The Pool Part A At last, your parents have finally agreed that it might be possible to put a small pool in the back yard. The only catch is, your parents are very busy and don t have time to spend figuring out the details of how much space it will take up and all of the related construction costs. You are not responsible for all of the details, but your parents have told you that if you want a pool, you are going to need to do some work convincing them that you are serious about having the pool. They have told you that you must figure out the some of the pool information and present it to them in the near future. 1) Your parents know that they want the pool to be a consistent depth, four feet. They want to use the fencing that they bought last year, and never used, to surround the pool for safety purposes. They have 96 feet of fencing and a four foot gate. The gate can be positioned anywhere you want. This fence needs to be five feet from the edge of the pool on all sides. The pool needs to be rectangular, two times as long as it is wide. Use the grid paper to help you figure the dimensions (length and width) of the pool, and where the fence and the gate will be. Your parents need to know how much of the yard the fenced area will be so that they will know if it is reasonable to fit the pool into the back yard with the existing landscaping. This will be a bird s eye view (a view from above) and will not show the depth of the pool. Tiling And Filling The Pool Student Materials Page 1 of 12
Scale: 1 square unit=1 square foot What will the dimensions (length and width) of the pool be? Tiling And Filling The Pool Student Materials Page 2 of 12
Once you have drawn the 2-dimensional diagram of the pool and fenced area, figure out what the total area inside the fence will be. Do this by first counting all of the square units inside of your fence. Record your answer. square units. Is there another way, besides counting them, that you could figure out how many square units it would be? If so, explain the method giving examples that refer back to your diagram. Does this method give you the same answer as when you counted the square units? 2) Next you will be making a three-dimensional model of the pool to determine its interior surface area and its volume. Surface area is the sum of the areas of all the faces of a three-dimensional object. You need to do this so that you can determine how many one square foot tiles it will take to tile the bottom and the four sides of the pool, and also so that your can determine the volume of water that will be in the pool. Your parents need to know the volume so they can make a decision on the water filtration system that they will use with the pool. To make the model and determine its surface area and volume, you will proceed through the steps listed and record your findings along the way. Step A Collect your supplies. You will need tag board, grid paper (scale: one square unit=1 square foot), a straight edge, scissors, tape, and cubes that match the dimensions of your grid paper. Step B Measure and cut out a piece of tag board that is 8 units longer and 8 units wider than the dimensions that you previously determined that the pool would be. Step C Next measure and cut out a four unit by four unit square from each corner of the tag board. Your tag board should look similar to this: Tiling And Filling The Pool Student Materials Page 3 of 12
Step D Fold your tag board figure as shown in the diagram (along the dotted lines). Step E Loosely tape the edges you have folded up together and you have created an open box which is your scale model for your pool. It is a rectangular prism (in this case it does not have a closed top since it is a swimming pool). Why did we originally cut the paper eight units wider and longer than the pool? 3) Now that the model is built, you are going to determine the interior surface area of the pool. Keep in mind that the top of this rectangular prism will be open. Cut pieces of grid paper out to match the size of the four walls and the bottom of the pool (cut on the lines). You can take the tape off and flatten the model if it is helpful. Of the five pieces you just cut out (not individual square units), how many pieces of different sizes did you need to cut? Answer and explain. Tiling And Filling The Pool Student Materials Page 4 of 12
a) How many square units was the piece of paper that covered the bottom of the pool? (count them) b) How many square units was the piece that covered one of the ends? (count them) Was there another one exactly the same size? (explain) c) How many square units was the piece that covered one of the sides? (count them) Was there another one exactly the same size? (explain) d) If you buy a pool cover, how many square units will it need to be to perfectly match the top of the pool? How do you know this? e) What is the surface area of the entire pool model (no top)? Make sure to think about what the label should be. Fill in the table below with the information that you have figured out. SQUARE UNITS NUMBER OF SURFACES WITH THESE DIMENSIONS TOTAL SQUARE UNITS BOTTOM END SIDE TOTAL SURFACE AREA OF POOL Tiling And Filling The Pool Student Materials Page 5 of 12
4) Now you are ready to figure out the volume of water that the pool will hold. In other words, how many cubic units it will take to fill the space inside the threedimensional rectangular prism. How will this be different than figuring out the surface area of the pool? Using cubes that match the dimensions of the grid paper you used in #2 and #3, fill your model with cubes to see how many cubic units it takes to fill your pool. Count them as you put them in. How many cubes did you stack on top of each other to get to the top of the pool? How many cubes did it take next to each other to go from one side to the other? How many cubes did it take to go from one end of the pool to the other? a) What else could you do to figure out how many cubes it would take to fill the pool besides counting them? Explain. b) What is the volume the pool? c) Was your label square units or cubic units? Explain why. 5) Now you are ready to present a summary to your parents about what you have figured out so that they can make further decisions about the pool. Keep in mind that you won t necessarily be there to answer questions for them, so make sure that your information is clear. Show your work using words, numbers and/or diagrams (grid paper is available for you to use if needed). Make sure that you include the following information in your report to them: The dimensions of the pool (include a drawing) Total area that will be taken up in the back yard including the fenced area (include a drawing) The surface area of the pool The volume of the pool Tiling And Filling The Pool Student Materials Page 6 of 12
Tiling And Filling The Pool Student Materials Page 7 of 12
Scale: 1 square unit=1 square foot Tiling And Filling The Pool Student Materials Page 8 of 12
The Pool Part B Your parents have reviewed your summary and have gotten some additional information about prices for different aspects of the pool s construction and maintenance. Based on the work that you have already done, they would like you to figure out the cost of the items below and explain it to them. Create an organized list for the different items costs and a total cost for all of these items combined. Edging for around the perimeter of the pool (called bullnose) that is sold by the foot and costs $1.25 per foot Tiles cost $4.00 per square foot (and will need to cover the entire surface area of the pool) The material that adheres (glues) the tiles to the cement wall and bottom is $0.90 per square foot The chemicals for the filtration system cost $0.25 per cubic foot (enough for a year, which is what your parents want to know) Tiling And Filling The Pool Student Materials Page 9 of 12
Show your work using words, numbers and/or diagrams. Total cost Tiling And Filling The Pool Student Materials Page 10 of 12
The Pool Part C Your parents want to look at other possible options before they commit to the exact construction plan, so they want you to make a few last calculations for them. 1) If they decided to double the width of the pool, what would the new surface area and volume of the pool be? Original perimeter (of pool) feet New perimeter (of pool) Original surface area New surface area Original volume New volume feet square feet square feet cubic feet cubic feet 2) What would happen to the volume of the pool (original pool volume) if seven steps, a half foot high (6 inches) and one foot deep (12 inches), were added across one end of the pool? See the side view diagram below for help. a) How much of the volume of the pool would be eliminated by the steps? cubic feet b) What would the remaining volume of the pool be? cubic feet Tiling And Filling The Pool Student Materials Page 11 of 12
3) What other design ideas do you have? How would they affect the surface area and volume of the pool? Explain using words, numbers, and/or pictures. Tiling And Filling The Pool Student Materials Page 12 of 12