Problem 1: The Woods' Dining Table Name Mr. Ness Bizz has an unusual business that offers suggestions to clients for their building. He presently has four jobs that need attention, and your expertise is needed. Each job will have some things to think about for the advice you offer. You will need to offer each client a) a set of drawings for each product; b) a table of all of the options; and c) suggesting an option that best meets the design of the situation. Your success depends on how thoughtful your product is, and how well your presentation deals with your customers with a table of choices, pictures of their product, and cost effectiveness. The first job is for the Woods family. They would like a dining room table that has an area of 36 square feet, but they are unsure of the dimensions of the table. They would like a wooden table with a metal edge on its outside. Your job is to draw every possible table (using only whole numbers) that has an area of 36 square feet and write the length (in feet) of metal needed to go around each dining table. The Woods would like two chairs on the long side and one chair at each end of the table. Offer a suggestion to the Woods family as to which of the options you offer is best, and why. [Be specific with your dimensions and the length of metal needed so they might find the cost.] You will be scored on correctness of your table; the choice and reasoning of dimensions for the table; the drawing of the table; and the process for finding the cost of the table. Minimal expectations can be met with the 4 questions, but the extensions will be evidence of stronger to exceptional performances. 1. (2 pts.) Write all of the dimensions (using whole numbers) of each dining table that could be made in the table below. When you find the dimensions of a dining table, also write the length of the metal needed to go around that dining table. Use w for the width of the table; l for the length of the table; and p for the length of metal needed to around the table. w l p 2. (3 pts.) The Woods family needs a suggestion from you. They have 6 chairs to be placed around their dining table. They would like to have about a 2 to 1 ratio of the side dimensions. What dimensions from your table do you suggest and why? How Far Around the Wrecked Tangles Student Materials 1 Page 1 of 9
3. (2 pts.) Draw a picture of the dining table as best you can. If you use a scale in the drawing, please include that as part of your drawing. 4. (3 pts.) The cost of the wood for the dining table is $2.50 per square foot and the metal going around the table is $1.75 for each foot. The 4 table legs are $15.25 each. The labor for the project is equal to the cost of materials. Find the total cost of your suggested table from #2. Please, show your work and label for the Woods family so they can understand the total cost of the dining table. Extensions: 5. Could you suggest another area that may better meet their needs (of a 2 to 1 ratio of the dimensions of the dining table)? Please, include the new area, the dimensions of the table and the length of metal needed in your suggestion. 6. If the Woods would like a dining table with two chairs on a side, what could a reasonable area be, understanding that we need at least 4 feet at the dining table for each chair? Keep the area of the dining table to a minimum, while leaving room for the chairs. Offer a new proposal to the Woods with those ideas in the plan. How Far Around the Wrecked Tangles Student Materials 1 Page 2 of 9
This business has been very good since the Woods family's business. Mr. Ness is encouraging you to think of making the dining table business bigger, but he needs to know that you can quickly find dimensions of each table. 7. He says, if he gives you the area of a table of 36 square feet, you should tell him what to do with that area and a width of a dimension of the dining table to find the length. a) Use everyday words to tell Mr. Ness how to find the length, and b) write an equation using w for the width, and l for the length. a) b) = 8. For a bonus in pay he would like to give you an area of 36 square feet and a width and you tell him what to do with that information to find the length of metal to go around the table. a) Use everyday words to tell Mr. Ness how to find the perimeter, and b) write an equation using w for the width, and p for perimeter of the metal. The equation must be written in terms of the width (w), that is, you must write an expression using w as the only variable that is equal to p. a) p = 9. Mr. Ness says if he gives you any area of a table, you should tell him what to do with that area and a width of a dimension of the table to find the other dimension.. a) Use everyday words to tell Mr. Ness how to find the length, and b) write an equation using A for the area; w for the width; l for the length; and p for perimeter of the metal. 10. For a double bonus in pay he would like to give you any area and a width, and you tell him what to do with that information to find the length of metal to go around the table. a) Use everyday words to tell Mr. Ness how to find the perimeter, and b) write an equation using A for the area; w for the width; l for the length; and p for perimeter of the metal. How Far Around the Wrecked Tangles Student Materials 1 Page 3 of 9
11. What could you do to an area of the dining table to find the width of the shortest side of a table that has dimensions that have a ratio of 2 to 1? That dimension might not be a whole number. You may offer an equation or everyday words. 12. What could you do to an area of the dining table to find the smallest perimeter of a table that has dimensions that have a ratio of 2 to 1? Those dimensions may not be whole numbers. You may offer an equation or everyday words. Technology: (choose one) 13. Write a program for a programmable, graphing calculator (TI) that will input the width of the dining table with the area of 36 square units and will generate a) the length of the table and b) the perimeter of the table; OR Write a program for a programmable, graphing calculator (TI) that will input any area and the width of the dining table to generate a) the length of the table and b) the perimeter of the table. 14. Incorporate into your program above (or another program) an output that finds the dimensions and the smallest perimeter, given an area. How Far Around the Wrecked Tangles Student Materials 1 Page 4 of 9
Scoring guides: Guiding Question: are there any dimensions that have about a 2 to 1 ratio of length to width? l w p 1 36 74 2 18 40 3 12 30 4 9 26 6 6 24 9 4 26 12 3 30 18 2 40 36 1 74 1. (2 pts) 1 pt for the correct l & w; 1 pts for the correct perimeters. [May have only gone to 6x6 to be correct.] Deduct 1 pt if computation error in perimeter; allow no more than one computational error. 2. (3 pts) Solution is 4x9 rectangle with perimeter of 26 feet. Score 1 pt for correct dimensions and 2 pts for correct perimeter. 3. (2 pts) 1 pt for a rough approximation of 2 to 1; 2 pts for rectangle with 2:1 ratio of side lengths and obvious use of tools (scale). (straightedge will not be considered a tool in this task) 4. (3 pts) $2.50 x 36 ft 2 = $90 cost for the wood; $1.75 x 26 ft = $45.50 cost for the metal; $15.25 x 4 legs = $61 cost for the legs; and $196.50 for labor. Total cost of $393.00 for the table. 1 pt for the cost of each item; 1 pt for the total cost; 1 pt for clear presentation. Allow one computation error (that may affect total cost). Extensions: (each is worth 2 pts.) 5. A suggestion of 32 ft 2 with dimensions of 4'x8' and a perimeter of 24 feet is appropriate. 6. A 6x6' table would be too small for chairs, so 8'x8' table with area of 64 ft 2 and perimeter of 32 feet. 7. Divide the 36 ft 2 (area) by the width of the table to find the length of the table. L = 36 / w 8. Add two widths to two (36 ft 2 divided by the width) to find the perimeter. P = 2w+ 2(36/w) or 2(w + 36/w) or allow w + w + 36/w + 36/w or any other permutation of perimeter. May not use p=2w+2l. Must be in terms of width (w). 9. Divide the area by the width of the table to find the length of the table. L = A / w. 10. Add two widths to two (area divided by the width) to find the perimeter. P = 2w+ 2(A/w) or 2(w + A/w) or allow w + w + A/w + A/w or any other permutation of perimeter. May not use p=2w+2l. Must be in terms of width (w). 11. A / 2 = w 12. 4 A / 2 = p 13. For TI: Input W: 36/W X: Disp X: Pause: 2(W+36/W) C: Disp C For TI: Prompt A, W: A/W X: Disp X: Pause: 2(W+A/W) C: Disp C Both programs are minimal and acceptable. 14. Another line after the Disp C command: (A / 2) D: Pause: Disp D: 4 (A / 2) E: Disp E How Far Around the Wrecked Tangles Student Materials 1 Page 5 of 9
Scoring suggestions: Grade Level A 15+ 18+ 4 B 9-14 9-17 3 C 5-8 4-8 2 D 2-4 1-3 1 How Far Around the Wrecked Tangles Student Materials 1 Page 6 of 9
Estimate for job BIZZ Construction Enterprises (Name of Estimator) There is no job that we can't handle. Customer Product: Cost Estimate from back Specifications for the product, i.e., area, perimeters, shapes, etc. 1. 2. 3. Table of product choices: Label columns (if a variable is used, define it) Construction Needs Assessment: our suggested product circled from the table with at least 2 reasons why we chose this product. 1. 2. 3. 4. Detailed Drawing for our customer. (you may use graph paper) The scale is: How Far Around the Wrecked Tangles Student Materials 1 Page 7 of 9
Cost Analysis: Detailed accounting of product with specific labels. Qty. Item Unit Cost Mathematics Cost for Item (totaled at the bottom) How Far Around the Wrecked Tangles Student Materials 1 Page 8 of 9
Scoring guide for Estimate-of-Job Sheet: [This form can be used as an alternative to the longer, more difficult lesson. This offers sameness to each job and an inside look at an occupation. It certainly can be modified for your needs.] Fill in the job name, customer product, cost, and their name as estimator - 2 pts. Specifications - 1 pt. for each named (could have more than 2) 2 pts. Table of product choices -1 pt. for the length & width (or height & base) 3 pts. 1 pt. for the third column 1 pt. for offering descriptions (labels) for columns Correctness is presumed for work; allow 1 computational error, if the process is correct. Needs Assessment - correctly decides which choice is best with reasons 3 pts. Detailed Drawing - shows evidence of using a tool; a scale that is appropriate; drawing meets demands of the prompt. 3 pts. Cost Analysis (*if used) - calculating or identifying correct quantity; *4 pts. plus cost / unit; cost of item(s) and a total cost. Total points 13 pts Variations may change point total depending on each problem. You may want to include other attributes such as neatness, extra responses that are appropriate, dimensions on the drawing, etc. Make it fit your needs. How Far Around the Wrecked Tangles Student Materials 1 Page 9 of 9
Student work for problem 2: The Bowser s Kennel Mr. Ness Bizz has an unusual business that offers suggestions to clients for their building. He presently has four jobs that need attention, and your expertise is needed. Each job will have some things to think about for the advice you offer. You will need to offer each client a) a set of drawings for each product; b) a table of all of the options; and c) suggesting an option that best meets the design of the situation. Your success depends on how thoughtful your product is, and how well your presentation deals with your customers with a table of choices, pictures of their product, and cost effectiveness. The second job is for Mr. & Ms. Bowser. They would like a rectangular dog run (kennel) for Nellie. She is a hunting dog that needs room to run while being kenneled. The Bowsers want to use 36 square meters for the kennel, but they too are unsure of the dimensions for the kennel. The kennel will have posts at most every 2 meters and strong netted wire for a fence. Your job is to draw every possible kennel using whole numbered meters with the number of posts and the length of fencing needed. Your drawings should be labeled with the dimensions of two sides of the rectangular kennel, the number of posts, and the length of fencing needed inside each kennel. Nellie is slightly longer than a meter in length (long tail) so her needs are room for her to run at the expense of the width of the kennel. The Bowsers are looking for your advice on the best kennel options, and why those dimensions would be best. [Include the number of posts needed and the length of the fencing in case they want to price the materials to build the kennel.] You will be scored on the correctness of your table; the choice and reasoning of dimensions for the table; the drawing of the table; and the process for finding the cost of the kennel. Minimal expectations can be met with the 5 questions, but the extensions will be evidence of stronger to exceptional performances. 1. (6 pts.) Draw on graph paper every possible kennel (with whole numbers) that could be made including the placement of the posts. Put the dimensions on each drawing and in the table below. When you find the dimensions of each possible kennel, also write the perimeter of the fencing needed for the kennel and the number of posts needed to go around the kennel. Use w for the width of the kennel; l for the length of the kennel; p for the perimeter of fencing needed to around the kennel; and m for the number of metal posts. W L P M 2. (3 pts.) Choose the dimensions of a kennel that will meet Nellie's needs, then tell the Bowsers why those are the best dimensions for the kennel. (Offer at least 2 reasons.) How Far Around the Wrecked Tangles Student Materials 2 Page 1 of 4
3. (2pts.) a) What is the perimeter of that kennel (how much wire is needed)? b) How many metal posts are needed for its construction? The Bowsers need m of fencing, and metal posts. 4. a) (2pts.) Find the difference between the perimeter of the kennel that you suggested and the perimeter of the kennel with the shortest perimeter. b) (1 pt.) What is the difference in the number of metal posts needed for both jobs? 5. (4 pts.) The cost of fencing is $10.00 for each meter of fencing; the cost of each metal post is $12.00; cement for the flooring is $75.00 for every 9 square meters; and labor costs are double the cost of material. Show the Bowsers what their costs for the construction will be with labels on each significant number. Extension: 6. (6 pts.) If the costs from #5 were extended to each of the other possible kennels, what will the total costs of the other kennels be? Make a table that includes the cost of fencing, posts, cement, labor, and total cost. Be sure to write the dimensions of the kennel so they know which kennel you are breaking down the costs. Table of above Which kennel is the most expensive? Which kennel is the cheapest? 7. (2 pts.) Use Excel to build a table using equations (for Excel) to find each column for the length and perimeter of the kennels. Consider using Excel to find the costs of fencing and the cement. (metal posts may be too difficult) How Far Around the Wrecked Tangles Student Materials 2 Page 2 of 4
Scoring guide for problem 2: Bowser's Kennel 1. (6 pts.) Table with width, length, perimeter, and metal posts of all possible kennels. Students may have gone to a 6m x 6m kennel. All other dimensions of kennel (after 6x6) may be considered rotations of previous kennel dimensions. 1 pt. each for W & L columns, P column, and M column: totals 3 pts. for table; 1 pt. for all rectangles to scale; 1 pt. for placing all of the metal posts correctly; and 1 pt. for putting all dimensions, perimeters, and posts. W 1 2 3 4 6 9 12 18 36 L 36 18 12 9 6 4 3 2 1 P 74 40 32 26 24 26 32 40 74 M 26 14 10 10 8 10 10 14 26 1 P = 74 M = 26 36 2 P = 40 M = 14 18 3 P = 30 M = 10 12 4 P = 26 M = 10 9 6 P = 24 M = 8 6 2. (3 pts.) Best kennel may be the 2x18, if length of kennel is cited and the width accommodating the dog's "more than 1 m in length" is also mentioned. [The 1x36 will also be acceptable, if the best length of the kennel is reasoned, and an acceptable width for the dog is cited.] 1 pt. for each: acceptable answer, 2 reasons 3. (2pts.) The Bowsers need 40m of fencing, and 14 metal posts (if the 2x18 kennel is used), [or the Bowsers need 76m of fencing, and 26 metal posts (if the 1x36 kennel is cited)]. 4. (2 pts.) a) Student should choose their perimeter (or 40m or 74m) and subtract 24 (the 6x6 perimeter) to get 16m (w/ 2x18) [or 50m (w/ 1x36)]. b) 14-8 = 6 post difference w/ 2x18, [or 26-8 = 18 post difference w/ 1x36]. How Far Around the Wrecked Tangles Student Materials 2 Page 3 of 4
5. (5 pts.) (($10/m of fencing x 40m) + ($12/ post x 14 posts) + ($75/ 9m 2 of concrete x (36 m 2 / 9 m 2 )) x 2 = ($400 for fencing + $168 for posts + $300 for cement) x 2 = $868 x 2 = $1736 is the total cost for a 2m x 18m kennel. [(($10/m of fencing x 74m) + ($12/ post x 26 posts) + ($75/ 9m 2 of concrete x (36 m 2 / 9 m 2 )) x 2 = ($740 for fencing + $312 for posts + $300 for cement) x 2 = $1352 x 2 = $2704 is the total cost for a 1m x 36m kennel.] 1 pt. each: fencing, posts, concrete, labor, and total. Extensions: 6. (6 pts.) 1x36: ($10*74+$12x26+$75x4) x 2=$2704 [1 pt. each] 2x18: ($10x40+$12x14+$75x4) x 2=$1736 3x12: ($10x30+$12x10+$75x4) x 2=$1440 4x9: ($10x26+$12x10+$75x4) x 2=$1360 6x6: ($10x24+$12x8+$75x4) x 2=$1272 (Allow 1 computational error if no calc.) (use calculators?) The 1x36 kennel is most expensive ($2704); the 6x6 is cheapest ($1272). (1 pt.) Table of costs: Kennel Fencing Posts Cement Labor Total 1 x 36 $740 $312 $300 $1352 $2704 2 x 18 $400 $168 $300 $868 $1736 3 x 12 $300 $120 $300 $720 $1440 4 x 9 $260 $120 $300 $680 $1360 6 x 6 $240 $80 $300 $636 $1272 7. (up to 6 pts.) Excel spreadsheet suggestions: Cell A B C D E F G H Width Length Perimeter Fencing Posts Cement Labor Total Key in =36/A =(A+B)*2 =10*C key in =75*4 =(D+E+F) =2*G widths values Scoring suggestions: Grade Level A 19 + 22+ 4 B 15-18 13-21 3 C 8-14 6-12 2 D 5-7 1-5 1 How Far Around the Wrecked Tangles Student Materials 2 Page 4 of 4
` 3: The Fisher's Aquarium Name Mr. Ness Bizz has an unusual business that offers suggestions to clients for their building. He presently has four jobs that need attention, and your expertise is needed. Each job will have some things to think about for the advice you offer. You will need to offer each client a) a set of drawings for each product; b) a table of all of the options; and c) suggesting an option that best meets the design of the situation. Your success depends on how thoughtful your product is, and how well your presentation deals with your customers with a table of choices, pictures of their product, and cost effectiveness. The third job is for the Fishers. They want an aquarium for their rare fish collection. It is best for them if it has a rectangular base. They have a tempered glass that will be 15 inches high for the sides, but they don't know how much to cut for the sides to the aquarium. They would like the bottom of the aquarium to be 100 square inches. To minimize the cost the Fishers would like the base with the least cost for the glass sides. Would you show them all of their options (using inches that are whole numbers) for an area of the base? Write the measurements of the base with the length of the glass sides needed for each, and then suggest which option fits their needs keeping the cost of the sides down. You will be scored on the correctness of your table, the choice and reasoning of dimensions for the aquarium, the drawing of the model, the process for finding the cost of the aquarium, and making sense of volume. Minimal expectations can be met with the 5 questions, but the extensions will be evidence of stronger to exceptional performances. 1. (2 pts.) From your understanding of the problem make a table with columns containing the measurements (use whole numbers) of the width (w) of the aquarium, the length (l) of the aquarium, and the total length of glass needed to go around the sides (p). [The empty column may be used later.] W L P How Far Around the Wrecked Tangles Student Materials 3 Page 1 of 6
2. (3 pts.) Draw a model with dimensions of the aquarium that needs the least glass for the sides. Tell the scale you used to represent 1 inch on your model. (Do not draw full scale.) 3. (4 pts.) With the bottom of the aquarium costing $22.25 for 100 square inches, the 15-inch glass sides costing $1.25 for each inch used, and the adhesive to hold the edges to the aquarium costing $0.15 per inch, what is the cost of the aquarium? Bottom's cost Sides' cost Adhesive cost Total cost Show your work below. 4. (2 pts.) Find the volume of the aquarium. Multiply the height of the aquarium by the area of the base. Please show your work. 5. (1 pt.) What is your estimate of the volume of the aquarium in cubic feet? (Remember 12 X 12 X 12 or 12 3 is a the number of cubic inches in a cubic foot) How Far Around the Wrecked Tangles Student Materials 3 Page 2 of 6
Extensions: 6. (4 pts.) After looking at the model the Fishers decided that their needs would be better met by doubling the dimensions of the bottom while keeping the height the same. You should draw the model of the new aquarium with dimensions. The Fishers want to also know the new volume of the aquarium. They are sure the new volume will also double. Do these things for the Fishers: Draw the model of the new aquarium. Find the volume of the new aquarium. Write a sentence addressing the Fishers thinking about the new volume doubling. How Far Around the Wrecked Tangles Student Materials 3 Page 3 of 6
7. (6 pts.) With the larger bottom to the aquarium, there were different constructions costs. The bottom is larger, so you need to find out how many times larger, then multiply by the $22.25 to find the new cost. The sides of glass also changed, so find the new perimeter. $1.25 is the cost for each inch used. Last, because of the structural changes in size, we must use metal fasteners when two faces meet and then use the adhesive. Because there is no top face to the aquarium we will use a metal cap around the top of the glass for safety. That distance is the perimeter of the top of the aquarium. There are two costs for the metal: where there are two faces meeting, it is $0.25 per inch, and $0.20 for the metal that covers an edge. The adhesive will be used for every edge. That was $0.15 per inch. Find the total cost of the new aquarium. Show all work relevant to the finding the total cost so the Fisher family can see the costs. Costs: Bottom Sides Metal (edges) Metal (top) Adhesive Total cost: 8. (2 pts.) Use your table from #1. Find the volumes of each of the other aquariums that could have been used. Write a statement about the volume of all of the aquariums. Be specific in your statement by using the length, width and height of the aquariums. W L P 9. (2 pts.) Double all of the dimensions of the aquarium from the original dimensions. What happens to the volume? Your shown work will be the evidence of your statement. How Far Around the Wrecked Tangles Student Materials 3 Page 4 of 6
Scoring Guide for problem 3: The Fisher's Aquarium 1. (2 pts.) W 1 2 4 5 10 20 25 50 100 L 100 50 25 20 10 5 4 2 1 P 202 104 58 50 40 50 58 104 202 I pt for W & L, and 1 pt. for P. (may go to w = 10 to be OK) Allow for one computational error. 15" 12 " 15" 12 " 12 " 12 " 2. (3 pts.) Either method of drawing is acceptable. There may be other methods of drawing that are fine. Check the use of scale. (1 pt. for proportionality of the drawing; 1 pt. for dimensions applied correctly; and 1 pt. for a correct scale using 1 inch in that scale.) 3. (4 pts.) Bottom's cost: $22.25 Sides' cost $50 $1.25/ inch x 40 inches = $50 Adhesive cost $16.20 $0.15/inch x (48 in.+60 in.) = $16.20 Total cost $87.45 (no top to the aquarium leaves no edges on top) 4. (2 pts.) Bh = V, where the area of the base is B, and h is the height. 100 in 2 x 15 in. = 1500 in 3 (1 pt. for choosing the correct dimensions, and 1 pt. for the correct answer.) 5. (1 pt.) If 12 x 12 x 12 is the volume of a cubic foot, then 1698 in 3 is about our volume. Our best answer is about 1 ft 3. How Far Around the Wrecked Tangles Student Materials 3 Page 5 of 6
Extensions: 6. (4 pts.) 2 pts. for drawing; 1 pt. for volume; and 1 pt. for correct statement. 15" 20 " 20 " V = Bh (above) Volume: 20" x 20" x 15" = 6000 in 3 The volume quadrupled from 1500 because we doubled two dimensions. The Fishers seemed to think in one dimension. 7. (6 pts.) 1 pt. for each calculation. Allow one error in "total cost," if process is correct. Bottom $90 $22.25 x 4 = $90 Sides $120 $1.25 x 80 = $120 Metal (edges) $35 $0.25 x (80 + 60) = $35 Metal (top) $16 $0.20 x 80 = $16 Adhesive $33 $0.15 x 220 = $33 Total cost: $294 (sum of all of the edges: 20 x 8 + 15 x 4 = 220) 8. (2 pts.) All of the volumes are the same. The area of the base is a constant 100 in 2. Multiply the area of the base by the height of 15 and all volumes are 1500 in 3. 1 pt. for noting all volumes are equal; 1 pt. for statement saying area of bases and ht. are all the same in each situation. 9. (2 pts.) The volume 8 times the original 1500in 3. Each dimension is doubled: 3 dimensions doubled is 2 3 or 8 times the original. 1500 x 8 = 12,000 in 3. 1 pt. for the correct response; 1 pt. for any shown work leading to conclusion. Suggestions for scoring: Grade Level A 14 + 16 + 4 B 10-12 9-15 3 C 6-9 4-8 2 D 4-5 1-3 1 How Far Around the Wrecked Tangles Student Materials 3 Page 6 of 6
Problem 4: The Housers' Deck Name Mr. Ness Bizz has an unusual business that offers suggestions to clients for their building. He presently has four jobs that need attention, and your expertise is needed. Each job will have some things to think about for the advice you offer. You will need to offer each client a) a set of drawings for each product; b) a table of all of the options; and c) suggesting an option that best meets the design of the situation. Your success depends on how thoughtful your product is, and how well your presentation deals with your customers with a table of choices, pictures of their product, and cost effectiveness. The Hausers need a deck with a rail all the way around it. It sits just above a pond and for safety; they've decided to make a safety rail. Their deck is going to be expensive, so they've decided to make the largest deck with the least railing. They know that they would like between 200 and 300 square feet of deck. You can help by investigating the most effective dimensions for a deck, and then calculate the length of railing needed to go around that deck. Railing comes in lengths that are multiples of 8 feet. They would like to know all of their options, so offer options to the Hausers that use only whole numbers for dimensions. Make a suggestion about their best option and why you think it is the best choice. 1. There is language in the problem that definitely hints to the shape of the deck. What are the words that offer a hint of the shape? Use 5 or 6 words for the quoted phrase: 2. What is the shape of the deck? 3. If you know that the dimensions of the deck are whole numbers, what is the range of areas for the deck? List the only areas that can be chosen between 200 and 300 square feet. 4. What are the dimensions for the deck that you will advise the Hausers to use for their deck, and why? x are the dimensions, and the reason is How Far Around the Wrecked Tangles Student Materials 4 Page 1 of 7
5. Draw an aerial view of the deck with the posts for the railing drawn in as well. Write the scale you used in your drawing and write dimensions for the Hausers. How Far Around the Wrecked Tangles Student Materials 4 Page 2 of 7
6. The Hausers would like to get an estimate of only the decking and the railing with the posts. The decking comes in any needed length, but the width is 6 inches. The railing comes in 8 foot lengths. We will need three levels of railing all the way around the deck. Last, we need posts to hold those railings up. Show the cost calculations for the decking (of the deck you selected for the Hausers), the railing, and the posts. Be sure to label each significant number so the Hausers are aware of what each is. Using a table is essential. Show a total cost that is the sum of the three building items. Decking material is $1.00 for each foot of length ("per linear foot" is the lumber store's language); the railing is $1.00 per linear foot; and the posts are $6.00 each. Extension: 7. Using a more expensive brand of decking material may change the Hausers minds. Even though the product has a much larger product-life (it is not wood) and essentially there is no maintenance for its life, its cost is quite a bit higher. It is the same width as our 2x6 decking material yet thinner. (We must have 16" between deck joists.) Its cost is $2.50 per linear foot. How does that change the total costs above (#6) for only the decking, post, and railing? [You can also factor that into the costs from the Project below.] Possible other direction: decking is what % of total with both materials? How Far Around the Wrecked Tangles Student Materials 4 Page 3 of 7
Project Extension: The Hausers have considered your initial costs and would like to know the cost of a whole package of building materials. Those other materials are the posts and beams to hold up the structure, the floor joists that go on top of the beams and hold the decking. We will need to use nails, and bolts with washers and nuts to hold it all together. The prices are as follows: 4x4 treated posts $1.50/ft. 4x8 beams 2x6 treated joists 16d galvanized nails $2.25/ft. $1.00/ft. $1.95/lb 3/8" by 6" galvanized bolt $0.50/ea 3/8" washer (need 2 per bolt) $0.10 3/8" nut for the bolt $0.10 Cement for each post $3.75 per 60 lb. bag Building codes say we should have joists every two feet for this deck. We should have beams no more than 12 feet apart (but you can overhang your deck joists by 2 feet, if needed). We must place boards at both ends of the deck's joists (called rim boards) and blocking between all of the joists in the middle of the deck (another 2x6). That's to keep the joists straight. The posts can be placed no further than 2 feet from the end of the beam, and cannot be more than 6 feet between posts. Each post will have 3 feet in the ground and one foot above ground. One bag of cement will be enough to hold one post for the beams. We will put 2 bolts with washers (2) and nuts on each post. We will need 10 lbs. of nails. Labor for the project will be same as the materials cost. For the building codes personnel you need to modify the first plan to show the layout of the beams, joists, and posts. For the Hausers create an easy to read cost sheet for them including the costs from the decking and railing. This could be very expensive. Please, be as cost effective as possible. Keep the costs down by reading the codes, minimizing the building materials but still keeping a strong product. How Far Around the Wrecked Tangles Student Materials 4 Page 4 of 7
Plan for Buildings & Codes: Name Use heavy, solid lines for the beams under the deck; use dashed lines for each joists, rims and blocking; and use "X" for each supporting post. Show only a top view of the deck. (Write your scale.) Cost analysis: (total is circled at the bottom of work) [When citing an "item" write its dimensions and its length, ie., 2x4 board - 8' means a 2 inch by 4 inch board that is 8 feet long.] Qty. Item Unit cost Math Cost for item How Far Around the Wrecked Tangles Student Materials 4 Page 5 of 7
Scoring Guide for problem 4: The Hauser Deck 1. (1 pt.) There is language in the problem that definitely hints to the shape of the deck. What are the words that offer a hint of the shape? Use 5 or 6 words for the quoted phrase: "the largest deck with the least railing" 2. (1 pt.) What is the shape of the deck? Square 3. (3 pts.) If you know that the dimensions of the deck are whole numbers, what is the range of areas for the deck? List the only areas that can be chosen between 200 and 300 square feet. 225 (15 2 ), 256 (16 2 ), 289 (17 2 ) 4. (2 pts.) What are the dimensions for the deck that you will advise the Hausers to use for their deck, and why? 16 x 16 are the dimensions, and the reason is: It must be square to minimize the railing, and it is a multiple of 8' (the length of the railing). 5. (10 pt.) Item Qty. Cost/unit Math Cost for item 2x6 Decking 16' 32 $1.00/ft. 32 x $16 (see next line) $512 [2x6 deck board 1 $1.00/ft. 16 x $1 = $16] cost of 1 board Posts for rail 8 $6.00 ea. 8 x $16 $48 Railing 24 $1.00/ft. 8 x 3 x $1 $192 Total $752 6. (36 pts. Project) Plan for Buildings & Codes: (4 pts.) 2' 12' 2' X 2' X 6' X X 16' 6' X X 2' 16' How Far Around the Wrecked Tangles Student Materials 4 Page 6 of 7
Cost analysis: (total is circled at the bottom of work) (26 pts.: 1 for correct quantity, 1 for correct math, & 1 for correct cost of the item; then sub-total & total.) Qty. Item Unit cost Math Cost for item 6 4x4 post 4' long $1.50/ft. 24 x $1.50 $36.00 6 60 lb. bags of cement $3.75 6 x $3.75 $28.50 2 4x8 beams 16' long $2.50/ft. 2 x 16 x $2.50 $80.00 12 2x6 joists 16' long $1.00/ft. 12 x 16 x $1.00 $192.00 (includes 2 rims & blocking) 16 galvanized 3/8" bolt $0.50 16 x $0.50 $8.00 16 galvanized 3/8" nuts $0.10 16 x $0.10 $1.60 32 galvanized washers $0.10 32 x $0.10 $3.20 10 16d nails $1.95/lb. 10 x $1.95 $19.50 $268.80 Add deck & railing package $752.00 $1020.80 $1020.80 (for materials) x 2 (for labor) makes a total estimate of $2041.60 How Far Around the Wrecked Tangles Student Materials 4 Page 7 of 7