Math Spring Operational 2015 Geometry PBA Item #18 Classmates in the Pool VH003506
Prompt
Rubric Task is worth a total of 6 points VH003506 Rubric Score Description 6 Student response includes the following 6 elements. Modeling component: Volumes Part 1 = 2 points o o The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas, setup, and work. The correct volume for the part of the pool that is currently without water is shown with work as needed. Calculation component: Conversion Part 2 = 1 point o Correct conversion of cubic feet to gallons or gallons to cubic feet Modeling component: Draw conclusions Part 3 = 1 point o Correct number of people is determined Modeling component: Interpretation Part 4 = 1 point o The number of people rounded to a whole person is given and is supported by work. Note: The interpretation should use a number that has been rounded down from the result of the model the student uses. Calculation component: Perform operations Part 5 = 1 point o All computations are correct. Note: Since incorrect calculations will cause a deduction in Part 1, this is applied to Part 2 Part 4. Calculations are expected and should be correct. If calculations are missing or incorrect, this part will not receive credit. Sample Student Response 1: The total volume of the pool is of the water in the pool is is an additional cubic feet. The volume cubic feet. Therefore, there cubic feet of space in the pool.
Given that 1 cubic foot is 7.48 gallons, 56.55 cubic feet is about 422.99 gallons. Let x represent the number of people in the water. This means approximately 23 classmates could be in the pool before the water begins to overflow. Sample Student Response 2: The total volume of the pool is of the water in the pool is is an additional cubic feet. The volume cubic feet. Therefore, there cubic feet of space in the pool. Given that 1 cubic foot is 7.48 gallons, 1 gallon is about 0.13 cubic feet. Each person would displace about 2.34 cubic feet of water. Let x represent the number of people in the water. This means approximately 24 classmates could be in the pool before the water begins to overflow. Note: Because of rounding issues, answers will vary on the task. However, because the gallon conversion was given as 7.48, the response must use 7.48 in the conversion component. 5 Student response includes 5 of the 6 elements 4 Student response includes 4 of the 6 elements 3 Student response includes 3 of the 6 elements. 2 Student response includes 2 of the 6 elements. 1 Student response includes 1 of the 6 elements. 0 Student response is incorrect or irrelevant.
Anchor Set A1 A14
A1 Score Point 6
Annotations Anchor Paper 1 Score Point 6 This response receives full credit. The student includes each of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved ( 6 2 4 = 452.16, 6 2 3.5 = 395.64). The correct volume for the part of the pool that is currently without water is shown with work as needed (452.16 395.54 = 56.62). This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (56.62 7.48 = 423.52). The number of people is determined (x18 = 423.52, divde both sides by 18... x = 23.52). The number of people rounded to a whole person is given (23). All computations are correct.
A2 Score Point 6
Annotations Anchor Paper 2 Score Point 6 This response receives full credit. The student includes each of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved ( 6 2 4 = V = 452.16, ( 6 2 3.5 = W = 395.64). The correct volume for the part of the pool that is currently without water is shown with work as needed (3382 2959 = 423g). This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (452.16 7.48 = 3382 g, 395 7.48 = 2959 g). The number of people is determined ( 423 18 = 23.5). The number of people rounded to a whole person is given (Only 23 people). All computations are correct.
A3 Score Point 5
Annotations Anchor Paper 3 Score Point 5 This response receives partial credit. The student includes five of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved ( 6 2 = 113.04, 113.04 4 = 452.16, 113.04 3.5 = 395.64). The correct volume for the part of the pool that is currently without water is shown with work as needed (452.16 395.64 = 56.52). This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (56.52 7.48 = 422.76). The number of people rounded to a whole person is given (52.845 So approximately 52 people). Note: This is acceptable based on the number of people found by the student. All computations are correct. There is a copy error in this response (422.76 8 = 52.845), which uses 8 instead of 18 as given in the prompt. All calculations and answers given after this copy error are correct based on using 8 instead of 18.
A4 Score Point 5
Annotations Anchor Paper 4 Score Point 5 This response receives partial credit. The student includes five of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved (( 62) 4 = (36 ) 4 = 144, ( 62) 3.5 = (36 ) 3.5 = 126 ). Note: The volumes may be left in terms of pi ( ). The correct volume for the part of the pool that is currently without water is shown with work as needed (144 126 = 18 56.5). This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (56.5 7.48 = 422.62). The number of people is determined ( 422.62 24). 18 Note: The method to find the number of people is correct but the answer is rounded up instead of down so the rounding point is not given credit, but this fraction with answer is sufficient. All computations are correct. The number of people is incorrectly rounded up instead of down to have a whole number of people.
A5 Score Point 4
Annotations Anchor Paper 5 Score Point 4 This response receives partial credit. The student includes four of the six required elements: The correct volume for the part of the pool that is currently without water is shown with work as needed (hold about 3,383.87 gallons of water... currently 2,960.88 gallons... meaning there can be 422.99 gallons of water that can be displaced by people). Note: The student explains how to find the difference after finding the total pool capacity and the current pool capacity in gallons. This is sufficient to show finding the empty space in the pool without seeing the calculations for either volume. This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (hold about 3,383.87 gallons... currently 2969.88 gallons... there can be 422.99 gallons of water). The number of people is determined (divide that by 18... about 23.4). The number of people rounded to a whole person is given (23 people). There is no setup or work for the amount of water currently in the pool or the total volume of the pool. Not enough calculations are shown or described for the All computations are correct part [see rubric note for part 5].
A6 Score Point 4
Annotations Anchor Paper 6 Score Point 4 This response receives partial credit. The student includes four of the six required elements: The correct volume for the part of the pool that is currently without water is shown with work as needed (3384-2961 = 423). This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (452.4 3 feet or 3383). The number of people is determined (423 18 = 23.5). The number of people rounded to a whole person is given (since you can not have half a person, 23 people can get in the pool). There is no setup or work for the amount of water currently in the pool or the total volume of the pool. Calculations are not shown for part 2, so no credit is awarded for part 5.
A7 Score Point 3
Annotations Anchor Paper 7 Score Point 3 This response receives partial credit. The student includes three of the six required elements: This response shows correct conversion of cubic feet to gallons or gallons to cubic feet (55.5... which equals about 423 gallons). The number of people is determined ( 423 = about 23 people). 18 Note: Showing the setup with the approximate number of people is sufficient for credit for part 4. The number of people rounded to a whole person is given (23 people). The computations and/or setup for finding the amount of water currently in the pool, the capacity of the pool, and the amount of empty space in the pool are missing. No credit is given for computations since only solutions are given.
A8 Score Point 3
Annotations Anchor Paper 8 Score Point 3 This response receives partial credit. The student includes three of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved (π 6 2 3.5 = 395 Current, π 6 2 4 = 452 MAX). The correct volume for the part of the pool that is currently without water is shown with work as needed (452 395 = 57). The number of people rounded to a whole person is given (3.1 people). No conversion from cubic feet is shown. Because the units were not converted, the resulting number of people is incorrect. Without conversion the calculation point is not awarded.
A9 Score Point 2
Annotations Anchor Paper 9 Score Point 2 This response receives partial credit. The student includes two of the six required elements: The correct volume for the part of the pool that is currently without water is shown with work as needed (452.2 395.64 = 56.56). The number of people rounded to a whole person is given (16.16, 16 people). The response does not show work or calculations for the two volumes. No correct conversion is shown, the number of people is incorrect, and not enough correct work [calculations] are present.
A10 Score Point 2
Annotations Anchor Paper 10 Score Point 2 This response receives partial credit. The student includes two of the six required elements: The correct volumes for the water currently in the pool and the volume of the capacity of the pool are shown with the formulas set up and solved (V = 4 6 2, V 452.389. V 1 = 3.5 6 2, V 1 395.841). The correct volume for the part of the pool that is currently without water is shown with work as needed (452.380 395.841 = 56.548). The conversion is incorrect since the operation of division is used instead of multiplication. The number of classmates in the pool was not found using 18 gallons per person. The number of people is not rounded down to a whole number. All computations are incorrect following the use of an incorrect operation.
A11 Score Point 1
Annotations Anchor Paper 11 Score Point 1 This response receives partial credit. The student includes one of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved (v = 3.14 6 2 4, v = 3.14 6 2 3.5). Note: Although the equations are not solved, the student did show how the formula is used so the correct solution is not necessary. The volume remaining in the pool is not found. The conversion explanation is incorrect, with division instead of multiplication shown. No number of people is shown, so no credit for rounding is given. No credit is given for the calculations without final values.
A12 Score Point 1
Annotations Anchor Paper 12 Score Point 1 This response receives partial credit. The student includes one of the six required elements: The correct volumes for the water currently in the pool and the capacity of the pool are shown with the formulas set up and solved (v = 3.14(6 2 ) 4 = 452, v = 3.14(6 2 ) 3.5 = 395). The volume remaining in the pool is not found. The conversion explanation is incorrect, with division instead of multiplication shown. No number of people is shown, so no credit for rounding is given. No credit is given for the calculations because the wrong operation is shown.
A13 Score Point 0
Annotations Anchor Paper 13 Score Point 0 This response receives no credit. The student includes none of the six required elements. The response shows a correct formula for the total volume of the pool ( 6 2 4) but does not show the quantity of water currently in the pool. The conversion from cubic feet to gallons is incorrect because division instead of multiplication is used. The number of people is incorrect. There is a computation error with the use of division.
A14 Score Point 0
Annotations Anchor Paper 14 Score Point 0 This response receives no credit. The student includes none of the six required elements. No volume is given for the capacity of the circular pool, the current amount of water, or the empty part of the pool. No conversion is used or shown. An incorrect number of people (10) is given with no rounding. No calculations are shown.
Practice Set P101 - P105
P101
P102
P103
P104
P105
Practice Set Paper Score P101 5 P102 2 P103 6 P104 0 P105 1