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