Once Xavier decides that he would like to tackle his own house construction, he begins to get his plans in order. The lot Xavier purchased many years ago is just perfect for the new, prefabricated house he wants to build for his family. To accomplish this large task, Xavier is going to need to consult with people from all three career clusters that we have considered in this unit—and you’re going to help! This activity will be broken up into two parts, each of which have their own assignment:

Part 1 will ask you to consider aspects of Xavier’s building project and complete math problems that help him make decisions about what to build.
Part 2 will have you take the answers to the math problems you completed in Part 1 and build a Job Board to keep Xavier organized during his construction project.
Let’s walk through this process with Xavier.

Part 1: The Math Behind Construction
For the design stage, Xavier hires a surveyor, Bradley, to look at his lot and decide what size house he would be able to have on the property.

Bradley sees that Xavier’s lot is the shape of a trapezoid, with the boundary line (or back edge of the lot) extending 100 feet from the front property line:
On your math sheet, complete the following problems to help Xavier find out how big a house he can build. Math Problem 1: What is the total area of Xavier’s lot? Use the formula for calculating the area of a trapezoid to help answer your question: A=a+b2c or front of lot+back of lot2length of lot Once Bradley has the total area of the lot, he explains to Xavier that the county only allows for 40 percent of any lot to be covered with buildings. This is in order to preserve the natural surroundings and allow water runoff. Bradley says that if a lot of land has too much house on it, there is little land for rain to drain, and that can cause flooding. Using the total lot area, calculate the available lot coverage that Xavier can use. This will give him an idea of how big of a house to look for. Math Problem 2: What is Xavier’s available lot coverage? (In other words, how big a house can he build?) Use the formula for calculating percentage to help answer your question: 40100=xTotal Area Now that Xavier has an idea of what size house his lot can accommodate, he has to decide what kind of house he wants. Xavier decides to visit a manufacturer that designs custom prefabricated homes. When he arrives at the large factory, he meets Sabrina, who is involved in designing and selling the prefab housing. Xavier tells Sabrina a basic idea of what he is looking for: how many square feet, perhaps three bedrooms, and one bathroom. Sabrina jots down Xavier’s requests and shows him some floor plans that her company has available. Sabrina explains how her company manufactures homes in three or more modules (or large pieces). Everything is put together on their factory site, and once the modules are complete, they are shipped individually to the lot where they will be put together. Xavier picks out a few floorplans he is interested in and Sabrina walks him through the factory to show him some sample modules on display. Sabrina is particularly excited to show Xavier a new material that her company has recently begun offering for siding on the homes. While the company still builds homes with traditional vinyl siding, they also offer a new product: fiber cement siding. Sabrina explains that even though vinyl siding is durable and easy to clean, over time it can chip and crack. It can also warp with just a little heat, like when a grill is placed nearby or with extreme amounts of sunlight. She shows Xavier a sample of a fiber cement board. He can see that this product is manufactured to be much thicker than vinyl. Sabrina points out that fiber cement siding is made with a chemical formula to make it extremely heat resistant. Because he is in construction, Sabrina has Xavier look under one of the sample sinks to view another special upgrade available: PEX piping. The new PEX pipe is made from polyethylene in contrast with traditional PVC or copper piping. PEX pipe does not require glue or cement and can simply be joined with fittings for a watertight seal. It is also resistant to freezing, a common issue seen with PVC pipes. It does not corrode like traditional copper piping. After the tour, Sabrina presents Xavier with two options that would fit his needs. Option 1: 1,811 square feet, 2-3 bedroom, 2 bath house that arrives in 4 modules. It includes the upgraded PEX piping and fiber cement siding that Xavier saw on the tour. The price for Option 1 would be $180 per square foot. Option 2: 2,600 square feet, 3-4 bedroom, 3 bath house that arrives in 5 modules. It also includes the upgraded PEX piping and fiber cement siding. The price for Option 2 is $195 per square foot. Sabrina also explains that Xavier must have certain things ready ahead of time, such as electric, sewer, and water systems, as well as a foundation in place. She gives him the name of a transport company that would oversee bringing Xavier’s modules to his house site. On your math sheet, complete the following problems that will help Xavier choose from the two options Sabrina has presented him: Math Problem 3: Calculate the total price for Option 1 Use this formula to help you solve the problem: Total Square Feet × Price per Square Foot=Total Price Math Problem 4: Calculate the total price for Option 2 Use this formula to help you solve the problem: Total Square Feet × Price per Square Foot=Total Price Xavier contacts the transport company and is put in touch with one of the drivers, Kevin. Because the modules need to be connected quickly once they reach his build site, Xavier wants to know if he can have them all delivered on the same day. Kevin says that this would be possible using one truck per module. The fee for transporting each module is 20 cents per truck per mile, plus the cost of fuel. The factory is 350 miles from Xavier’s build site, and Kevin estimates that each truck will need $500 worth of gas. On your math sheet, complete the following problem to help Xavier find out how much he will spend on transportation costs: Math Problem 5: Calculate Xavier’s transportation cost to have the modules delivered on the same day Use this formula to calculate Xavier’s cost: [(.20 × miles)+500]× number of modules Part 2: Job Board Xavier is excited but knows this is a huge project. Help Xavier stay organized by creating a job board for him. A job board is like a bulletin board that holds important information about a big project. This way, he can see the important aspects of his job, along with his costs. To do this, you will be taking the answers to the math questions above and creating items that Xavier can hang on his job board to remind him of the choices he should make in this project. You may select to create your job board in poster form or digitally in a word processing document. Either way, the job board should include the following pieces of content: A rough drawing of Xavier’s lot that includes the lot measurements provided above. Make sure that you include the total area of the lot that you calculated in Math Problem 1 somewhere on this drawing. A sketch of the prefabricated house option that you suggest Xavier purchases (either Option 1 or Option 2). Make sure that you include his final price that you calculated in Math Problem 3 or 4. Also, be sure to label the upgraded technology that was included in the option you chose so that Xavier can point it out to his building inspector when the time comes. A graphic representation (photo, clip art, etc.) of a truck with the final transportation cost on it (this is the answer to Math Problem 5). You will turn in this job board along with your math sheet.