Rane Anderson - On the Job: Contractors: Perimeter and Area

0covercover.xhtmlOn the job Contractors Perimeter and Area Rane Andersoncover3page0003page0003.xhtml44page0004page0004.xhtmlTable of Contents Build It, Fix It 4 Prepping for the Job 6 Outside Work 14 Inside Work 18 A Job Well Done 27 Problem Solving 28 Glossary 30 Index 31 Answer Key 3255page0005page0005.xhtmlBuild It, Fix It Contractors are go-to people for anyone who wants to renovate an indoor or outdoor space. You can find them on any construction project, big or small. It is the contractors job to bring ideas to life. Some clients have unique requests. They want houses made from glass bottles and walls made from tires. They want houses built in trees and rooms hidden behind bookcases. Regardless of the request, contractors find ways to get the work done. Most of the time, clients have much simpler requests. They might ask for a new kitchen countertop. They might need a new backyard fence. In either case, contractors are there to help. They measure spaces, buy supplies, use tools to fix problems. They might even hire other skilled workers to help. Contractors work hard to make dreams come true. plans for a kitchen remodel66page0006page0006.xhtmlThe David Wenzel Treehouse at Nay Aug Park in Pennsylvania, overlooks a gorge from 150 feet (46 meters) above.77page0007page0007.xhtmlPrepping for the Job Contractors must be ready to take on any challenge. One frequent request from clients is deck repair. First, contractors must gather information and plan what they want to do. That means they must inspect the space. By doing so, contractors can figure out the exact repairs that must be done. Perhaps the wood is in good shape, but the paint is old. In that case, refinishing might be the answer. Or, a few boards might be damaged. Those can be replaced. If too many boards need to be replaced, a contractor might suggest building a new deck in its place. Perhaps the deck appears unstable. No one wants a deck to collapse while they are standing on it! In this instance, the decks braces and posts must be checked. Contractors will then decide the best way to fix the problem.88page0008page0008.xhtmlnew safe deck unsafe deck99page0009page0009.xhtmlContractors love to give good news to clients. In one case, a clients deck may be stable and safe. But, its floor needs to be refinished. And the top of the railing around three sides of the deck may be rotted. It needs to be replaced. The contractor takes out a tape measure and measures some lengths. This is a vital part of the job. And doing this wrong could mean wasting a lot of time or money. It could result in a bad reputation. While measuring the railing, the contractor is sure to write a linear unit. If the contractor buys from a lumberyard that sells lumber by the foot, the contractor will order using that unit. The contractors next step is to measure the floor to plan for the correct amount of stain. For this, square units are used.1010page0010page0010.xhtmlLet's1111page0011page0011.xhtmlContractors use math every day. They add, subtract, multiply, and divide. They also have to find the perimeter and area of spaces. Perimeter is a word with Greek roots. Peri means around, and metron means measure. So, it makes sense that the distance around the outside of a shape is called the perimeter. When contractors need to find out how much railing a deck should have, they must measure the perimeter. They measure the distance around the deck. Once the lengths and widths are known, they are added together. This is the perimeter of the deck. perimeter area1212page0012page0012.xhtmlBut what if a contractor wants to refinish a decks floor? Do they measure the perimeter? No, this is when finding area can help. Area is the amount of space on the surface of a shape or place. If a clients deck is a rectangle, the contractor must find the length and width first. Then, the length and width can be used to find the area of the deck. Finding the perimeter and area of a space can help a contractor save time and money by doing the project right the first time. Contractors must first calculate the areas and perimeters of spaces they are designing.1313page0013page0013.xhtml1414page0014page0014.xhtmlBefore clients will hire anyone to work on a deck, they will want to see a bid. A bid is a written estimate of all the costs for a project. Clients might ask for bids from a lot of contractors. They want to find the best price. Placing bids can be tricky. If a bid is too low, the contractor will not make money from the job. But if a bid is too high, the clients might choose someone else to do the work. Being precise when adding expenses helps contractors write accurate bids. Expenses are the costs of the job. Contractors must answer many questions to figure out costs. What materials are needed? Are permits required? How many workers are needed? All of these things have to be carefully considered before placing a bid. Once contractors figure out the total cost, they can submit bids to clients. Then, they wait. If they got it right, they will be chosen for the project!1515page0015page0015.xhtmlOutside Work Some clients have more than one project. This often happens when people buy a new house. They ask a few contractors to submit bids for projects they have in mind. Contractors write cost estimates for the whole job. Careful calculations help them get the bid ready. One contractor has clients who have a big, green front lawn at their new house. They love it! Of course, they want to keep it healthy and give it plenty of water. But, it takes them hours to water with the hose every night! Plus, the hose never seems to be long enough. So, they bought a lawn sprinkler. That did not work out as well as they had hoped. The sprinkler cant reach every corner of the unusual lawn. The clients are hoping a contractor can figure out a solution to their problem.1616page0016page0016.xhtml1717page0017page0017.xhtmlThe contractor studies the lawn. It looks like the best option is to install a sprinkler system. The system will start on a timer. The sprinklers will turn on at a certain time each night. The contractor tells the clients his plan. They are excited! Now, they wont have to fight the hose that is always too short. They wont have to move the sprinkler throughout the day. This sounds like the best option. With a sprinkler system, the yard will always look fresh and lush. To make the system work, pipes will have to be placed underground and around the outside of the lawn. These pipes will take water to the sprinkler heads. The contractor needs to figure out how much pipe to buy. Step 1 : Lay underground pipes. Step 2 : Cut pipes to attach the sprinkler heads. Step 3 : Attach sprinkler heads to pipes.1818page0018page0018.xhtmlLet's1919page0019page0019.xhtmlInside Work The clients love the plan for their new sprinkler system. They are excited to see their lawn grow to a beautiful, crisp green color. But now, they have a second job for the bid. The color of their dining room is getting on their nerves. The color is too bright and distracting. The clients decide they want a totally new color on the wall. So, they ask a contractor for help. The contractor wants to know what color the clients want for their dining room. The clients like the natural colors they now see in their front yard. They decide they want a more natural color. Now that the contractor knows which color to buy, it is time to figure out how much of the wall will need paint. Then, the right amount of paint can be purchased. Finding the area of the wall will help. paint sample swatches2020page0020page0020.xhtmlLet's2121page0021page0021.xhtmlThe plan for the dining room is perfect! The natural walls will look beautiful as people eat their meals. But now, the carpet in the living room looks old and out of place! The contractor is happy to add a third job to the bid. The first step will be to measure the living room floor. The living room floor is shaped like a rectangle. First, the contractor must find an accurate length and width. These measurements will help determine the amount of carpet and baseboard that is needed. After finding the area and perimeter, the contractor can find out prices from the flooring supplier. Carpet is sold in square units. So, the floors area tells how much carpet is needed. Baseboard surrounds the carpet along the bottom of the walls. It is sold in linear units. Perimeter is helpful here. Area and perimeter let the flooring supplier give correct prices to the contractor. carpet cutter2222page0022page0022.xhtmlA circular saw cuts baseboard to exact measurements. Let's2323page0023page0023.xhtmlThe clients are not finished with the bid yet! Now, they turn their attention to the kitchen. The countertops are in bad condition. They are stained from years of use. And there is a burn mark next to the stove where the previous owners set a hot pan. The clients want their counters upgraded with strong and stylish granite. A contractor installs granite countertops2424page0024page0024.xhtmlThere are many types and colors of granite. The contractor chooses four options that would look good in the kitchen. One type of granite is shiny and black. It reminds the clients of the night sky. A second type is gray, with glittery specks that sparkle in the sunlight. The third option is dark brown, like a rich fudge brownie. The fourth option is a sandy beige. It reminds the clients of the beach. They have a hard decision to make! granite samples Let's2525page0025page0025.xhtmlBuy It! The contractor knows that a lot of materials will need to be purchased. Bundles of pipes, cans of paint, rolls of carpet, sections of baseboard, and slabs of granite are all on the shopping list. And the contractor will need tools, too. Nails, glue, paintbrushes, and masking tape are added to the list. All of these must be taken into account in the bid. If the contractor does not do so, all of the costs might not be covered. That might work out well for the clients. But, it would be bad for business. The contractor would lose money from the job. This is when careful estimating is important. Doing this well helps clients understand the costs and work involved. And it helps contractors plan wisely.2626page0026page0026.xhtml2727page0027page0027.xhtml2828page0028page0028.xhtmlA Job Well Done The contractor has taken all the measurements. Area and perimeter were used to help make the bid. Just to be on the safe side, the contractor checks the cost of all the materials and labor charges a second time. The last step is to give the clients the finished bid. It is up to the clients to decide. The clients look at all of their options. But in the end, they make a wise choice. They think the bid is fair. And, they appreciate how detailed it is. It gives them confidence that the job will be done on time. They think the contractor can do quality work and give them everything they hope for. All that is left is for the contractor to buy the supplies and get started on the job!2929page0029page0029.xhtmlProblem Solving Word of mouth is a great way for contractors to get new clients. Ben wants some work done around his house. His neighbor just hired a contractor to do some work for her. She told Ben how pleased she was with the projects. So, Ben chose the same contractor to do some work in his backyard. Ben wants the contractor to build a sandbox for his children. He already has 16 meters of new lumber for the sides of the sandbox. He would like the contractor to use this lumber instead of buying anything else. Bens children want the sandbox to be either a rectangle or a square. 1. Make a list of all the rectangular-or square-shaped sandboxes that would have a perimeter of 16 meters. 2. Bens children want the biggest sandbox possible. Find the area of each of the sandboxes in the proposal. Which has the largest area? 3. Which sandbox do you think would be best? Why?3030page0030page0030.xhtml3131page0031page0031.xhtmlGlossary area the amount of space covered by square units inside a two-dimensional shape bid a written estimate of the price to do a job clients people who pay other people or companies for services contractors people who manage construction projects estimate an educated guess about how much a job will cost expenses money spent regularly to pay for things linear unit a unit of measurement of length perimeter the distance around the outside of a shape refinishing putting a new coat on the surface of something renovate to make changes and repairs to an old house, building, room, etc. so that it is back in good condition reputation the common opinion that people have about someone or something square units units of measurement used to measure area3232page0032page0032.xhtmlIndex area, bid, costs, deck, estimate, expenses, Greek, kitchen, lawn, linear unit, living room, materials, measure, perimeter, square units,3333page0033page0033.xhtmlAnswer Key Let's Explore Math page 9 : 1. 32 ft. 2. 120 sq. ft. 3. Area is measured in squares. So, area uses square units and not linear units. page 17 : 1. 112 ft. 2. Responses will vary. Example : Finding the perimeter of the lawn is different from finding the perimeter of a rectangle because the lawn does not have two sets of equal sides; the lawn has more than four sides. It is similar because the lengths of all sides need to be added; it is measured in linear units. page 19 : 1. 18 sq. m 2. Yes; Two coats will require 36 sq. m of paint, and the paint will cover 40 sq. m. 3. 18 m of molding; linear units page 21 : 1. 24 sq. yd. 2. 20 yd. 3. 18 yd. page 23 : 1. $660 2. $160 Problem Solving 1. 1 m by 7 m; 2 m by 6 m; 3 m by 5 m; 4 m by 4 m 2. 7 sq. m; 12 sq. m; 15 sq. m; 16 sq. m. The 4 m by 4 m sandbox has the greatest area. 3. Answers will vary but may include : The 4 m by 4 m sandbox is best because it has the greatest area. It is a square, and other choices might be long and narrow.3434page0034page0034.xhtmlMath Talk 1. What information do you need to calculate the area of a square? 2. How are the units that describe perimeter different from the units that describe area? 3. What are two ways to calculate the perimeter of a rectangle? 4. Imagine a square that has an area of 25 square units. What are the lengths of the sides? 5. Would you use area or perimeter to describe the size of a room? Why? 6. Can area and perimeter help you describe a three-dimensional shape? Why or why not?3535page0035page0035.xhtmlOn the job Contractors Perimeter and Area The job of a contractor can be a balancing act. Clients want to pay the lowest price possible. But contractors still need to charge enough to make money. That means they need to use precise measurements to buy only what they need. Follow contractors as they use area and perimeter to balance wants and needs to make dreams come true. Measurement and Data36