Number Theory Rules......What??

 When I first heard of the number theory rules I was AMAZED!! I could not believe I was not taught this in school. Now I have the pleasure of teaching sixth graders these rules to help make math easier for them. Tricks that help math become easier is awesome. Like the nines trick on your fingers.....genius, and now the number theory rules.





Although the number theory rules don't give an exact answer they do help make math work less time consuming. In school I hated playing around with numbers to figure out if a certain number can divide into another number. Now I have a way to do that quicker. 

Learning these number rules takes practice. Students should not be overwhelmed with rules. A couple rules at a time per day might help, and then practicing those rules with games and visual aids. The following site has a fun game that practices putting the rules to the test.
Divisibility Games

 I look forward to more rules and tricks to help make math less time consuming for everyone.

Memorization of Place Value

Place value I personally think it is quite easy for me. In all honesty I think it is all about memorization, and that is my strong suit. Going through school I don't recall having a big lesson on place value. Once place value is learned I think games are a fun way to keep students on top of their knowledge related to place value. A site that has fun games related to place value that I found entertaining is; Place Value Games.   

Since this topic isn't really that fun it can be made more exciting. I love making songs out of something that I need to memorize. The song below is catchy and may help students memorize the ones, tens, and hundreds place.
Ones, Tens, Hundreds Song

Visual aids such as blocks helped me in school understand place value a bit more. Also money is helped out as well. Ten pennies turn into one dime worth ten cents. Ten dimes are worth one hundred cents. When students see that place value can help them in their future they might be more willing to want to learn the concept. For a good tutorial on place value watch the following video.
Place Value Video 

When you get into standard form and expanded form that is when the teaching gets a little more difficult for students to understand. When students get understanding of that it goes a lot more smoother.

Negative Integers

I feel that negative integers are confusing for many people. As a teacher I am sure it is hard to introduce the topic after years of teaching students positive integers. 

I would say the best way to introduce negative integers would be to use a number line. Students that use a number line are able to actually count down or up and see the negative numbers.I have heard that using chips of different colors to signify positive and negative numbers help out as visual aids. When I become a teacher I hope to introduce negative integers by using these visual aids below.

 Knowing how to add and subtract integers correctly involves knowing the following rules from the site Math is Fun. The site explains a great way to introduce negative integers as well as how to add and subtract positive and negative integers.

	Rule		Example
	Two like signs become a positive sign	+(+)	3+(+2) = 3 + 2 = 5
		−(−)	6−(−3) = 6 + 3 = 9
	Two unlike signs become a negative sign	+(−)	7+(−2) = 7 − 2 = 5
		−(+)	8−(+2) = 8 − 2 = 6

I don't know if there is any right way to add or subtract integers but I have learned an odd way to subtract negative integers. For example if someone asks what is -9 - 3, I just add them and then put a negative sign on the front. The only problem with the way I do it is it is hard to explain why to someone who might be learning how to add or subtract negative integers. After time and examples it is quite easy to master.

Problem Solving

In school I HATED word problems. I thought they were time consuming. I hated taking the time to read it, then go back and read it again and slowly figure it out. Many times I found myself guessing the answer because I was lazy. Now that I have grown up a bit, and I work in a school, I love problem solving. I personally think it is challenging and fun. As I help other students do word problems I see the same mind set in them that I once had in school. They hate taking the time to actually figure out how to do the problem. I feel like it is my job in school to help them figure out a way to make solving the word problems worth the time and effort. Also making it fun to solve.

What I have learned from problem solving is that it is a lot easier to work the problem out hands on. I describe it  by saying make the problem come ALIVE. I have learned to break up the problem into pieces and put the pieces together while solving it. I tell the students I work with to use a highlighter when first reading the problem and highlight the most important parts of the problem. I prefer to use visual aids to work through the problem. I think that is what is most helpful. If a problem is talking about people draw the people out. If the problem is talking about groups of different items draw the items or find something around you to sub for the groups like markers, pencils, or even game pieces.

The girl I work with now has trouble with math. I constantly get at her about making the word problems come alive. Even making non-word problems come alive works too. She seems to figure it out so much better. I love seeing a child work through a problem and watching that light bulb come on.

Although my method for problem solving is still a bit time consuming. I feel like the more a person does word problems with highlighting, using visuals, and making the problem come alive, the more a person will soon not have to do it hands on, and most likely they will be able to do it in their heads. I feel that word problems that relate to a child's life is more relevant and meaningful. A site I found helpful with the skills to problem solving is below.

Problem solving skills

Estimation.....What's the point??

Growing up, when thinking about the term estimation I thought, "what's the point?" I mean we spent years and years figuring out how to get the exact answers to problems and now we are required to learn estimation skills, which is just close to the right answer! I would also wonder why we don't just use estimation skills for everything instead of doing all the work to find the right answer. My thoughts have changed since then. :)

As I think about everything that I do during the day that relates to estimation, the list is long! I woke up looked out the window and thought to myself its probably 8:00 am so I should probably wake up. By the way it was 7:52 am. I then started making my shake for breakfast which needed a tablespoon of cocoa and a teaspoon of lemon juice. I don't know about you but I hate dirtying dishes when I don't have to, so I just ESTIMATED. By the way I don't know how close I was to the right amount but it did taste good. I am also decorating my house and need to go to the store today and buy two shelves, both about six feet, then I thought to myself, I better measure before hand or it will look dumb. But before I get those shelves I need to make sure that they will fit on the wall above my bed and end tables. That is where my theory of "what's the point" comes along. Although estimation may be easier to do, its not always going to work. A lot of times we need the EXACT answer. My list could go on an on about everything that I have estimated today.

So now the question is how do you teach estimation? I really don't think that their is any perfect way to teach estimation. I mean growing up I don't recall any certain method to estimate. I do remember estimating length though. I feel like that was the first for me was learning from measurements. I work with a student at the school I work at with his estimation skills as well. I was told to first work with him on measurement. I see that as a benefit for two key reasons. Number one measurement is a huge part of our everyday lives, at least that's what I think. Number two is measurement is very much visualization. I know what a ruler looks like, which leads to me KNOWING about what an estimate is for a foot. I know that my thumb is about an inch. Little ideas like these stick in your brain and help you with estimation. Other ideas help as well, like when the sun is straight above you, it is probably around Noon. While reading and article called, "Estimation," by Robert J. Doman Jr. I could understand how you should start teaching a student estimation with adding and subtraction through rounding. That is a probably the best way I could estimate. On the other hand he gave an example of 298 + 403. Saying that 298 is 2 less than 300 and 403 is three more than 400, so you should be able to estimate knowing that information. Students can certainly do that but I feel like that is way to many steps.

When I am a teacher I hope to make estimation fun for all the students. maybe have a candy jar filled with  something and they must estimate the number in the jar. Or even estimate the length of something without measuring. I also found this website that I found pretty fun. I played an estimation game with multiplication, and I did horrible. I can not estimate very fast. If I did it enough I think I would be great at it. I will definitely be using this site in the classroom.

Math is FUN!

How do you memorize everything??

What is your username and password for your email, Facebook, bank accounts, school login, or even your answers to your security questions? What was your locker combination for school, as well as your locker for gym or extra curricular activities? What number stands for pi? Whats the formula for volume, area, or circumference? Need I say more?

 In today's world it is RIDICULOUS how much you need to remember to get through your day. It's almost impossible to remember all your usernames and passwords without some kind of cheat sheet with them all written down. But what about in school, having to remember multiple mathematical formulas to solve equations. Rarely do teachers pass out cheat sheets with formulas already written down for tests. Students are expected to remember a lot, and I mean A LOT of formulas throughout school. I don't understand how it is possible.

Many people including myself would probably say that students should just have to memorize essential formulas that are used in our daily lives, but who determines which formulas are essential to know, or which ones are more important?

In my math class that I am currently taking we are learning to not so much memorize formulas, but to understand why we would use a certain formula and how it works. Doing that helps to understand and REMEMBER the formula needed. But in reality they still need to be memorized then, and that is extremely difficult, unless your a genius or something. So the questions stands how is one supposed to memorized everything?

More thoughts go to the following link. Memorizing Formulas