This Personal Finance unit has been designed to be taught in approximately 11 lessons in periods that are 60 minutes long. The unit will focus on the applications of the objectives in the Personal Finance unit that corresponds to Chapter 9 in the Mathpower 11 text. The unit will begin at the start of the semester and will run every other Friday until the end of the semester. As there is a lot of work involved in the projects, the students will need time to develop their ideas and to do research. For this reason, the unit will run on "Finance Friday's" instead of consecutively.
The Personal Finance unit is perhaps the most relevant unit in the Pure Mathematics 20 course. The material lends itself to be taught in a project or application format. The amount of 'pure' mathematics that the students need to know in order to complete this unit is very little. The applications, on the other hand, are many. For this reason I have decided to dispense with the traditional unit plan format for this unit and approach it in a completely applied and contextual manner.
The concepts that the students need to know for this unit are simple interest, compound interest, earning a wage, taxes, loans, mortgages and annuities. Many of these topics have already been introduced to the students in their mathematics careers so the math concepts of the unit are not entirely new. Instead of spending time developing these concepts with direct teaching strategies, they will be used in a practical sense. This will give the students a better understanding of the concepts and how they relate to every day lives.
The chapter in the textbook that deals with Personal Finance will be introduced at the beginning of the unit as a valuable resource. As not all of the students come in to the class with the same amount of understanding of the topic, some will need to have a place that they can refer to if they need to brush up on some terms or skills on their own. The textbook topics will not be approached in order or individually, but will be referred to when necessary.
In order to address the concepts of the unit, the students will work on projects. They will work in pairs or groups of three, which will be left up to their discretion. They will have a set time in which to complete the projects, present them and turn them in. The projects will then be used as the unit evaluation. The students will also complete a group evaluation to assess the project experience. This evaluation will be valuable for teaching the unit in future classes. These evaluations will also be valuable for the students to reflect about what they actually learned through the project.
The unit will start off with the introduction and development of a situation that has some financial aspects. As a class, we will develop the project by answering questions posed by both myself and the class. We will then discuss where solutions to these answers could be found. The students will be introduced to a method of approaching their project. As many students would not have an idea of where to start, this exercise will give everyone in the class a place to begin.
The class will then brainstorm to generate a set of possible project ideas. The groups can either choose from the list or generate an idea of their own. Different groups will be allowed to work on the same project. As different students have various ideas regarding the topic and how to go about finding information, the same project idea could result in an entirely unique result. Similar project ideas ending in multiple results would provide interesting class discussion at the conclusion of the projects.
The groups will also be given a general outline of what is expected in their project. Parameters with regards to the math content, the organization and format of the project as well as the general presentation of the results will be given. At least four of the seven mathematical concepts that were listed above must be addressed in the project in order to receive a passing grade. Each of the groups must also provide a list of references so that confirmation of the information can be made if necessary.
The initial topic presentation in the first class to introduce the unit will be along the following lines:
Fred is a high school student that wants earn some money to go to the University of Alberta in two years. He would like to earn enough money that if he invested it at the end of the summer he could have enough saved for his first year of tuition by the time he is ready to go to school in September of 2002. He is either willing to start his own business or to work for somebody else. Fred enjoys painting, gardening and accounting.
The class would then generate ideas for jobs that he could do or a business that he could start. We would also take a look at investment options for Fred and how much would he have to earn this summer to have enough tuition for university. We would then need to find out how much university tuition would be for Fred. We would also need to see whether starting his own business or working for someone else would be better suited to generate the needed money (given that there are costs involved in both).
After discussing possible avenues to follow, the class would be encouraged to come up with some other possible project ideas. Other possible ideas might concern purchasing a computer or a car or choosing between different jobs based on wages, benefits, bonuses, etc. Additional ideas might involve purchasing stocks and comparing universities based on tuition, housing costs, books, etc. The options for students are many. Students would pick projects based on their interests and concerns.
By the end of the second period of the unit, the students will have had their project idea approved. The students then use the class time to do research and to put their ideas together. The students will have access to computers as well as phones to gather the necessary information. Each class period, the groups will give a progress report on how far they have come and what their plan is for that day and for the following weeks. The progress reports will either be given individually or as a large group. The class will also come together periodically to generate ideas for other groups if there are issues or to give general suggestions if groups found useful sources of information.
Each lesson will begin with a mental math section of approximately 5 minutes. This will bring the students in to the mode of mathematics class and will improve their mental math abilities in fractions and percents. Even though the design of the unit is not traditional (as in a new topic for every day led by the teacher plan), there still needs to be a flow and organization in the individual periods.
After the mental math activity, there will be a general class discussion on how the work is progressing for each group and if there are any difficulties finding any information or if there are any difficulties with the concepts. If there needs to be any remedial full class instruction on a topic it will be done at this time. If concerns come up individually, they will be given individual lessons for that topic.
At the end of the unit, each group will present their projects and their findings to the rest of the class. The groups will be given approximately 10 minutes each for their presentation. The projects will then be turned in for evaluation and for possible display. There will not be a unit exam on the topic as the projects will be the source of evaluation.
The unit will end with a class discussion on the project experience. The discussion will highlight where difficulties were encountered, where interesting things were discovered and how well the project as a whole had gone. The groups will then write a one-to-two page summary of the experience. Included in the summary will be how their group worked together, what interesting findings that they discovered as well as evaluating themselves in the project or group. The written evaluation will be handed in and will count towards 5% of the unit mark.
Pure Math 20: Personal Finance Unit Text: Mathpower 11, Chapter 9
11 Lessons - 60 minute periods
Text Sections
Each lesson will begin with a 'Mental Math' activity that will last approximately 5 minutes. The mental math will consist of converting fractions to decimals, decimals to fractions, decimals to percent, fractions to percent, percent to decimals, percent to fractions, finding the percent of a number, finding the percent per term in compound interest given the percent per annum and the number of terms given the compounding period and the number of years.
The individual lessons, which will be every second Friday, will then proceed in the following order:
The evaluation for the unit will consist of the submitted projects and of the written group evaluation. The projects will be evaluated on how well they have met the parameters given to them at the beginning of the unit.
The resources used for this unit are many. The students will have access to the Internet as well as people in the community. They may want to contact banks, businesses, universities, government facilities, hiring agencies, Hire-a-Student offices as well as many others. Surveys may need to be conducted formally or informally. The students will have access to these resources during class time as well as on their own time. As the projects can grow to be quite large, the students are expected to do much of the research on their own time.