Module 7 Summary

Module 7 Summary

Hobbies can provide an occasional diversion that gives relief from the everyday pressures of work, chores, and studies. Many hobbies can also be pursuits that fulfill the individual and provide purpose. These purposes can range from achieving a personal goal to helping others. For example, if you enjoy reading in your leisure time, you may have a personal goal of reading certain books because they are classics or because they improve your knowledge in a particular area. However, you could also take your enjoyment of reading to a seniors’ home or the pediatric ward of a hospital where you can read to those who enjoy listening to stories or who have difficulties reading by themselves.

For some, a hobby can become a way of generating money to supplement their income. If, for example, you are a collector who enjoys perusing the neighborhood garage sales in the summer, you may find that there is a demand in the online community for what you collect. You may end up selling some of your collection and connecting with others who share your interests. Some people have even quit their regular jobs in order to pursue their hobbies on a full-time basis because they have discovered that they can earn enough money to do something for which they have an enormous amount of passion.

In this module you learned that you can solve problems even when there are multiple unknown variables. You can do this by writing a system of linear equations. You learned that as long as you have at least as many equations as unknowns, you will be able to formulate equations that can be used to solve the system.

You learned multiple strategies, both graphical and algebraic, for solving systems of linear equations. The graphing strategies that you employed were based on the notion that the solution of the linear system is found where the lines representing each equation in the system intersected. These strategies help you to visualize the solution, but cannot always provide exact solutions. However, you also learned algebraic method—namely substitution and elimination—that can provide exact solutions. The number of solutions from a linear system can vary. Depending on the way that the lines of the system are oriented, you can have a system with one solution, no solutions, or an infinite number of solutions.

In this module you worked on a project that involved vacation planning. You modelled and solved problems related to leisure pursuits that you might encounter while on vacation. Throughout each lesson, you also learned about interesting hobbies ranging from photography to shopping to origami. By working through interactive lessons and engaging in inquiry activities and exercises, you increased and enriched your understanding of linear systems and their solution strategies.

The Outcomes for Module 7 table summarizes the learning outcomes in this unit. As a review of what you have learned, complete the table by identifying those activities that you undertook to address the corresponding outcomes. An example of what the table could look like can be found in the Unit 1 Summary. Save a copy of this completed table with your work from this module in your course folder.

The strategies you used to solve systems of linear equations will be helpful to you as you continue your math studies beyond this course. Whether you find yourself investigating systems of non-linear equations or analyzing puzzles and games, you will draw on the knowledge and experience you have gained in this module. In addition, you may find that while the math may become more abstract, it will remain just as useful as ever in describing and explaining the phenomena around you, whether you are at school, at work, or on vacation!

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