In this discussion, you will work in small groups in online discussions to solve a mathematics problem involving changes of units. This group discussion will help prepare you for activity M1A2, in which you will write and submit an individual complete solution to a similar problem.
Solve the following problem, and post your solutions to the discussion forum.
Jill has a swimming pool in her backyard. It is shaped like a rectangle and measures approximately 16.3 feet wide and 26.2 feet long. It is an average of 5 feet deep. During a few hot weeks during the summer, some water evaporates from the pool, and Jill needs to add 8 inches of water to the depth of the pool, using her garden hose. Although her water pressure varies, the water flows through Jill’s garden hose at an average rate of 10 gallons/minute.
- Convert the dimensions of the pool to meters. Round all meter measurements to one decimal place (nearest tenth of a meter).
- How many liters will Jill need to add to her pool to return the water level to its original depth? How many gallons of water is this? Reminder: Volume = Length x Width x Depth
- How long will Jill need to run the hose? Express your answer in hours and minutes.
Be sure to answer all parts of the question above. It is possible that you will not be successful at answering all parts of the question at this point, and that is okay.Describe what you were able to solve and what questions you have remaining.
Since this module focuses on measurement it will be very important that mathematical conversions be clearly demonstrated throughout your problem write-up. For example, if you must convert 28 yards to meters, you must track your calculations with cancellation of units as seen below:
It is important to follow the Discussion Problem Instructions
Discussion Problem Instructions
This is intended to be a challenging problem that will require you to work together for a successful solution. Just as you learn from others’ ideas, they will learn from your questions and contributions. Whether you understand a complete solution to the problem or are struggling to work it through, you are expected to participate actively in the discussion throughout the module and to work collaboratively with your classmates on a thorough problem solution.
Goals for this discussion, while working with your classmates:
- The focus here is not only on finding the “right” answers but on explaining and justifying your reasoning for all mathematical steps and ideas you present.
- Engage with and reflect on the issues being discussed, which will be critical for your course grade.
- Demonstrate that you understand all parts of the problem and its solution by the end of the module.
This will prepare you for the next activity, in which you will write and submit an individual complete solution to a similar problem.
To earn the maximum number of points for this discussion:
- Your solution postings:
- For your initial posting, create a new discussion thread with a solution attempt or a question to help you get started. Your initial post is due by Tuesday for the 8-week course or Thursday of the first week for the 15-week course.
- Present a complete solution to all parts of the problem by the end of the Module.
- Show your justification for every step in your solution, using clear mathematically-accurate language. You can use phrases to explain your reasoning step-by-step, but clearly state your final conclusions using complete English sentences (for example, “Jill needs to add 43 gallons of water to her pool.”)
- Label all numbers with the units they represent (e.g. 0.3048 ft/meter).
- Your responses to your groupmates:
- Post at least three (3) separate days throughout the module, with a total of at least six (6) thoughtful responses to others.
- Communicate clearly. Do not use abbreviations common in texting.
- At least 4 of your posts must make important contributions to solving or understanding the problem. This can include your initial posting. These posts must be relevant, unique (not repeating ideas from someone else’s post), and justified (you explain your reasoning in a way that others can understand). You do not need to write extensively but contribute thoughtfully in ways that help us all learn about important mathematical ideas. Thoughtful questions are valid contributions.