Algebraic expressions are very beneficial when it comes to solving real life problems. Of course most students do not see algebraic expressions as helpful and they won't until they are done with school. A classic example of when you will use such expressions is when it comes to your money. When you enter the working world you will want to know if you have received the right amount of money for the amount of work performed. Also, you will want to know how to balance your checkbook so that you do not over spend.

Below is a video on how to write algebraic expressions for real life situations.

The first thing you will want to do when writing any algebraic expression is to define the unknown.The unknown will become the variable you are trying to solve for. In most cases x is used for the variable, but you can use any letter you wish. A lot of the time people will use the first letter of what they are solving for as their variable. An example would be using w as the variable when solving for the number of workers at a ballpark

The second most important thing when writing an algebraic expression is highlighting key words. Key words are helpful in writing the final expression. Some examples of key words are more than.less than, or the sum of. Also, it is important to highlight what you are trying to solve for because this will become your variable. You will need to know what side of the equation your variable needs to be on, so that you get the correct answer you are trying to solve for.

Articles that I found helpful:

http://www.algebra-class.com/algebra-word-problems.html

http://www.mathgoodies.com/lessons/vol7/expressions.html

http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-140s.html

## Sunday, July 24, 2011

### Rational numbers ... What are they exactly??? Math 1510

It is sad that my class is coming to an end, but it has been a great help at teaching me how to be a good math teacher. Over the course of the class I was able to learn math, while also learning how to effectively teach it to elementary students. I am hoping to take what I have learned from this class and apply it to my daily math lessons. We did cover one more unit on rational numbers and so that it is what I am going to write about for my last blog.

When I first learned we were going to cover rational numbers I thought to myself, "do I even know what those are?" Being the detective I am, I immediately went online and looked up the definition. A rational number is any number (whole, decimal, or fraction) that can be expressed as a fraction with the denominator being anything except 0. The number 6 is a rational number because it can be written as 6/1, making it a fraction whose denominator does not equal 0.

I picked rational numbers to define and describe because I have been reading that it is one of the most difficult concepts for students to grasp. Since rational numbers are mostly written as fractions, students have a hard time performing operations because they cannot conceptualize what the numbers really mean. Too many teachers are just focusing on teaching their students the procedural steps in working with rational numbers, without giving a prior background knowledge of the basic concept. I am a classic example to this dilemma since I didn't even know that fractions were considered rational numbers. I think math classes need to have an introduction day for every new math lesson, so that teachers can go in depth and explain what students are going to be learning about. The second link posted below talks about problems students are having with rational numbers.

Articles on Rational Numbers

http://www.mathsisfun.com/rational-numbers.html

http://epcae.org/docs/Rational%20numbers_Sept%2020.pdf

When I first learned we were going to cover rational numbers I thought to myself, "do I even know what those are?" Being the detective I am, I immediately went online and looked up the definition. A rational number is any number (whole, decimal, or fraction) that can be expressed as a fraction with the denominator being anything except 0. The number 6 is a rational number because it can be written as 6/1, making it a fraction whose denominator does not equal 0.

I picked rational numbers to define and describe because I have been reading that it is one of the most difficult concepts for students to grasp. Since rational numbers are mostly written as fractions, students have a hard time performing operations because they cannot conceptualize what the numbers really mean. Too many teachers are just focusing on teaching their students the procedural steps in working with rational numbers, without giving a prior background knowledge of the basic concept. I am a classic example to this dilemma since I didn't even know that fractions were considered rational numbers. I think math classes need to have an introduction day for every new math lesson, so that teachers can go in depth and explain what students are going to be learning about. The second link posted below talks about problems students are having with rational numbers.

Articles on Rational Numbers

http://www.mathsisfun.com/rational-numbers.html

http://epcae.org/docs/Rational%20numbers_Sept%2020.pdf

## Thursday, July 21, 2011

### Algeblocks are the wave of the future! Math 1510

This week I was introduced to algeblocks. Algeblocks are a visual representation of integers, polynomials, and unknown variables. It is an effective way to teach algebra to really bright students and students who struggle. The main purposes of these blocks are to help students physically see the problem they are trying to solve and to manipulate the answer with their hands.

Algeblocks come in three different colors: orange, yellow, and green. Each color represents a different quantity and is placed on a special mat. The mat used with algeblocks is a plain piece of paper split in half with one side being positive and the other negative. Then when you have an equation you must set the right number of blocks on the side of the mat it belongs. So if you are solving -2+1, you would want to stick two blocks on the negative side of the mat and one block on the positive side. Then you will need to use a technique called “making zero” to attain your answer. To “make zero” you must pair blocks from both sides of the mat together to cancel each other out. When you can’t pair any more blocks together then you are done. The video below is a great example of how to use algeblocks since it is understood best when viewed.

I think algeblocks are a brilliant idea. When I was a student first learning algebra, I always had problems with understanding equations. I think if I would have had blocks to manipulate the answers I would have had a better understanding about unknown variables. This method is especially effective for students who are struggling in math because they can physically see where they are messing up if they get the wrong answer. I do believe this method should be taught during early algebra years, so students are familiar with algeblocks all throughout school.

Article from class

Algeblocks breakdown

http://205.174.118.254/resources/math4MomandDad/HS_Algebra/equations.pdfhttp://www.etacuisenaire.com/algeblocks/algeblocks_resources.jsp

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