How to solve a problem? What tools can I use to make a decision?
The basic problem solving techniques include
Understanding the problem
The problem needs to be understood well by engaging in group discussion. Get help from the instructor and the Teaching Assistants/Outstanding Students as you need them.
There are often more than one way to solve a problem. The group assignment must show combined thinking and high level of analysis. Therefore, even when you split up the tasks among the group members, the report needs to be coherent.
The scope needs to be well defined within the context of the course and assignment duration. The solution criterion needs to be defined before delving into analyzing/developing criterion.
There are often conflicting arguments for a particular solution. Therefore your analysis and solution often needs evidences to persuade the audience. This could be done using tools like Brainstorming, Trend Charts, Five Why’s, Story Boards, Scatter Diagrams, Surveys, Check Sheets, Histograms, Fail-Safing, Pareto diagrams, Fishbone Diagrams, and Flowcharts.
Use a Methodology
The solution you recommend needs to be in the context of real world situation. Cycle through problem solving steps as necessary to ensure a high quality output.
There are various methods for problem solving. Though all the methods are similar, some might be advantages for a particular scenario compared to others.
Review the PDCA or the Grow Model methodology and other ones as appropriate.
What tools can I use to make decision?
You can use different models. One interesting model you can use is the "Six Thinking Hats" (ref: http://www.toolshero.com/decision-making/six-thinking-hats-de-bono/)
For complex decisions that allows for quantitative evaliations you can use the "Decision Tree Analysis" method (ref: http://www.toolshero.com/decision-making/decision-tree-analysis/).