This week, you will reflect on this week's resources and your personal connection to them. This will give you practice in writing about these ideas and help you to apply these tools in different areas

MATH125: Unit 1 Submission Assignment Answer Form

Mathematical Modeling and Problem Solving

ALL questions below regarding PAINTING A BEDROOM must be answered. Show ALL step-by-step calculations, round all of your final answers correctly, and include the units of measurement. For full credit all explanations must be given in the spaces provided. Upload this modified Answer Form to the Intellipath Unit 1 Submission lesson. Make sure you submit your work in a modified MS Word document; scanned/handwritten work will not be accepted. If you need assistance, please contact your course instructor.

All commonly used formulas for geometric objects are really mathematical models of the characteristics of physical objects. For example, a basketball, because it is approximately a sphere, can be partially modeled by its distance from one side through the center (radius, r) and then to the other side by the diameter formula for a sphere: D = 2r.

For familiar two-dimensional variables length, L, and width, W, the perimeter and area formulas for a rectangle are mathematical models for distance around the rectangle (perimeter, P) and the region enclosed by the sides (area, A), respectively:

P = 2L + 2W and A = L x W

Along with another variable, height, H, a three-dimensional rectangular prism’s volume and surface area can be measured. For example, the formulas for a common closed cardboard box’s inside space (volume, V) and outside covering (surface area, SA) are respectively:

V = L x W x H and SA = 2(L x W) + 2(W x H) + 2(L x H)

For this Submission Assignment follow Polya’s principles to solve your problems.

1. Understand the problem

2. Devise a plan

3. Carry out the plan

Include the following in your assignment:

• Explain your interpretation of what the problem is about.

• Develop and write down a strategy for solving this problem; show the steps in the correct order for your attempted solution.

• Did your strategy actually solve the problem? How do you know?

• Suppose your solution did not solve the problem—what would be your next action?

PAINTING A BEDROOM

The walls and ceiling inside your bedroom need to be painted, and to save money, you decide that you will paint the bedroom yourself. Below is the information to help you solve the problem:

• The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.

• The inside of the bedroom door is to be painted the same color as the walls.

• Two coats of paint will be applied to all painted surfaces.

• The room has one window, measuring 3 feet, 9 inches by 4 feet, which will not be painted.

POLYA’S PRINCIPLE STEP 1: UNDERSTAND THE PROBLEM

1. Describe, in detail, what you understand the problem to be. In other words, what problem will you need to solve? Is there enough information to enable you to find a solution to your problem?

Show your work here: (10 points)

1. Discuss different ways to construct the room that will be painted. Are there any restrictions on where the window and door will be located? Will the overall amount of paint needed, change based on where these are placed in the room?

Show your work here: (10 points)

1. Begin to list the facts you know. First, find the room dimensions in feet that make a good model for this situation. One strategy would be to sketch the room as follows. Please use this model to complete the table below. (3 points)

1. Using the measurements diagrammed above, label all rectangular faces with feet in this table. (5 points)

1. Because all ending values are given in feet, find the window dimensions in feet. Convert the length of 3 feet, 9 inches strictly into feet. The answer will be in decimal format. Do not round. (Make sure to use the conversion where 12 inches are in 1 foot.)

Show your work here: (5 points)

Diagram 2

Wall

14.25’ by 8’

POLYA’S PRINCIPLE STEP 2: DEVISE A PLAN

1. Using Polya’s technique for problem solving, describe in detail, what your plan will be to solve this problem. In other words, what is your solution strategy? Discuss the strategy, steps, formulas, and procedures you will use to answer this problem.

Show your work here: (10 points)

POLYA’S PRINCIPLE STEP 3: CARRY OUT THE PLAN

1. Using the formula concepts and dimensions from above, find the bedroom’s total painted surface area around all of the walls. Also, determine the amount for two coats by doubling the paint previously found.

Show all step-by-step calculations, including the units of measurement, and round your final answers up to the nearest whole measurement unit:

Show your work here: (8 points)

1. Using the formula concepts and dimensions from above, find the ceiling’s total painted surface area, including both coats.

Show all step-by-step calculations, including the units of measurement, and round your final answers up to the nearest whole measurement unit:

Show your work here: (8 points)

1. Combining the answers from above, find the total painted surface area, including both coats for the walls and ceilings.

Show all step-by-step calculations, including the units of measurement, and round your final answers up to the nearest whole measurement unit:

Show your work here: (5 points)

1. Do not forget to subtract the window’s area.

Show all step-by-step calculations, including the units of measurement, and round your final answers up to the nearest whole measurement unit:

Show your work here: (8 points)

1. Assuming you can paint 100 square feet per hour, what will be the work time needed to paint your bedroom?

Show all step-by-step calculations, including the units of measurement, and round your final answers to the nearest whole hour amount:

Show your work here: (8 points)

POLYA’S PRINCIPLE STEP 4: TAKE A LOOK BACK

1. Did this strategy actually solve the problem? How do you know? Demonstrate that your solution is correct. In other words, explain why the values you have created are the best times for the job. Was this the best way to solve this problem? If you had to do this again, what would you do differently? What would you do the same? Show your work here: (10 points)