Objectives
The purpose of this unit is to supple students with the basic tools and ideas they will need to begin their study of linear equations. I will help students go from simple to more complex problems by having them recognize the similarities and differences between problems. I believe that once a student can recognize and categorize the given problems, then will they feel confident enough to attempt to solve theses and the more complex problems we will study in the latter part of the year. This is just another way of saying we are going to categorize or group problems. It is important for students to recognize what "red flags" there are in each problem that categorizes a problem as such, by identifying the subtle differences or similarities. This is a good exercise for students of any age. I benefit from the idea of having to categorize problems because I am forced to stop and think about the problem. Then I think about what I am trying to accomplish before I even begin. I hope to get my students to stop and think about the problem and the process. This will hopefully lead them to a better understanding of math, as well as more success at solving word problems.
We have all met the student who looks at a problem and instantly determines he/she either can or can not do the problem - end of story! There is not much thought or questioning in this response - it is a knee jerk reaction to the problem. This reaction happens more in mathematics than in other classes. If a student is asked a question in a history class and they do not know the answer, their first reaction is to go back in the book and look for the answer. The same is true in literature and world language classes. In math students have a very different response. They determine that they can or can not do the problem. That is it. There is no going back in the book to look for the answer. I can sympathize with this issue as many math texts are poorly written. I am a math teacher, and I have a hard time finding different examples of problems I am discussing in the poorly organized book. I am hoping to change that for my student. This unit is designed to help my students recognize various problems and use several different tools to derive at an answer that makes sense. In addition, I hope to add some fun to their math experience.
It is fun to do things that you are good at and you only get good at something by doing it. If my students find success with word problems from the beginning they will be more inclined to attempt them, thereby strengthening their skills. Success breeds success.
I will be presenting three types of problems and each could be solved several different ways. Applying variables, using substitution to eliminate one of the variables, combining variables, solving for one variable and plugging it into one of the equations to solve for the other variable, are several methods that we will work our way towards. The students will find this sm"rgåsbord of options for solving confusing at first, so I will be introducing a less abstract way of looking at the information first and then progress to these method.
My target students are freshman, ages 13 to 14. They will be coming from various feeder schools with a wide range of skill levels. It is unwise of me to assume that they have a solid understanding of linear equations. I have found that it is worth my time to check skill levels early and often. I spend the beginning of every school year going over the basic skills needed to move on in the Algebra 1 class. This lesson is designed to be used at the beginning of my Algebra 1 class, the first week/weeks of class. I hope to build a solid foundation for students for their present and future math classes. Students are really learning a new language, the language of mathematics. There are many different dialects and different ways to say or ask the same question. I can not expect my students to answer a question if they do not understand what I am asking them. For this reason, I will spend time on language and math jargon. For example, I want my students to know that "increased by" and "more than" are just different ways of saying add and that when someone says double they are just multiplying by two.
After clarifying the language we will be using, I will then focus on another valuable tool for beginning word problems and that is sketching a picture of the problem. This simplistic visual image of the problem will enable my students to organize the information of the problem better in their minds. Drawing a simple line can enhance their comprehension level immensely. It is amazing what a line can represent. I will demonstrate problems when a line represents a log cut into sections or that same line can represent the amount of apples and oranges in a box. The use of this visual will be helpful in understanding, writing, and solving the equations.
I also plan on teaching the students to use "mental math" as a tool. Instead of concentrating on the actual numbers in the problems, which may be confusing, I sometimes simplify the numbers so I can do the math in my head. This trick helps me check if I am headed in the right direction because I can easily figure out if my answer makes sense. I have a few other tricks up my sleeve which I will go into more detail later. However, the whole point of this unit is to give students the tools, the confidence and the success needed to become life long learners. Like I said before, success breeds success.
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