Objective
The unit that I have written is based on developing and using word problems in the classroom to satisfy an important objective in the North Carolina curriculum. I teach seventh grade mathematics in an urban district, Charlotte Mecklenburg Schools. The district itself is large and within the district there are 32 middle schools. The school where I teach, Carmel Middle School, has a culturally diverse population that is around 60 percent white, 40 percent minority: African-American, Asian, and Hispanic. There are a few obstacles that I would like to overcome with the students to make them successful.
There are three levels of math classes in my school district. Standard math is for students that are at or below grade level. Standard plus is for students that are on grade level. Honors is the third level. Students in this class are above grade level. Within the seventh grade, I teach a couple of different levels of students varying from ones that are below grade level to others that are well above grade level. Also, within each class, there is an academically assorted group of students. This is the first challenge or obstacle. The second challenge deals with reaching individuals in a culturally diverse group of students. Using several different types of word problems varying in difficulty and subject matter to successfully teach my students an important topic is my main goal for this unit.
In mathematics, it seems that the most difficult skill for students to grasp is solving word problems. This is noticeable in any age group. The students may be able to perform basic math tasks such as multiplying or dividing, but if that same skill is surrounded by excess words, it really confuses most students. To solve my own math problem I will begin by introducing the students to word problems that are fairly simple to make the students feel successful so they will be comfortable dealing with the more difficult ones. In doing this, I hope it will build confidence in each of the students so they are not intimidated when looking at word problems. They will be more confident when given the challenge of a difficult word problem.
One of the largest objectives in the seventh grade math curriculum in the state of North Carolina is one that deals with ratios, rates and proportions. Within the state standards, there are several indicators that involve using proportions to solve a problem. Along with solving proportions, students also need to be able to evaluate problems that deal with scaling, similar figures, unit rates and percent proportions. Students tend to be at ease solving a proportion that is already set up just by using the method of cross-multiplying. It is more difficult to set it up on their own when reading a word problem because of the units. They tend to set them up incorrectly because they choose the numbers in the order that they appear in the word problem and do not focus on the units that are attached to the numbers themselves. This occurs with the majority of the students that I teach, regardless of their academic level. Setting up proportions is a difficult and sometimes confusing process that my unit will be able to address and help students to become more successful.
I have put together a large selection of problems based on the objective. I have taken the problems and split them into groups based on different topics within the goal. From there, the problems are broken down into different categories. The different groups or categories are word problems that include unit rates, similar figures and scale drawings/models, along with percent proportions. All of the word problems that I have put together can be solved by setting up proportions. Students need an understanding of preparing a proportion because it is a skill that will help them in school and throughout their lives. As adults, there are many different problems solved on a daily basis using proportions such as reading maps, figuring out tips to leave at a restaurant and also determining a sale price on an item. Students who are successful in setting up proportions will be able to use that skill in many ways and situations.
I hope this unit will be beneficial to teachers at different levels. It is based on the standards for students in seventh grade math, but it is not limited to just that grade or subject. Proportions are used throughout middle school and high school. For example, in science, proportions are used in converting measurements, and in social studies, scales are used to read maps. The difficulty of the sample problems themselves, (see Appendix A), can be modified to meet the needs of other subject areas or grade levels.
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