the Thousandths and Ten Thousandths places for the third and fourth place values on the right hand side of the decimal point. Take a peek that the chart below. When you watch the Olympics this summer you will see a lot of these numbers!

If you are still having problems with place values with a decimal please view the video below and then go here for more information.

 

Once you think that you have built onto your previous knowledge of place values and are proficient with place values with decimals try this fun Pirate Game! Have fun and I will see you all on the Math Trek!

What place will you finish in?

            As I continue my trek I think abut the lessons in the past and about what place I will finish in this trek that we are all running. Does the place that we finish in really matter? Is this trek a competition or is it a trek that we all learn from? Some of us will take one path and some will take another, but if we all end up at the same place at the same time that would be the best finish ever! That is the struggle with the Math trek and basically our trek as future teachers. We have to make sure and do our best to lead and help our students on their trek of learning, understanding and hopefully mastering of the content. What place will you finish in? I hope to be running all over helping everyone no matter where they are in their trek!

            You may or may not care what place you are in, but in math place value is very important! The first number is called the ones place, the next is the tens place, next is the hundreds place and then comes the thousands place. Take a peek at this picture; it will help you understand what I am talking about. The numbers in these different places gives the number its value.

          There is also a song below that will help you understand place values that are larger than the place values shown in the picture above. Listen to this song and sing along with your parents. If you still do not feel comfortable with your place values go take a look at the place value tutorial.

When you feel confident in your place value skills go here and try a fun game! Next time we will be talking about place values when we are working with decimals!

Prime and Composite Numbers

As I continue my trek I am a bit daunted by the mass amounts of information that is being thrown at me. As I go on I need to take this trek one step at a time. Sometimes I try to run when I need to jog and at other times I need to walk instead of jog. I need some form of math gator aid or some nice cold water. That drink comes in the form of guidance from my brother in law who is a middle school math teacher. When I am tired and sweaty and I cannot stand my high heels anymore I call him when I am about to fall. He won’t let me give up and I am so close to the finish line! As we take this trek we need to make sure that we have an energy source, someone that is there for us to rejuvenate us and help keep our spirits up. This is what we need to keep in mind when we are teachers. We need to be there for our students we need to be the proverbial drink of cold water and make this trek less painful and daunting. We need to be our student’s biggest fans; we need to cheer them on!

As I went though these chapters I found myself being slowed down to a crawl with all of the information so this is why I wanted to focus on Prime and Composite Numbers. If we can fully understand this we can move onto more complex activities such as prime factorization, Greatest common factor, and least common multiple.

Let’s start by defining prime and composite number;

Prime Number:  can be divided evenly only by 1 or itself, and it must be a whole number greater than 1.

Composite Number: can be divided evenly by numbers other than 1 or itself.

Remember: The number 1 is not a prime number and it is not a composite number!

                              

Watch this video and then take a peek at the Composite number list and then the Prime number list. Then head to AAA Math and do some practice problems and see how well you can do with finding prime and composite numbers.

After you have mastered this take a peek and my fellow Trekkers blog on factorization!

Starting the Trek: Math History

As we start off this trek I feel like I am wearing the wrong type of shoes. My toes are being crunched forward and I feel as if I am going to fall and twist my ankle with every step. With each movement forward I feel a new type of pain, a pain that is somehow very familiar. I look down at my purple toes sticking out of the 6” high heel stilettos that I am wearing as the other trekkers walk, jog, or sprint past me. “How am I going to make it to the end of this trek?” I ask myself. I look back and there are a few people there with me and there are a few more just ahead of me. I could slow down or speed up and see if we can help each other. “How can we help each other to make it to the end of this trek?”

I dig into my math again and open my book. “Oh man, not ancient calculating methods again!” I push past my initial frustration and start with Roman numerals. As I trudge on I feel as if my stiletto's have lost an inch or two and the shooting pains in my toes and ankles are somewhat reduced. “I know how to get out of these shoes!” I read on and as I do my high heels turn into flats and I begin to move more quickly. I look back and leave some of my fellow classmates far behind. I wonder what will become of them, and if I was a proper person I would slow down or even stop to make sure that they are able to finish the treck with minimal pain and torment.   

As I went through this chapter I struggled every time I was encountered a problem using the Babylonian system as well as a few others. I became even more frustrated when I began to think of when I was going to use any of this information again. As I continued I felt the inches on my heels growing again. Being a past history major I can see the value in these systems even if it was not apparent at my initial frustration. We have to know where we came from to help us see where we are going. By learning these other methods I have come to appreciate our methods more as well as see how math has both transformed and stayed the same throughout history as well how it shapes our world today.

Here are a few links that may help in your struggles with math calculations from other cultures as well as give you some history behind the math.

http://www.math.wichita.edu/history/topics/num-sys.html

http://egypt.mrdonn.org/math.html